TPTP Problem File: SLH0385^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Separation_Logic_Unbounded/0001_Combinability/prob_00257_011288__6626448_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1732 ( 589 unt; 519 typ; 0 def)
% Number of atoms : 3844 (1406 equ; 0 cnn)
% Maximal formula atoms : 51 ( 3 avg)
% Number of connectives : 13693 ( 422 ~; 13 |; 192 &;11752 @)
% ( 0 <=>;1314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 41 ( 40 usr)
% Number of type conns : 7892 (7892 >; 0 *; 0 +; 0 <<)
% Number of symbols : 482 ( 479 usr; 21 con; 0-14 aty)
% Number of variables : 4695 ( 293 ^;4342 !; 60 ?;4695 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:04:46.441
%------------------------------------------------------------------------------
% Could-be-implicit typings (40)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_J_J_J,type,
set_Pr7868159745199425715_a_d_c: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_J_J,type,
produc6150846815813599699_a_d_c: $tType ).
thf(ty_n_t__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
option721982914780012405_b_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J_J,type,
set_as5068551873036484673_b_c_d: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J,type,
assert5325495410138902753_b_c_d: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J,type,
produc3509355604313844263tion_a: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J,type,
assert5894900919346993214_a_c_d: $tType ).
thf(ty_n_t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
option2300553739515653951_b_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
set_op7160277562814721357od_a_a: $tType ).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_J,type,
option2362401199305441953_a_d_c: $tType ).
thf(ty_n_t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
set_as1616228751320511321_b_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
set_option_option_a: $tType ).
thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
option5210160422955383789od_a_a: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
assertion_a_b_c_d: $tType ).
thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__a_Mtf__c_Mtf__d_J,type,
assertion_a_a_c_d: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Option__Ooption_Itf__a_J_J_J,type,
set_set_option_a: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
set_Product_prod_b_b: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
set_Product_prod_a_a: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J,type,
product_prod_a_d_c: $tType ).
thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
option_option_a: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__b_J_J,type,
set_option_b: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
set_option_a: $tType ).
thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__b_J_J,type,
option_set_b: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
product_prod_b_b: $tType ).
thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
product_prod_a_a: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
set_set_b: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
set_set_a: $tType ).
thf(ty_n_t__Option__Ooption_Itf__d_J,type,
option_d: $tType ).
thf(ty_n_t__Option__Ooption_Itf__b_J,type,
option_b: $tType ).
thf(ty_n_t__Option__Ooption_Itf__a_J,type,
option_a: $tType ).
thf(ty_n_t__Option__Ooption_I_Eo_J,type,
option_o: $tType ).
thf(ty_n_t__Set__Oset_Itf__d_J,type,
set_d: $tType ).
thf(ty_n_t__Set__Oset_Itf__c_J,type,
set_c: $tType ).
thf(ty_n_t__Set__Oset_Itf__b_J,type,
set_b: $tType ).
thf(ty_n_t__Set__Oset_Itf__a_J,type,
set_a: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
thf(ty_n_tf__d,type,
d: $tType ).
thf(ty_n_tf__c,type,
c: $tType ).
thf(ty_n_tf__b,type,
b: $tType ).
thf(ty_n_tf__a,type,
a: $tType ).
% Explicit typings (479)
thf(sy_c_BNF__Def_OGrp_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Option__Ooption_Itf__a_J,type,
bNF_Gr1758829368316449381tion_a: set_op7160277562814721357od_a_a > ( option5210160422955383789od_a_a > option_a ) > option5210160422955383789od_a_a > option_a > $o ).
thf(sy_c_BNF__Def_OGrp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bNF_Gr5654676046521400910tion_a: set_option_a > ( option_a > option_a ) > option_a > option_a > $o ).
thf(sy_c_BNF__Def_OGrp_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_Gr5825982120753023526_b_c_d: set_as5068551873036484673_b_c_d > ( assert5325495410138902753_b_c_d > assertion_a_b_c_d ) > assert5325495410138902753_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_BNF__Def_OGrp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_Gr3951314207136893198_b_c_d: set_as1616228751320511321_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_BNF__Def_OGrp_001tf__a_001tf__a,type,
bNF_Grp_a_a: set_a > ( a > a ) > a > a > $o ).
thf(sy_c_BNF__Def_OGrp_001tf__b_001tf__b,type,
bNF_Grp_b_b: set_b > ( b > b ) > b > b > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001t__Option__Ooption_Itf__a_J,type,
bNF_eq_onp_option_a: ( option_a > $o ) > option_a > option_a > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_eq117459932171339370_b_c_d: ( assertion_a_b_c_d > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001tf__a,type,
bNF_eq_onp_a: ( a > $o ) > a > a > $o ).
thf(sy_c_BNF__Def_Oeq__onp_001tf__b,type,
bNF_eq_onp_b: ( b > $o ) > b > b > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re409307387072406315_b_c_d: ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re4165358468115902493_b_c_d: ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > $o ) > ( ( ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re7094559677772665647_b_c_d: ( ( ( d > c ) > a > $o ) > ( ( d > c ) > a > $o ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_re507190721467377699_b_c_d: ( ( ( d > c ) > a > $o ) > ( ( d > c ) > a > $o ) > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J,type,
bNF_re8007680959799151545on_a_o: ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( ( option_option_a > $o ) > ( option_option_a > $o ) > $o ) > ( ( option_a > $o ) > option_option_a > $o ) > ( ( option_a > $o ) > option_option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_Mt__Option__Ooption_I_Eo_J_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_Mt__Option__Ooption_I_Eo_J_J,type,
bNF_re5724521104517466949tion_o: ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( ( option_option_a > option_o ) > ( option_option_a > option_o ) > $o ) > ( ( option_a > $o ) > option_option_a > option_o ) > ( ( option_a > $o ) > option_option_a > option_o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_062_I_Eo_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_I_Eo_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_J,type,
bNF_re294699121693105817on_a_o: ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( ( option_a > $o > option_a > $o ) > ( option_a > $o > option_a > $o ) > $o ) > ( ( option_a > $o ) > option_a > $o > option_a > $o ) > ( ( option_a > $o ) > option_a > $o > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5728513783986320277_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5409697069149878421_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J,type,
bNF_re5882599885548590485_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J,type,
bNF_re5572834386292656789_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J,type,
bNF_re4584742235003721621_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re6521478211583210845_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J,type,
bNF_re1385902664069430737_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J,type,
bNF_re1434271726693436637_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J,type,
bNF_re2045653869035528613_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re5347999660430809193_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J,type,
bNF_re857753254652161629_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re1042997550465084509_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re5092460513005817693_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > ( option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J,type,
bNF_re7200934695671800889_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re2787993636544139229_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J,type,
bNF_re2241830251785289705_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re706445162651761793_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re4346972822711717245_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__Option__Ooption_Itf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__Option__Ooption_Itf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re188506143030329217_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re3402983428571792885_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re7065123807510049385_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option2300553739515653951_b_c_d > assertion_a_b_c_d ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re2162194351488232737_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re2130736366441412457_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re5340157310235046645_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re3141103876165256041_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_J,type,
bNF_re3412046433515172957on_a_o: ( ( a > option_a > $o ) > ( a > option_a > $o ) > $o ) > ( ( option_a > option_option_a > $o ) > ( option_a > option_option_a > $o ) > $o ) > ( ( a > option_a > $o ) > option_a > option_option_a > $o ) > ( ( a > option_a > $o ) > option_a > option_option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
bNF_re4921454823102592605on_a_o: ( ( a > a > $o ) > ( a > a > $o ) > $o ) > ( ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > $o ) > ( ( a > a > $o ) > option_a > option_a > $o ) > ( ( a > a > $o ) > option_a > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_Eo_J_001_062_Itf__a_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re4859868158825367505on_a_o: ( ( a > $o ) > ( a > $o ) > $o ) > ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( ( a > $o ) > option_a > $o ) > ( ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_Eo_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re2369685550566307625tion_a: ( ( a > $o ) > ( a > option_a ) > $o ) > ( ( option_a > $o ) > ( option_a > option_a ) > $o ) > ( ( a > $o ) > option_a > $o ) > ( ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_Eo_J_001_062_Itf__a_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J,type,
bNF_re102678143051736477on_a_a: ( ( a > $o ) > ( a > a ) > $o ) > ( ( option_a > $o ) > ( option_a > a ) > $o ) > ( ( a > $o ) > option_a > $o ) > ( ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re6058157240589548841on_a_o: ( ( a > option_a ) > ( a > $o ) > $o ) > ( ( option_a > option_a ) > ( option_a > $o ) > $o ) > ( ( a > option_a ) > option_a > option_a ) > ( ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
bNF_re2496629990708770829tion_a: ( ( a > option_a ) > ( a > option_a ) > $o ) > ( ( option_a > option_option_a ) > ( option_a > option_option_a ) > $o ) > ( ( a > option_a ) > option_a > option_option_a ) > ( ( a > option_a ) > option_a > option_option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re2722752998287985793tion_a: ( ( a > option_a ) > ( a > option_a ) > $o ) > ( ( option_a > option_a ) > ( option_a > option_a ) > $o ) > ( ( a > option_a ) > option_a > option_a ) > ( ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J_001_062_Itf__a_M_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_J,type,
bNF_re4933961146405920325tion_a: ( ( a > option_a ) > ( a > option_a ) > $o ) > ( ( a > option_a > a > option_a ) > ( a > option_a > a > option_a ) > $o ) > ( ( a > option_a ) > a > option_a > a > option_a ) > ( ( a > option_a ) > a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bNF_re5527783635739595829tion_a: ( ( a > option_a ) > ( a > option_a ) > $o ) > ( option_a > option_a > $o ) > ( ( a > option_a ) > option_a ) > ( ( a > option_a ) > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J,type,
bNF_re5072729714030605557on_a_a: ( ( a > option_a ) > ( a > a ) > $o ) > ( ( option_a > option_a ) > ( option_a > a ) > $o ) > ( ( a > option_a ) > option_a > option_a ) > ( ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re4058884933032857501on_a_o: ( ( a > a ) > ( a > $o ) > $o ) > ( ( option_a > a ) > ( option_a > $o ) > $o ) > ( ( a > a ) > option_a > a ) > ( ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re7263069294043397365tion_a: ( ( a > a ) > ( a > option_a ) > $o ) > ( ( option_a > a ) > ( option_a > option_a ) > $o ) > ( ( a > a ) > option_a > a ) > ( ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_001_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re8471833820502647285tion_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( option_a > option_a ) > ( option_a > option_a ) > $o ) > ( ( a > a ) > option_a > option_a ) > ( ( a > a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_001_062_It__Option__Ooption_Itf__a_J_Mtf__a_J,type,
bNF_re1079736789768479081on_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( option_a > a ) > ( option_a > a ) > $o ) > ( ( a > a ) > option_a > a ) > ( ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_Itf__b_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_M_Eo_J_J,type,
bNF_re7611673848298757341_c_d_o: ( ( b > option_a > $o ) > ( b > option_a > $o ) > $o ) > ( ( assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > ( assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > $o ) > ( ( b > option_a > $o ) > assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > ( ( b > option_a > $o ) > assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re4988404192636484745_b_c_d: ( ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__b_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_J_J_J_J_J,type,
bNF_re8177534222179943037_b_c_d: ( ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J_J,type,
bNF_re263456917604132445_c_d_o: ( ( b > b > $o ) > ( b > b > $o ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > $o ) > ( ( b > b > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( b > b > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J,type,
bNF_re4274080607382512101_c_d_o: ( ( b > $o ) > ( b > $o ) > $o ) > ( ( assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > $o ) > $o ) > ( ( b > $o ) > assertion_a_b_c_d > $o ) > ( ( b > $o ) > assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re2761730750983628277_b_c_d: ( ( b > b ) > ( b > b ) > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( b > b ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( b > b ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J,type,
bNF_re1151994453571696261_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_J,type,
bNF_re3466685140808306565_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J_001_062_I_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_J,type,
bNF_re510987944908516713_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_Itf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_Itf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re2842133318421313373_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__Option__Ooption_Itf__d_J_Mt__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_It__Option__Ooption_Itf__d_J_Mt__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re7892989858577796701_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( option_d > option721982914780012405_b_c_d ) > ( option_d > option721982914780012405_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > option721982914780012405_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > option721982914780012405_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J,type,
bNF_re5229488851107796445_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_Itf__d_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J_001_062_Itf__d_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_J,type,
bNF_re2236548867734660665_b_c_d: ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_Mtf__c_J_001_062_Itf__d_Mtf__c_J_001_062_Itf__d_M_062_Itf__c_M_062_Itf__d_Mtf__c_J_J_J_001_062_Itf__d_M_062_Itf__c_M_062_Itf__d_Mtf__c_J_J_J,type,
bNF_re6057820304915472923_c_d_c: ( ( d > c ) > ( d > c ) > $o ) > ( ( d > c > d > c ) > ( d > c > d > c ) > $o ) > ( ( d > c ) > d > c > d > c ) > ( ( d > c ) > d > c > d > c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_062_It__Option__Ooption_Itf__a_J_M_Eo_J_M_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_J_001_062_I_062_It__Option__Ooption_Itf__a_J_M_Eo_J_M_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_J,type,
bNF_re7775980886671535221on_a_o: ( $o > $o > $o ) > ( ( ( option_a > $o ) > option_option_a > $o ) > ( ( option_a > $o ) > option_option_a > $o ) > $o ) > ( $o > ( option_a > $o ) > option_option_a > $o ) > ( $o > ( option_a > $o ) > option_option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
bNF_re1464701735350397069on_a_o: ( $o > $o > $o ) > ( ( ( a > $o ) > option_a > $o ) > ( ( a > $o ) > option_a > $o ) > $o ) > ( $o > ( a > $o ) > option_a > $o ) > ( $o > ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re5310993362035161937on_a_o: ( $o > $o > $o ) > ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( $o > option_a > $o ) > ( $o > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Option__Ooption_Itf__a_J_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re7078363273947182481tion_a: ( $o > option_a > $o ) > ( ( ( a > $o ) > option_a > $o ) > ( ( a > option_a ) > option_a > option_a ) > $o ) > ( $o > ( a > $o ) > option_a > $o ) > ( option_a > ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001_Eo_001tf__a_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J,type,
bNF_re4337018088969878591on_a_a: ( $o > a > $o ) > ( ( ( a > $o ) > option_a > $o ) > ( ( a > a ) > option_a > a ) > $o ) > ( $o > ( a > $o ) > option_a > $o ) > ( a > ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001_Eo_001_Eo,type,
bNF_re669219658517073757_a_o_o: ( option_option_a > option_option_a > $o ) > ( $o > $o > $o ) > ( option_option_a > $o ) > ( option_option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_I_Eo_J_001t__Option__Ooption_I_Eo_J,type,
bNF_re7165334401771760221tion_o: ( option_option_a > option_option_a > $o ) > ( option_o > option_o > $o ) > ( option_option_a > option_o ) > ( option_option_a > option_o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re3325060626551612777_b_c_d: ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001t__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re1839893911826710025_b_c_d: ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ) > ( option721982914780012405_b_c_d > option721982914780012405_b_c_d > $o ) > ( option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > ( option2300553739515653951_b_c_d > option721982914780012405_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re1760841454573502429_b_c_d: ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ) > ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ) > ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_re6421063287152323421_b_c_d: ( option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d ) > ( option2300553739515653951_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001_Eo_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
bNF_re4311958519388381497on_a_o: ( option_a > $o > $o ) > ( ( ( a > option_a ) > option_a > option_a ) > ( ( a > $o ) > option_a > $o ) > $o ) > ( option_a > ( a > option_a ) > option_a > option_a ) > ( $o > ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re1266155380144051773tion_a: ( option_a > option_a > $o ) > ( ( ( a > option_a ) > option_a > option_a ) > ( ( a > option_a ) > option_a > option_a ) > $o ) > ( option_a > ( a > option_a ) > option_a > option_a ) > ( option_a > ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_Mt__Option__Ooption_Itf__a_J_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re5708320262762544989tion_a: ( option_a > option_a > $o ) > ( ( ( a > option_a ) > option_a ) > ( ( a > option_a ) > option_a ) > $o ) > ( option_a > ( a > option_a ) > option_a ) > ( option_a > ( a > option_a ) > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_I_Eo_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J_001_062_I_Eo_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
bNF_re8312531103195455325on_a_o: ( option_a > option_a > $o ) > ( ( $o > option_a > $o ) > ( $o > option_a > $o ) > $o ) > ( option_a > $o > option_a > $o ) > ( option_a > $o > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J_001_062_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_M_Eo_J,type,
bNF_re3043890739735069381on_a_o: ( option_a > option_a > $o ) > ( ( option_option_a > $o ) > ( option_option_a > $o ) > $o ) > ( option_a > option_option_a > $o ) > ( option_a > option_option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re1541143192665202257on_a_o: ( option_a > option_a > $o ) > ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_001_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J,type,
bNF_re8162217253061806133tion_a: ( option_a > option_a > $o ) > ( ( a > option_a ) > ( a > option_a ) > $o ) > ( option_a > a > option_a ) > ( option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_Eo_001_Eo,type,
bNF_re905040088260304477_a_o_o: ( option_a > option_a > $o ) > ( $o > $o > $o ) > ( option_a > $o ) > ( option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_Eo_001t__Option__Ooption_Itf__a_J,type,
bNF_re1129020316103814665tion_a: ( option_a > option_a > $o ) > ( $o > option_a > $o ) > ( option_a > $o ) > ( option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_Eo_001tf__a,type,
bNF_re8815814597387604803_a_o_a: ( option_a > option_a > $o ) > ( $o > a > $o ) > ( option_a > $o ) > ( option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
bNF_re1595600300046643805tion_a: ( option_a > option_a > $o ) > ( option_option_a > option_option_a > $o ) > ( option_a > option_option_a ) > ( option_a > option_option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_Eo,type,
bNF_re2070578767941953969on_a_o: ( option_a > option_a > $o ) > ( option_a > $o > $o ) > ( option_a > option_a ) > ( option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bNF_re8713957294334624093tion_a: ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > ( option_a > option_a ) > ( option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a,type,
bNF_re4157831115608716439on_a_a: ( option_a > option_a > $o ) > ( option_a > a > $o ) > ( option_a > option_a ) > ( option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a_001_Eo,type,
bNF_re8895294753853352567_a_a_o: ( option_a > option_a > $o ) > ( a > $o > $o ) > ( option_a > a ) > ( option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a_001t__Option__Ooption_Itf__a_J,type,
bNF_re1935317234069921315tion_a: ( option_a > option_a > $o ) > ( a > option_a > $o ) > ( option_a > a ) > ( option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__a,type,
bNF_re6951206947496014429_a_a_a: ( option_a > option_a > $o ) > ( a > a > $o ) > ( option_a > a ) > ( option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__a_J_001tf__a_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J,type,
bNF_re5218620495166150379on_a_a: ( option_a > a > $o ) > ( ( ( a > option_a ) > option_a > option_a ) > ( ( a > a ) > option_a > a ) > $o ) > ( option_a > ( a > option_a ) > option_a > option_a ) > ( a > ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__d_J_001t__Option__Ooption_Itf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re4152538054372293993_b_c_d: ( option_d > option_d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( option_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__Option__Ooption_Itf__d_J_001t__Option__Ooption_Itf__d_J_001t__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001t__Option__Ooption_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re7977768539823379977_b_c_d: ( option_d > option_d > $o ) > ( option721982914780012405_b_c_d > option721982914780012405_b_c_d > $o ) > ( option_d > option721982914780012405_b_c_d ) > ( option_d > option721982914780012405_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_001_Eo_001_Eo,type,
bNF_re7564118739466000477_d_o_o: ( assert5894900919346993214_a_c_d > assert5894900919346993214_a_c_d > $o ) > ( $o > $o > $o ) > ( assert5894900919346993214_a_c_d > $o ) > ( assert5894900919346993214_a_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re7119773978271877369_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__Option__Ooption_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re8287430210025019109_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > $o ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re2297306203449973469_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mt__Option__Ooption_Itf__a_J_Mtf__c_Mtf__d_J_M_Eo_J,type,
bNF_re7785604200236268829_c_d_o: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( assert5894900919346993214_a_c_d > $o ) > ( assert5894900919346993214_a_c_d > $o ) > $o ) > ( assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > ( assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re6925915701013295965_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J,type,
bNF_re6323699832948026919_c_d_o: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > $o ) > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re8352491382599487721_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_Eo_001_Eo,type,
bNF_re1650022584898132253_d_o_o: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( $o > $o > $o ) > ( assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bNF_re2060205161886013149_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001_Eo_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J_001_062_I_062_Itf__a_M_Eo_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
bNF_re8717284581917077363on_a_o: ( a > $o > $o ) > ( ( ( a > a ) > option_a > a ) > ( ( a > $o ) > option_a > $o ) > $o ) > ( a > ( a > a ) > option_a > a ) > ( $o > ( a > $o ) > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001t__Option__Ooption_Itf__a_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J_001_062_I_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_M_062_It__Option__Ooption_Itf__a_J_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re1882382041600142455tion_a: ( a > option_a > $o ) > ( ( ( a > a ) > option_a > a ) > ( ( a > option_a ) > option_a > option_a ) > $o ) > ( a > ( a > a ) > option_a > a ) > ( option_a > ( a > option_a ) > option_a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_It__Option__Ooption_Itf__a_J_Mtf__a_J_J,type,
bNF_re6523360481052543525on_a_a: ( a > a > $o ) > ( ( ( a > a ) > option_a > a ) > ( ( a > a ) > option_a > a ) > $o ) > ( a > ( a > a ) > option_a > a ) > ( a > ( a > a ) > option_a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J_001_062_It__Option__Ooption_Itf__a_J_M_062_Itf__a_Mt__Option__Ooption_Itf__a_J_J_J,type,
bNF_re845666378725559389tion_a: ( a > a > $o ) > ( ( option_a > a > option_a ) > ( option_a > a > option_a ) > $o ) > ( a > option_a > a > option_a ) > ( a > option_a > a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re6100770640034910033on_a_o: ( a > a > $o ) > ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( a > option_a > $o ) > ( a > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__a_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
bNF_re6468246989568818141_o_a_o: ( a > a > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_Eo_001_Eo,type,
bNF_rel_fun_a_a_o_o: ( a > a > $o ) > ( $o > $o > $o ) > ( a > $o ) > ( a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_Eo_001t__Option__Ooption_Itf__a_J,type,
bNF_re905553932590079753tion_a: ( a > a > $o ) > ( $o > option_a > $o ) > ( a > $o ) > ( a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_Eo_001tf__a,type,
bNF_rel_fun_a_a_o_a: ( a > a > $o ) > ( $o > a > $o ) > ( a > $o ) > ( a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J_001_Eo,type,
bNF_re1847112384428219057on_a_o: ( a > a > $o ) > ( option_a > $o > $o ) > ( a > option_a ) > ( a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bNF_re1187871780581372509tion_a: ( a > a > $o ) > ( option_a > option_a > $o ) > ( a > option_a ) > ( a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__a,type,
bNF_re5794519239126689175on_a_a: ( a > a > $o ) > ( option_a > a > $o ) > ( a > option_a ) > ( a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__a_001_Eo,type,
bNF_rel_fun_a_a_a_o: ( a > a > $o ) > ( a > $o > $o ) > ( a > a ) > ( a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J,type,
bNF_re3572005357587894051tion_a: ( a > a > $o ) > ( a > option_a > $o ) > ( a > a ) > ( a > option_a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__a_001tf__a,type,
bNF_rel_fun_a_a_a_a: ( a > a > $o ) > ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
bNF_re6771475999719625105on_a_o: ( b > b > $o ) > ( ( option_a > $o ) > ( option_a > $o ) > $o ) > ( b > option_a > $o ) > ( b > option_a > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re2222577296431909853_b_c_d: ( b > b > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re7904742758403352937_b_c_d: ( b > b > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
bNF_re4413358128099268379_o_b_o: ( b > b > $o ) > ( ( b > $o ) > ( b > $o ) > $o ) > ( b > b > $o ) > ( b > b > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_Eo_001_Eo,type,
bNF_rel_fun_b_b_o_o: ( b > b > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( b > $o ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001tf__b_001tf__b,type,
bNF_rel_fun_b_b_b_b: ( b > b > $o ) > ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__c_001_062_Itf__d_Mtf__c_J_001_062_Itf__d_Mtf__c_J,type,
bNF_re8281275612740045991_c_d_c: ( c > c > $o ) > ( ( d > c ) > ( d > c ) > $o ) > ( c > d > c ) > ( c > d > c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J_001_062_I_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_M_062_Itf__d_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_J,type,
bNF_re8856927315010765021_b_c_d: ( d > d > $o ) > ( ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_J,type,
bNF_re8703476271064895581_b_c_d: ( d > d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
bNF_re7418416730241609193_b_c_d: ( d > d > $o ) > ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001_062_Itf__c_M_062_Itf__d_Mtf__c_J_J_001_062_Itf__c_M_062_Itf__d_Mtf__c_J_J,type,
bNF_re1711706644904726749_c_d_c: ( d > d > $o ) > ( ( c > d > c ) > ( c > d > c ) > $o ) > ( d > c > d > c ) > ( d > c > d > c ) > $o ).
thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001tf__c_001tf__c,type,
bNF_rel_fun_d_d_c_c: ( d > d > $o ) > ( c > c > $o ) > ( d > c ) > ( d > c ) > $o ).
thf(sy_c_Combinability_Ologic_Ocombinable_001tf__a_001tf__b_001tf__d_001tf__c,type,
combinable_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( a > $o ) > ( ( d > c ) > set_a ) > assertion_a_b_c_d > $o ).
thf(sy_c_Combinability_Ologic_Ounambiguous_001tf__a_001tf__b_001tf__d_001tf__c,type,
unambiguous_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( ( d > c ) > set_a ) > assertion_a_b_c_d > d > $o ).
thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_Itf__a_J,type,
comple2307003609928055243_set_a: set_set_a > set_a ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
finite8114217219359860531tion_a: set_option_option_a > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__a_J,type,
finite1674126218327898605tion_a: set_option_a > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
finite_finite_a: set_a > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__b,type,
finite_finite_b: set_b > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__d,type,
finite_finite_d: set_d > $o ).
thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_Itf__b_J_001t__Option__Ooption_It__Set__Oset_Itf__b_J_J,type,
finite4684332809091328718_set_b: ( set_b > option_set_b > option_set_b ) > option_set_b > set_set_b > option_set_b ).
thf(sy_c_Finite__Set_Ofold_001tf__a_001t__Option__Ooption_Itf__a_J,type,
finite6501707464432451470tion_a: ( a > option_a > option_a ) > option_a > set_a > option_a ).
thf(sy_c_Fun_Obij__betw_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bij_be5431266891817924854tion_a: ( option_a > option_a ) > set_option_a > set_option_a > $o ).
thf(sy_c_Fun_Obij__betw_001t__Option__Ooption_Itf__a_J_001tf__a,type,
bij_betw_option_a_a: ( option_a > a ) > set_option_a > set_a > $o ).
thf(sy_c_Fun_Obij__betw_001t__Option__Ooption_Itf__a_J_001tf__b,type,
bij_betw_option_a_b: ( option_a > b ) > set_option_a > set_b > $o ).
thf(sy_c_Fun_Obij__betw_001tf__a_001t__Option__Ooption_Itf__a_J,type,
bij_betw_a_option_a: ( a > option_a ) > set_a > set_option_a > $o ).
thf(sy_c_Fun_Obij__betw_001tf__a_001tf__a,type,
bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
thf(sy_c_Fun_Obij__betw_001tf__a_001tf__b,type,
bij_betw_a_b: ( a > b ) > set_a > set_b > $o ).
thf(sy_c_Fun_Obij__betw_001tf__b_001t__Option__Ooption_Itf__a_J,type,
bij_betw_b_option_a: ( b > option_a ) > set_b > set_option_a > $o ).
thf(sy_c_Fun_Obij__betw_001tf__b_001tf__a,type,
bij_betw_b_a: ( b > a ) > set_b > set_a > $o ).
thf(sy_c_Fun_Obij__betw_001tf__b_001tf__b,type,
bij_betw_b_b: ( b > b ) > set_b > set_b > $o ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
comp_o1254687777855551975tion_a: ( option_option_a > option_a ) > ( option_a > option_option_a ) > option_a > option_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Nat__Onat_001t__Option__Ooption_Itf__a_J,type,
comp_o8583038678572498833tion_a: ( option_a > nat ) > ( option_a > option_a ) > option_a > nat ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
comp_o3154387707078715297tion_a: ( option_a > option_a ) > ( option_a > option_a ) > option_a > option_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a,type,
comp_o6087033147929006299on_a_a: ( option_a > option_a ) > ( a > option_a ) > a > option_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001t__Set__Oset_Itf__a_J_001tf__a,type,
comp_o6143895765626710849et_a_a: ( option_a > set_a ) > ( a > option_a ) > a > set_a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__a_001t__Option__Ooption_Itf__a_J,type,
comp_o3864519266390211175tion_a: ( option_a > a ) > ( option_a > option_a ) > option_a > a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__a,type,
comp_option_a_a_a: ( option_a > a ) > ( a > option_a ) > a > a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__b,type,
comp_option_a_a_b: ( option_a > a ) > ( b > option_a ) > b > a ).
thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__b_001tf__a,type,
comp_option_a_b_a: ( option_a > b ) > ( a > option_a ) > a > b ).
thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
comp_s1419921648917501825_set_a: ( set_option_a > set_a ) > ( set_a > set_option_a ) > set_a > set_a ).
thf(sy_c_Fun_Ocomp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__Nat__Onat_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
comp_a8591870773727454801_b_c_d: ( assertion_a_b_c_d > nat ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > nat ).
thf(sy_c_Fun_Ocomp_001tf__a_001_Eo_001tf__a,type,
comp_a_o_a: ( a > $o ) > ( a > a ) > a > $o ).
thf(sy_c_Fun_Ocomp_001tf__a_001t__Nat__Onat_001tf__a,type,
comp_a_nat_a: ( a > nat ) > ( a > a ) > a > nat ).
thf(sy_c_Fun_Ocomp_001tf__a_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
comp_a6249931511552232923tion_a: ( a > option_a ) > ( option_a > a ) > option_a > option_a ).
thf(sy_c_Fun_Ocomp_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__a,type,
comp_a_option_a_a: ( a > option_a ) > ( a > a ) > a > option_a ).
thf(sy_c_Fun_Ocomp_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__b,type,
comp_a_option_a_b: ( a > option_a ) > ( b > a ) > b > option_a ).
thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Option__Ooption_Itf__a_J,type,
comp_a_a_option_a: ( a > a ) > ( option_a > a ) > option_a > a ).
thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__a,type,
comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001t__Option__Ooption_Itf__a_J,type,
comp_a_b_option_a: ( a > b ) > ( option_a > a ) > option_a > b ).
thf(sy_c_Fun_Ocomp_001tf__b_001_Eo_001tf__b,type,
comp_b_o_b: ( b > $o ) > ( b > b ) > b > $o ).
thf(sy_c_Fun_Ocomp_001tf__b_001t__Nat__Onat_001tf__b,type,
comp_b_nat_b: ( b > nat ) > ( b > b ) > b > nat ).
thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__b,type,
comp_b_b_b: ( b > b ) > ( b > b ) > b > b ).
thf(sy_c_Fun_Ocomp_001tf__c_001tf__c_001tf__d,type,
comp_c_c_d: ( c > c ) > ( d > c ) > d > c ).
thf(sy_c_Fun_Ofcomp_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__a,type,
fcomp_a_option_a_a: ( a > option_a ) > ( option_a > a ) > a > a ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001_Eo,type,
fun_upd_option_a_o: ( option_a > $o ) > option_a > $o > option_a > $o ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
fun_up1079276522633388797tion_a: ( option_a > option_a ) > option_a > option_a > option_a > option_a ).
thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_Itf__a_J_001tf__a,type,
fun_upd_option_a_a: ( option_a > a ) > option_a > a > option_a > a ).
thf(sy_c_Fun_Ofun__upd_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
fun_up5063514507276981217_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Fun_Ofun__upd_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
fun_up1040808460924108221_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Fun_Ofun__upd_001tf__a_001t__Option__Ooption_Itf__a_J,type,
fun_upd_a_option_a: ( a > option_a ) > a > option_a > a > option_a ).
thf(sy_c_Fun_Ofun__upd_001tf__a_001tf__a,type,
fun_upd_a_a: ( a > a ) > a > a > a > a ).
thf(sy_c_Fun_Ofun__upd_001tf__b_001t__Option__Ooption_Itf__a_J,type,
fun_upd_b_option_a: ( b > option_a ) > b > option_a > b > option_a ).
thf(sy_c_Fun_Ofun__upd_001tf__b_001tf__a,type,
fun_upd_b_a: ( b > a ) > b > a > b > a ).
thf(sy_c_Fun_Ofun__upd_001tf__d_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
fun_up3232119017247106793_b_c_d: ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Fun_Ofun__upd_001tf__d_001tf__c,type,
fun_upd_d_c: ( d > c ) > d > c > d > c ).
thf(sy_c_Fun_Oid_001t__Option__Ooption_Itf__a_J,type,
id_option_a: option_a > option_a ).
thf(sy_c_Fun_Oid_001t__Set__Oset_Itf__a_J,type,
id_set_a: set_a > set_a ).
thf(sy_c_Fun_Oid_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
id_assertion_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Fun_Oid_001tf__a,type,
id_a: a > a ).
thf(sy_c_Fun_Oid_001tf__b,type,
id_b: b > b ).
thf(sy_c_Fun_Oinj__on_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
inj_on2224753519991154999tion_a: ( option_a > option_option_a ) > set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
inj_on8559383841115902449tion_a: ( option_a > option_a ) > set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Option__Ooption_Itf__a_J_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
inj_on7881382345526841553tion_a: ( option_a > set_option_a ) > set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Option__Ooption_Itf__a_J_001tf__a,type,
inj_on_option_a_a: ( option_a > a ) > set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Option__Ooption_Itf__a_J_001tf__b,type,
inj_on_option_a_b: ( option_a > b ) > set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J_001t__Set__Oset_Itf__a_J,type,
inj_on8475384959944041899_set_a: ( set_option_a > set_a ) > set_set_option_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__Set__Oset_Itf__a_J_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
inj_on478642083548346935tion_a: ( set_a > set_option_a ) > set_set_a > $o ).
thf(sy_c_Fun_Oinj__on_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
inj_on8546820862575520945_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d ) > set_as1616228751320511321_b_c_d > $o ).
thf(sy_c_Fun_Oinj__on_001tf__a_001t__Option__Ooption_Itf__a_J,type,
inj_on_a_option_a: ( a > option_a ) > set_a > $o ).
thf(sy_c_Fun_Oinj__on_001tf__a_001t__Set__Oset_Itf__a_J,type,
inj_on_a_set_a: ( a > set_a ) > set_a > $o ).
thf(sy_c_Fun_Oinj__on_001tf__a_001tf__a,type,
inj_on_a_a: ( a > a ) > set_a > $o ).
thf(sy_c_Fun_Oinj__on_001tf__a_001tf__b,type,
inj_on_a_b: ( a > b ) > set_a > $o ).
thf(sy_c_Fun_Oinj__on_001tf__b_001t__Option__Ooption_Itf__a_J,type,
inj_on_b_option_a: ( b > option_a ) > set_b > $o ).
thf(sy_c_Fun_Oinj__on_001tf__b_001tf__a,type,
inj_on_b_a: ( b > a ) > set_b > $o ).
thf(sy_c_Fun_Oinj__on_001tf__b_001tf__b,type,
inj_on_b_b: ( b > b ) > set_b > $o ).
thf(sy_c_Fun_Oinj__on_001tf__d_001tf__c,type,
inj_on_d_c: ( d > c ) > set_d > $o ).
thf(sy_c_Fun_Omonotone__on_001t__Option__Ooption_Itf__a_J_001tf__a,type,
monoto4483592047695070497on_a_a: set_option_a > ( option_a > option_a > $o ) > ( a > a > $o ) > ( option_a > a ) > $o ).
thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_Itf__b_J_001t__Set__Oset_Itf__b_J,type,
monoto8660672184891397159_set_b: set_set_b > ( set_b > set_b > $o ) > ( set_b > set_b > $o ) > ( set_b > set_b ) > $o ).
thf(sy_c_Fun_Omonotone__on_001tf__a_001t__Option__Ooption_Itf__a_J,type,
monoto2261078166156275373tion_a: set_a > ( a > a > $o ) > ( option_a > option_a > $o ) > ( a > option_a ) > $o ).
thf(sy_c_Fun_Omonotone__on_001tf__a_001tf__a,type,
monotone_on_a_a: set_a > ( a > a > $o ) > ( a > a > $o ) > ( a > a ) > $o ).
thf(sy_c_Fun_Ooverride__on_001tf__d_001tf__c,type,
override_on_d_c: ( d > c ) > ( d > c ) > set_d > d > c ).
thf(sy_c_Fun_Othe__inv__into_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
the_in2538339130118444083tion_a: set_option_a > ( option_a > option_a ) > option_a > option_a ).
thf(sy_c_Fun_Othe__inv__into_001t__Option__Ooption_Itf__a_J_001tf__a,type,
the_in1757154643552616557on_a_a: set_option_a > ( option_a > a ) > a > option_a ).
thf(sy_c_Fun_Othe__inv__into_001t__Option__Ooption_Itf__a_J_001tf__b,type,
the_in1757154643552616558on_a_b: set_option_a > ( option_a > b ) > b > option_a ).
thf(sy_c_Fun_Othe__inv__into_001tf__a_001t__Option__Ooption_Itf__a_J,type,
the_in8758012798868597241tion_a: set_a > ( a > option_a ) > option_a > a ).
thf(sy_c_Fun_Othe__inv__into_001tf__a_001tf__a,type,
the_inv_into_a_a: set_a > ( a > a ) > a > a ).
thf(sy_c_Fun_Othe__inv__into_001tf__a_001tf__b,type,
the_inv_into_a_b: set_a > ( a > b ) > b > a ).
thf(sy_c_Fun_Othe__inv__into_001tf__b_001t__Option__Ooption_Itf__a_J,type,
the_in5672256556878602680tion_a: set_b > ( b > option_a ) > option_a > b ).
thf(sy_c_Fun_Othe__inv__into_001tf__b_001tf__a,type,
the_inv_into_b_a: set_b > ( b > a ) > a > b ).
thf(sy_c_Fun_Othe__inv__into_001tf__b_001tf__b,type,
the_inv_into_b_b: set_b > ( b > b ) > b > b ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
minus_1574173051537231627tion_a: set_option_a > set_option_a > set_option_a ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b_J,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__d_J,type,
minus_minus_set_d: set_d > set_d > set_d ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
uminus6205308855922866075tion_a: set_option_a > set_option_a ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__a_J,type,
uminus_uminus_set_a: set_a > set_a ).
thf(sy_c_HOL_OThe_001t__Option__Ooption_Itf__a_J,type,
the_option_a: ( option_a > $o ) > option_a ).
thf(sy_c_HOL_OThe_001tf__a,type,
the_a: ( a > $o ) > a ).
thf(sy_c_HOL_OThe_001tf__b,type,
the_b: ( b > $o ) > b ).
thf(sy_c_HOL_OUniq_001tf__a,type,
uniq_a: ( a > $o ) > $o ).
thf(sy_c_HOL_Oundefined_001tf__a,type,
undefined_a: a ).
thf(sy_c_If_001t__Option__Ooption_Itf__a_J,type,
if_option_a: $o > option_a > option_a > option_a ).
thf(sy_c_If_001tf__a,type,
if_a: $o > a > a > a ).
thf(sy_c_If_001tf__b,type,
if_b: $o > b > b > b ).
thf(sy_c_If_001tf__c,type,
if_c: $o > c > c > c ).
thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
inf_in5160421943901843420on_a_o: ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > option_a > option_a > $o ).
thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
inf_inf_a_a_o: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
inf_inf_set_option_a: set_option_a > set_option_a > set_option_a ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__b_J,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
sup_sup_set_option_a: set_option_a > set_option_a > set_option_a ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__b_J,type,
sup_sup_set_b: set_b > set_b > set_b ).
thf(sy_c_Lattices__Big_Osemilattice__set_001t__Option__Ooption_Itf__a_J,type,
lattic4111267149900974290tion_a: ( option_a > option_a > option_a ) > $o ).
thf(sy_c_Lattices__Big_Osemilattice__set_001tf__a,type,
lattic5961991414251573132_set_a: ( a > a > a ) > $o ).
thf(sy_c_Lattices__Big_Osemilattice__set_OF_001t__Option__Ooption_Itf__a_J,type,
lattic5543840709497872670tion_a: ( option_a > option_a > option_a ) > set_option_a > option_a ).
thf(sy_c_Lattices__Big_Osemilattice__set_OF_001tf__a,type,
lattic5116578512385870296ce_F_a: ( a > a > a ) > set_a > a ).
thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin_001t__Set__Oset_Itf__b_J,type,
lattic2918178361130032022_set_b: set_set_b > set_b ).
thf(sy_c_Map_Odom_001t__Option__Ooption_Itf__a_J_001tf__a,type,
dom_option_a_a: ( option_a > option_a ) > set_option_a ).
thf(sy_c_Map_Odom_001tf__a_001tf__a,type,
dom_a_a: ( a > option_a ) > set_a ).
thf(sy_c_Map_Odom_001tf__b_001tf__a,type,
dom_b_a: ( b > option_a ) > set_b ).
thf(sy_c_Map_Omap__add_001t__Option__Ooption_Itf__a_J_001tf__a,type,
map_add_option_a_a: ( option_a > option_a ) > ( option_a > option_a ) > option_a > option_a ).
thf(sy_c_Map_Omap__add_001tf__a_001tf__a,type,
map_add_a_a: ( a > option_a ) > ( a > option_a ) > a > option_a ).
thf(sy_c_Map_Omap__add_001tf__b_001tf__a,type,
map_add_b_a: ( b > option_a ) > ( b > option_a ) > b > option_a ).
thf(sy_c_Map_Oran_001tf__a_001tf__a,type,
ran_a_a: ( a > option_a ) > set_a ).
thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_Itf__a_J_001tf__a,type,
restri3984065703976872170on_a_a: ( option_a > option_a ) > set_option_a > option_a > option_a ).
thf(sy_c_Map_Orestrict__map_001tf__a_001tf__a,type,
restrict_map_a_a: ( a > option_a ) > set_a > a > option_a ).
thf(sy_c_Map_Orestrict__map_001tf__b_001tf__a,type,
restrict_map_b_a: ( b > option_a ) > set_b > b > option_a ).
thf(sy_c_Option_Obind_001tf__a_001tf__a,type,
bind_a_a: option_a > ( a > option_a ) > option_a ).
thf(sy_c_Option_Ocombine__options_001tf__a,type,
combine_options_a: ( a > a > a ) > option_a > option_a > option_a ).
thf(sy_c_Option_Ois__none_001tf__a,type,
is_none_a: option_a > $o ).
thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__a_J,type,
none_option_a: option_option_a ).
thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_Itf__b_J,type,
none_set_b: option_set_b ).
thf(sy_c_Option_Ooption_ONone_001tf__a,type,
none_a: option_a ).
thf(sy_c_Option_Ooption_ONone_001tf__b,type,
none_b: option_b ).
thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__a_J,type,
some_option_a: option_a > option_option_a ).
thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J,type,
some_P377817780860425132_a_d_c: product_prod_a_d_c > option2362401199305441953_a_d_c ).
thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_Itf__b_J,type,
some_set_b: set_b > option_set_b ).
thf(sy_c_Option_Ooption_OSome_001tf__a,type,
some_a: a > option_a ).
thf(sy_c_Option_Ooption_OSome_001tf__b,type,
some_b: b > option_b ).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Option__Ooption_Itf__a_J,type,
case_o3426643154261757367tion_a: $o > ( option_a > $o ) > option_option_a > $o ).
thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001tf__a,type,
case_option_o_a: $o > ( a > $o ) > option_a > $o ).
thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_Itf__a_J_001tf__a,type,
case_o3148979394504432965on_a_a: option_a > ( a > option_a ) > option_a > option_a ).
thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b_J_001t__Set__Oset_Itf__b_J,type,
case_o6570817238820213323_set_b: set_b > ( set_b > set_b ) > option_set_b > set_b ).
thf(sy_c_Option_Ooption_Ocase__option_001tf__a_001t__Option__Ooption_Itf__a_J,type,
case_o926465512965637841tion_a: a > ( option_a > a ) > option_option_a > a ).
thf(sy_c_Option_Ooption_Ocase__option_001tf__a_001tf__a,type,
case_option_a_a: a > ( a > a ) > option_a > a ).
thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_Itf__a_J_001_Eo,type,
map_op2529087131052605791on_a_o: ( option_a > $o ) > option_option_a > option_o ).
thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
map_op788413144570152203tion_a: ( option_a > option_a ) > option_option_a > option_option_a ).
thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_Itf__a_J_001tf__a,type,
map_op4563205767754224965on_a_a: ( option_a > a ) > option_option_a > option_a ).
thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001tf__a,type,
map_op713297920823408162_a_a_a: ( product_prod_a_a > a ) > option5210160422955383789od_a_a > option_a ).
thf(sy_c_Option_Ooption_Omap__option_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
map_op7273698777129206611_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option721982914780012405_b_c_d ).
thf(sy_c_Option_Ooption_Omap__option_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
map_op4138611287120429003_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > option2300553739515653951_b_c_d ).
thf(sy_c_Option_Ooption_Omap__option_001tf__a_001t__Option__Ooption_Itf__a_J,type,
map_op2340691886215429841tion_a: ( a > option_a ) > option_a > option_option_a ).
thf(sy_c_Option_Ooption_Omap__option_001tf__a_001tf__a,type,
map_option_a_a: ( a > a ) > option_a > option_a ).
thf(sy_c_Option_Ooption_Omap__option_001tf__b_001tf__b,type,
map_option_b_b: ( b > b ) > option_b > option_b ).
thf(sy_c_Option_Ooption_Omap__option_001tf__d_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
map_op1826348495503636827_b_c_d: ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > option721982914780012405_b_c_d ).
thf(sy_c_Option_Ooption_Opred__option_001t__Option__Ooption_Itf__a_J,type,
pred_option_option_a: ( option_a > $o ) > option_option_a > $o ).
thf(sy_c_Option_Ooption_Opred__option_001tf__a,type,
pred_option_a: ( a > $o ) > option_a > $o ).
thf(sy_c_Option_Ooption_Opred__option_001tf__b,type,
pred_option_b: ( b > $o ) > option_b > $o ).
thf(sy_c_Option_Ooption_Orec__option_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
rec_op6099162144272762835_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Option_Ooption_Orec__option_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001tf__d,type,
rec_op905682932589663963_c_d_d: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > option_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Option_Ooption_Orec__option_001_Eo_001t__Option__Ooption_Itf__a_J,type,
rec_op1346285999958695467tion_a: $o > ( option_a > $o ) > option_option_a > $o ).
thf(sy_c_Option_Ooption_Orec__option_001_Eo_001tf__a,type,
rec_option_o_a: $o > ( a > $o ) > option_a > $o ).
thf(sy_c_Option_Ooption_Orec__option_001t__Option__Ooption_Itf__a_J_001tf__a,type,
rec_op3997991240598549433on_a_a: option_a > ( a > option_a ) > option_a > option_a ).
thf(sy_c_Option_Ooption_Orec__option_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
rec_op3341093412072267839_b_c_d: assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > option2300553739515653951_b_c_d > assertion_a_b_c_d ).
thf(sy_c_Option_Ooption_Orel__option_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
rel_op2232639710186594644_b_c_d: ( ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o ) > option721982914780012405_b_c_d > option721982914780012405_b_c_d > $o ).
thf(sy_c_Option_Ooption_Orel__option_001_Eo_001_Eo,type,
rel_option_o_o: ( $o > $o > $o ) > option_o > option_o > $o ).
thf(sy_c_Option_Ooption_Orel__option_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
rel_op4798662380513671176tion_a: ( option_a > option_a > $o ) > option_option_a > option_option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001t__Option__Ooption_Itf__a_J_001tf__a,type,
rel_op3736390606718109634on_a_a: ( option_a > a > $o ) > option_option_a > option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001t__Option__Ooption_Itf__a_J_001tf__b,type,
rel_op3736390606718109635on_a_b: ( option_a > b > $o ) > option_option_a > option_b > $o ).
thf(sy_c_Option_Ooption_Orel__option_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
rel_op1902716345276195528_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > option2300553739515653951_b_c_d > option2300553739515653951_b_c_d > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__a_001t__Option__Ooption_Itf__a_J,type,
rel_op1513876725179314510tion_a: ( a > option_a > $o ) > option_a > option_option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__a_001tf__a,type,
rel_option_a_a: ( a > a > $o ) > option_a > option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__a_001tf__b,type,
rel_option_a_b: ( a > b > $o ) > option_a > option_b > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__b_001t__Option__Ooption_Itf__a_J,type,
rel_op7651492520044095757tion_a: ( b > option_a > $o ) > option_b > option_option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__b_001tf__a,type,
rel_option_b_a: ( b > a > $o ) > option_b > option_a > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__b_001tf__b,type,
rel_option_b_b: ( b > b > $o ) > option_b > option_b > $o ).
thf(sy_c_Option_Ooption_Orel__option_001tf__d_001tf__d,type,
rel_option_d_d: ( d > d > $o ) > option_d > option_d > $o ).
thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_Itf__a_J,type,
set_option_option_a2: option_option_a > set_option_a ).
thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
set_op3367984300228426933od_a_a: option5210160422955383789od_a_a > set_Product_prod_a_a ).
thf(sy_c_Option_Ooption_Oset__option_001tf__a,type,
set_option_a2: option_a > set_a ).
thf(sy_c_Option_Ooption_Oset__option_001tf__b,type,
set_option_b2: option_b > set_b ).
thf(sy_c_Option_Ooption_Osize__option_001tf__a,type,
size_option_a: ( a > nat ) > option_a > nat ).
thf(sy_c_Option_Ooption_Othe_001t__Option__Ooption_Itf__a_J,type,
the_option_a2: option_option_a > option_a ).
thf(sy_c_Option_Ooption_Othe_001t__Set__Oset_Itf__b_J,type,
the_set_b: option_set_b > set_b ).
thf(sy_c_Option_Ooption_Othe_001tf__a,type,
the_a2: option_a > a ).
thf(sy_c_Option_Ooption_Othe_001tf__b,type,
the_b2: option_b > b ).
thf(sy_c_Option_Othese_001t__Option__Ooption_Itf__a_J,type,
these_option_a: set_option_option_a > set_option_a ).
thf(sy_c_Option_Othese_001tf__a,type,
these_a: set_option_a > set_a ).
thf(sy_c_Option_Othese_001tf__b,type,
these_b: set_option_b > set_b ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
bot_bo4163488203964334806tion_a: set_option_option_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
bot_bot_set_option_a: set_option_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
bot_bot_set_a: set_a ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
bot_bot_set_b: set_b ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__d_J,type,
bot_bot_set_d: set_d ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
ord_le5631237216984945872tion_a: set_option_a > set_option_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
ord_less_set_a: set_a > set_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_Itf__a_J_M_062_It__Option__Ooption_Itf__a_J_M_Eo_J_J,type,
ord_le3058241657886854542on_a_o: ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
ord_le8889544289526388249on_a_o: ( option_a > $o ) > ( option_a > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J_J,type,
ord_le3165238294362408398_c_d_o: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_M_Eo_J,type,
ord_le6795694934652756260_c_d_o: ( assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J,type,
ord_less_eq_b_b_o: ( b > b > $o ) > ( b > b > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__b_M_Eo_J,type,
ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
ord_le1955136853071979460tion_a: set_option_a > set_option_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
ord_le746702958409616551od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
ord_le182087997850975847od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_I_062_Itf__d_Mtf__c_J_M_062_Itf__a_M_Eo_J_J_M_Eo_J,type,
top_top_d_c_a_o_o: ( ( d > c ) > a > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
top_to1659475022456381882tion_a: set_option_option_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
top_top_set_option_a: set_option_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
top_top_set_set_b: set_set_b ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J,type,
top_to5797442083933759657_b_c_d: set_as1616228751320511321_b_c_d ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
top_top_set_a: set_a ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
top_top_set_b: set_b ).
thf(sy_c_Product__Type_OPair_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
produc9011544418120257559tion_a: option_a > option_a > produc3509355604313844263tion_a ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_J,type,
produc5208860900648697099_a_d_c: product_prod_a_d_c > option2362401199305441953_a_d_c > produc6150846815813599699_a_d_c ).
thf(sy_c_Product__Type_OPair_001tf__a_001_062_Itf__d_Mtf__c_J,type,
product_Pair_a_d_c: a > ( d > c ) > product_prod_a_d_c ).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001_Eo,type,
produc7248784972643495020on_a_o: ( option_a > option_a > $o ) > produc3509355604313844263tion_a > $o ).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001tf__a_001_Eo,type,
produc6436628058953941356_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b_001tf__b_001_Eo,type,
produc4772849988445941548_b_b_o: ( b > b > $o ) > product_prod_b_b > $o ).
thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001tf__a,type,
product_fst_a_a: product_prod_a_a > a ).
thf(sy_c_Product__Type_Oprod_Ofst_001tf__b_001tf__b,type,
product_fst_b_b: product_prod_b_b > b ).
thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001tf__a,type,
product_snd_a_a: product_prod_a_a > a ).
thf(sy_c_Product__Type_Oprod_Osnd_001tf__b_001tf__b,type,
product_snd_b_b: product_prod_b_b > b ).
thf(sy_c_Relation_Oconversep_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Option__Ooption_Itf__a_J,type,
conver6736784915673013132tion_a: ( option5210160422955383789od_a_a > option_a > $o ) > option_a > option5210160422955383789od_a_a > $o ).
thf(sy_c_Relation_Oconversep_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
conver2091984906772465269tion_a: ( option_a > option_a > $o ) > option_a > option_a > $o ).
thf(sy_c_Relation_Oconversep_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
conver6185760717984097101_b_c_d: ( assert5325495410138902753_b_c_d > assertion_a_b_c_d > $o ) > assertion_a_b_c_d > assert5325495410138902753_b_c_d > $o ).
thf(sy_c_Relation_Oconversep_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
conver81709274662576437_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_Relation_Oconversep_001tf__a_001tf__a,type,
conversep_a_a: ( a > a > $o ) > a > a > $o ).
thf(sy_c_Relation_Oconversep_001tf__b_001tf__b,type,
conversep_b_b: ( b > b > $o ) > b > b > $o ).
thf(sy_c_Relation_Orelcompp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Option__Ooption_Itf__a_J,type,
relcom7597457113570619114tion_a: ( option_a > option5210160422955383789od_a_a > $o ) > ( option5210160422955383789od_a_a > option_a > $o ) > option_a > option_a > $o ).
thf(sy_c_Relation_Orelcompp_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
relcom1089236864311994323tion_a: ( option_a > option_a > $o ) > ( option_a > option_a > $o ) > option_a > option_a > $o ).
thf(sy_c_Relation_Orelcompp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
relcom6640016704938620384_b_c_d: ( assertion_a_b_c_d > assert5325495410138902753_b_c_d > $o ) > ( assert5325495410138902753_b_c_d > assertion_a_b_c_d > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_Relation_Orelcompp_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
relcom5312131986986172104_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_Relation_Orelcompp_001tf__a_001tf__a_001tf__a,type,
relcompp_a_a_a: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
thf(sy_c_Relation_Orelcompp_001tf__b_001tf__b_001tf__b,type,
relcompp_b_b_b: ( b > b > $o ) > ( b > b > $o ) > b > b > $o ).
thf(sy_c_Set_OCollect_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
collec431113534271933400od_a_a: ( option5210160422955383789od_a_a > $o ) > set_op7160277562814721357od_a_a ).
thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__a_J,type,
collect_option_a: ( option_a > $o ) > set_option_a ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
collec3336397797384452498od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
collec548942219715005266od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(sy_c_Set_OCollect_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J,type,
collec1337203158693800140_b_c_d: ( assert5325495410138902753_b_c_d > $o ) > set_as5068551873036484673_b_c_d ).
thf(sy_c_Set_OCollect_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
collec747544926041312740_b_c_d: ( assertion_a_b_c_d > $o ) > set_as1616228751320511321_b_c_d ).
thf(sy_c_Set_OCollect_001tf__a,type,
collect_a: ( a > $o ) > set_a ).
thf(sy_c_Set_OCollect_001tf__b,type,
collect_b: ( b > $o ) > set_b ).
thf(sy_c_Set_OCollect_001tf__d,type,
collect_d: ( d > $o ) > set_d ).
thf(sy_c_Set_OPow_001t__Option__Ooption_Itf__a_J,type,
pow_option_a: set_option_a > set_set_option_a ).
thf(sy_c_Set_OPow_001tf__a,type,
pow_a: set_a > set_set_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
image_2132136900116418507tion_a: ( option_a > option_option_a ) > set_option_a > set_option_option_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
image_7439109396645324421tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001tf__a,type,
image_option_a_a: ( option_a > a ) > set_option_a > set_a ).
thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001tf__b,type,
image_option_a_b: ( option_a > b ) > set_option_a > set_b ).
thf(sy_c_Set_Oimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
image_a_option_a: ( a > option_a ) > set_a > set_option_a ).
thf(sy_c_Set_Oimage_001tf__a_001t__Set__Oset_Itf__a_J,type,
image_a_set_a: ( a > set_a ) > set_a > set_set_a ).
thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(sy_c_Set_Oimage_001tf__a_001tf__b,type,
image_a_b: ( a > b ) > set_a > set_b ).
thf(sy_c_Set_Oimage_001tf__b_001t__Option__Ooption_Itf__a_J,type,
image_b_option_a: ( b > option_a ) > set_b > set_option_a ).
thf(sy_c_Set_Oimage_001tf__b_001tf__a,type,
image_b_a: ( b > a ) > set_b > set_a ).
thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
image_b_b: ( b > b ) > set_b > set_b ).
thf(sy_c_Set_Oimage_001tf__d_001tf__c,type,
image_d_c: ( d > c ) > set_d > set_c ).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
insert605063979879581146tion_a: option_option_a > set_option_option_a > set_option_option_a ).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_Itf__a_J,type,
insert_option_a: option_a > set_option_a > set_option_a ).
thf(sy_c_Set_Oinsert_001tf__a,type,
insert_a: a > set_a > set_a ).
thf(sy_c_Set_Oinsert_001tf__b,type,
insert_b: b > set_b > set_b ).
thf(sy_c_Set_Oinsert_001tf__c,type,
insert_c: c > set_c > set_c ).
thf(sy_c_Set_Oinsert_001tf__d,type,
insert_d: d > set_d > set_d ).
thf(sy_c_Set_Ovimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
vimage1562710927270423099tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
thf(sy_c_Set_Ovimage_001t__Option__Ooption_Itf__a_J_001tf__a,type,
vimage_option_a_a: ( option_a > a ) > set_a > set_option_a ).
thf(sy_c_Set_Ovimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
vimage_a_option_a: ( a > option_a ) > set_option_a > set_a ).
thf(sy_c_Set_Ovimage_001tf__a_001tf__a,type,
vimage_a_a: ( a > a ) > set_a > set_a ).
thf(sy_c_Set_Ovimage_001tf__b_001t__Option__Ooption_Itf__a_J,type,
vimage_b_option_a: ( b > option_a ) > set_option_a > set_b ).
thf(sy_c_Set_Ovimage_001tf__b_001tf__a,type,
vimage_b_a: ( b > a ) > set_a > set_b ).
thf(sy_c_Transfer_Obi__unique_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
bi_uni6217441781253053455tion_a: ( option_a > option_a > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J,type,
bi_uni3681814365736818383_b_c_d: ( assertion_a_b_c_d > assertion_a_b_c_d > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__a_001tf__a,type,
bi_unique_a_a: ( a > a > $o ) > $o ).
thf(sy_c_Transfer_Obi__unique_001tf__d_001tf__d,type,
bi_unique_d_d: ( d > d > $o ) > $o ).
thf(sy_c_UnboundedLogic_Oassertion_OAnd_001tf__a_001tf__b_001tf__c_001tf__d,type,
and_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OBounded_001tf__a_001tf__b_001tf__c_001tf__d,type,
bounded_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OExists_001tf__d_001tf__a_001tf__b_001tf__c,type,
exists_d_a_b_c: d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OForall_001tf__d_001tf__a_001tf__b_001tf__c,type,
forall_d_a_b_c: d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OImp_001tf__a_001tf__b_001tf__c_001tf__d,type,
imp_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OMult_001tf__b_001tf__a_001tf__c_001tf__d,type,
mult_b_a_c_d: b > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OOr_001tf__a_001tf__b_001tf__c_001tf__d,type,
or_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OPred_001tf__a_001tf__b_001tf__c_001tf__d,type,
pred_a_b_c_d: assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OSem_001tf__d_001tf__c_001tf__a_001tf__b,type,
sem_d_c_a_b: ( ( d > c ) > a > $o ) > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OStar_001tf__a_001tf__b_001tf__c_001tf__d,type,
star_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OWand_001tf__a_001tf__b_001tf__c_001tf__d,type,
wand_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_OWildcard_001tf__a_001tf__b_001tf__c_001tf__d,type,
wildcard_a_b_c_d: assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_Ocase__assertion_001tf__d_001tf__c_001tf__a_001_062_It__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_Mt__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_J_001tf__b,type,
case_a3730527612158903040_c_d_b: ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_Ocase__assertion_001tf__d_001tf__c_001tf__a_001t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__c_Mtf__d_J_001tf__b,type,
case_a3488927611849131102_c_d_b: ( ( ( d > c ) > a > $o ) > assertion_a_b_c_d ) > ( b > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > ( d > assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_Omap__assertion_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001tf__b_001tf__a_001tf__c_001tf__d,type,
map_as225457026910506420_a_c_d: ( product_prod_b_b > b ) > assert5325495410138902753_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_Omap__assertion_001tf__b_001tf__b_001tf__a_001tf__c_001tf__d,type,
map_as4919457480576020172_a_c_d: ( b > b ) > assertion_a_b_c_d > assertion_a_b_c_d ).
thf(sy_c_UnboundedLogic_Oassertion_Opred__assertion_001tf__b_001tf__a_001tf__c_001tf__d,type,
pred_a8195579292382433461_a_c_d: ( b > $o ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__c_001tf__d,type,
rel_as660020871172297353_a_c_d: ( option_a > option_a > $o ) > assert5894900919346993214_a_c_d > assert5894900919346993214_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001t__Option__Ooption_Itf__a_J_001tf__b_001tf__a_001tf__c_001tf__d,type,
rel_as8093967732909205902_a_c_d: ( option_a > b > $o ) > assert5894900919346993214_a_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__a_001tf__b_001tf__a_001tf__c_001tf__d,type,
rel_as3981545127228379208_a_c_d: ( a > b > $o ) > assertion_a_a_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__c_001tf__d,type,
rel_as6688652118001638340_a_c_d: ( b > option_a > $o ) > assertion_a_b_c_d > assert5894900919346993214_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__a_001tf__a_001tf__c_001tf__d,type,
rel_as3160482565473489034_a_c_d: ( b > a > $o ) > assertion_a_b_c_d > assertion_a_a_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Orel__assertion_001tf__b_001tf__b_001tf__a_001tf__c_001tf__d,type,
rel_as4648444602768287561_a_c_d: ( b > b > $o ) > assertion_a_b_c_d > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001t__Option__Ooption_Itf__a_J_001tf__c_001tf__d,type,
set_as3758641881469047763_a_c_d: assert5894900919346993214_a_c_d > set_option_a ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001tf__c_001tf__d,type,
set_as9022474982623750902_b_c_d: assert5325495410138902753_b_c_d > set_Product_prod_b_b ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001tf__a_001tf__c_001tf__d,type,
set_as4423919284370888077_a_c_d: assertion_a_a_c_d > set_a ).
thf(sy_c_UnboundedLogic_Oassertion_Oset__assertion_001tf__a_001tf__b_001tf__c_001tf__d,type,
set_as796765862704242958_b_c_d: assertion_a_b_c_d > set_b ).
thf(sy_c_UnboundedLogic_Oassertion_Osize__assertion_001tf__a_001tf__b_001tf__c_001tf__d,type,
size_a5396279667297198487_b_c_d: ( a > nat ) > ( b > nat ) > ( c > nat ) > ( d > nat ) > assertion_a_b_c_d > nat ).
thf(sy_c_UnboundedLogic_Ologic_001tf__a_001tf__b,type,
logic_a_b: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( b > b > b ) > ( b > b ) > b > ( a > $o ) > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oentails_001tf__a_001tf__b_001tf__c_001tf__d,type,
entails_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_c_d > ( ( d > c ) > set_a ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oequal__outside_001tf__d_001tf__c,type,
equal_outside_d_c: ( d > c ) > ( d > c ) > set_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oequivalent_001tf__a_001tf__b_001tf__c_001tf__d,type,
equivalent_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_c_d > ( ( d > c ) > set_a ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Oframe__property_001tf__a_001tf__d_001tf__c,type,
frame_property_a_d_c: ( a > a > option_a ) > ( a > $o ) > set_Pr7868159745199425715_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ointuitionistic_001tf__a_001tf__b_001tf__d_001tf__c,type,
intuit4720955538653295669_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( d > c ) > ( ( d > c ) > set_a ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Omodified_001tf__a_001tf__d_001tf__c,type,
modified_a_d_c: set_Pr7868159745199425715_a_d_c > set_d ).
thf(sy_c_UnboundedLogic_Ologic_Onot__in__fv_001tf__a_001tf__b_001tf__c_001tf__d,type,
not_in_fv_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_c_d > set_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Opure_001tf__a_001tf__b_001tf__c_001tf__d,type,
pure_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osafe_001tf__a_001tf__d_001tf__c,type,
safe_a_d_c: set_Pr7868159745199425715_a_d_c > product_prod_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osafety__monotonicity_001tf__a_001tf__d_001tf__c,type,
safety7280469885071620222_a_d_c: ( a > a > option_a ) > ( a > $o ) > set_Pr7868159745199425715_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Osat_001tf__a_001tf__b_001tf__d_001tf__c,type,
sat_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > a > ( d > c ) > ( ( d > c ) > set_a ) > assertion_a_b_c_d > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ovalid__command_001tf__a_001tf__d_001tf__c,type,
valid_command_a_d_c: ( a > $o ) > set_Pr7868159745199425715_a_d_c > $o ).
thf(sy_c_UnboundedLogic_Ologic_Ovalid__hoare__triple_001tf__a_001tf__b_001tf__c_001tf__d,type,
valid_8824771084768397689_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_c_d > set_Pr7868159745199425715_a_d_c > assertion_a_b_c_d > ( ( d > c ) > set_a ) > $o ).
thf(sy_c_UnboundedLogic_Opre__logic_Ocompatible_001tf__a,type,
pre_compatible_a: ( a > a > option_a ) > a > a > $o ).
thf(sy_c_UnboundedLogic_Opre__logic_Olarger_001tf__a,type,
pre_larger_a: ( a > a > option_a ) > a > a > $o ).
thf(sy_c_member_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
member5113800082084363315tion_a: option_option_a > set_option_option_a > $o ).
thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
member8183384484874023062od_a_a: option5210160422955383789od_a_a > set_op7160277562814721357od_a_a > $o ).
thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
member_option_a: option_a > set_option_a > $o ).
thf(sy_c_member_001t__Option__Ooption_Itf__b_J,type,
member_option_b: option_b > set_option_b > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__d_Mtf__c_J_J_J_J,type,
member2052822272342364412_a_d_c: produc6150846815813599699_a_d_c > set_Pr7868159745199425715_a_d_c > $o ).
thf(sy_c_member_001t__UnboundedLogic__Oassertion_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__c_Mtf__d_J,type,
member2208103261226737034_b_c_d: assert5325495410138902753_b_c_d > set_as5068551873036484673_b_c_d > $o ).
thf(sy_c_member_001tf__a,type,
member_a: a > set_a > $o ).
thf(sy_c_member_001tf__b,type,
member_b: b > set_b > $o ).
thf(sy_c_member_001tf__c,type,
member_c: c > set_c > $o ).
thf(sy_c_member_001tf__d,type,
member_d: d > set_d > $o ).
thf(sy_v_A,type,
a2: assertion_a_b_c_d ).
thf(sy_v__092_060Delta_062,type,
delta: ( d > c ) > set_a ).
thf(sy_v_mult,type,
mult: b > a > a ).
thf(sy_v_one,type,
one: b ).
thf(sy_v_plus,type,
plus: a > a > option_a ).
thf(sy_v_sadd,type,
sadd: b > b > b ).
thf(sy_v_sinv,type,
sinv: b > b ).
thf(sy_v_smult,type,
smult: b > b > b ).
thf(sy_v_valid,type,
valid: a > $o ).
% Relevant facts (1203)
thf(fact_0_commutative,axiom,
! [A: a,B: a] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ) ).
% commutative
thf(fact_1_can__divide,axiom,
! [P: b,A: a,B: a] :
( ( ( mult @ P @ A )
= ( mult @ P @ B ) )
=> ( A = B ) ) ).
% can_divide
thf(fact_2_sadd__comm,axiom,
! [P: b,Q: b] :
( ( sadd @ P @ Q )
= ( sadd @ Q @ P ) ) ).
% sadd_comm
thf(fact_3_assms,axiom,
pure_a_b_c_d @ plus @ mult @ valid @ a2 ).
% assms
thf(fact_4_unique__inv,axiom,
! [A: a,P: b,B: a] :
( ( A
= ( mult @ P @ B ) )
= ( B
= ( mult @ ( sinv @ P ) @ A ) ) ) ).
% unique_inv
thf(fact_5_logic_Ocombinable_Ocong,axiom,
combinable_a_b_d_c = combinable_a_b_d_c ).
% logic.combinable.cong
thf(fact_6_one__neutral,axiom,
! [A: a] :
( ( mult @ one @ A )
= A ) ).
% one_neutral
thf(fact_7_combinable__and,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( and_a_b_c_d @ A2 @ B2 ) ) ) ) ).
% combinable_and
thf(fact_8_combinable__forall,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( forall_d_a_b_c @ X @ A2 ) ) ) ).
% combinable_forall
thf(fact_9_combinable__wand,axiom,
! [Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d,A2: assertion_a_b_c_d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) ) ) ).
% combinable_wand
thf(fact_10_combinable__star,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) ) ) ) ).
% combinable_star
thf(fact_11_combinable__mult,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,Pi: b] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( mult_b_a_c_d @ Pi @ A2 ) ) ) ).
% combinable_mult
thf(fact_12_valid__mono,axiom,
! [A: a,B: a] :
( ( ( valid @ A )
& ( pre_larger_a @ plus @ A @ B ) )
=> ( valid @ B ) ) ).
% valid_mono
thf(fact_13_larger__same,axiom,
! [A: a,B: a,P: b] :
( ( pre_larger_a @ plus @ A @ B )
= ( pre_larger_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% larger_same
thf(fact_14_distrib__mult,axiom,
! [P: b,Q: b,X: a] :
( ( some_a @ ( mult @ ( sadd @ P @ Q ) @ X ) )
= ( plus @ ( mult @ P @ X ) @ ( mult @ Q @ X ) ) ) ).
% distrib_mult
thf(fact_15_compatible__iff,axiom,
! [A: a,B: a,P: b] :
( ( pre_compatible_a @ plus @ A @ B )
= ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% compatible_iff
thf(fact_16_compatible__imp,axiom,
! [A: a,B: a,P: b] :
( ( pre_compatible_a @ plus @ A @ B )
=> ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).
% compatible_imp
thf(fact_17_compatible__multiples,axiom,
! [P: b,A: a,Q: b,B: a] :
( ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) )
=> ( pre_compatible_a @ plus @ A @ B ) ) ).
% compatible_multiples
thf(fact_18_move__sum,axiom,
! [A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X1: a,X2: a] :
( ( ( some_a @ A )
= ( plus @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( plus @ B1 @ B22 ) )
=> ( ( ( some_a @ X )
= ( plus @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( plus @ A1 @ B1 ) )
=> ( ( ( some_a @ X2 )
= ( plus @ A22 @ B22 ) )
=> ( ( some_a @ X )
= ( plus @ X1 @ X2 ) ) ) ) ) ) ) ).
% move_sum
thf(fact_19_asso1,axiom,
! [A: a,B: a,Ab: a,C: a,Bc: a] :
( ( ( ( plus @ A @ B )
= ( some_a @ Ab ) )
& ( ( plus @ B @ C )
= ( some_a @ Bc ) ) )
=> ( ( plus @ Ab @ C )
= ( plus @ A @ Bc ) ) ) ).
% asso1
thf(fact_20_asso3,axiom,
! [A: a,B: a,C: a,Bc: a] :
( ~ ( pre_compatible_a @ plus @ A @ B )
=> ( ( ( plus @ B @ C )
= ( some_a @ Bc ) )
=> ~ ( pre_compatible_a @ plus @ A @ Bc ) ) ) ).
% asso3
thf(fact_21_asso2,axiom,
! [A: a,B: a,Ab: a,C: a] :
( ( ( ( plus @ A @ B )
= ( some_a @ Ab ) )
& ~ ( pre_compatible_a @ plus @ B @ C ) )
=> ~ ( pre_compatible_a @ plus @ Ab @ C ) ) ).
% asso2
thf(fact_22_sum__both__larger,axiom,
! [X3: a,A3: a,B3: a,X: a,A: a,B: a] :
( ( ( some_a @ X3 )
= ( plus @ A3 @ B3 ) )
=> ( ( ( some_a @ X )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ A3 @ A )
=> ( ( pre_larger_a @ plus @ B3 @ B )
=> ( pre_larger_a @ plus @ X3 @ X ) ) ) ) ) ).
% sum_both_larger
thf(fact_23_larger__first__sum,axiom,
! [Y: a,A: a,B: a,X: a] :
( ( ( some_a @ Y )
= ( plus @ A @ B ) )
=> ( ( pre_larger_a @ plus @ X @ Y )
=> ? [A4: a] :
( ( ( some_a @ X )
= ( plus @ A4 @ B ) )
& ( pre_larger_a @ plus @ A4 @ A ) ) ) ) ).
% larger_first_sum
thf(fact_24_larger__def,axiom,
! [A: a,B: a] :
( ( pre_larger_a @ plus @ A @ B )
= ( ? [C2: a] :
( ( some_a @ A )
= ( plus @ B @ C2 ) ) ) ) ).
% larger_def
thf(fact_25_larger__implies__compatible,axiom,
! [X: a,Y: a] :
( ( pre_larger_a @ plus @ X @ Y )
=> ( pre_compatible_a @ plus @ X @ Y ) ) ).
% larger_implies_compatible
thf(fact_26_compatible__smaller,axiom,
! [A: a,B: a,X: a] :
( ( pre_larger_a @ plus @ A @ B )
=> ( ( pre_compatible_a @ plus @ X @ A )
=> ( pre_compatible_a @ plus @ X @ B ) ) ) ).
% compatible_smaller
thf(fact_27_plus__mult,axiom,
! [A: a,B: a,C: a,P: b] :
( ( ( some_a @ A )
= ( plus @ B @ C ) )
=> ( ( some_a @ ( mult @ P @ A ) )
= ( plus @ ( mult @ P @ B ) @ ( mult @ P @ C ) ) ) ) ).
% plus_mult
thf(fact_28_combinable__def,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
= ( ! [P2: b,Q2: b] : ( entails_a_b_c_d @ plus @ mult @ valid @ ( star_a_b_c_d @ ( mult_b_a_c_d @ P2 @ A2 ) @ ( mult_b_a_c_d @ Q2 @ A2 ) ) @ Delta @ ( mult_b_a_c_d @ ( sadd @ P2 @ Q2 ) @ A2 ) ) ) ) ).
% combinable_def
thf(fact_29_unambiguous__star,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d,B2: assertion_a_b_c_d] :
( ( unambiguous_a_b_d_c @ plus @ mult @ valid @ Delta @ A2 @ X )
=> ( unambiguous_a_b_d_c @ plus @ mult @ valid @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) @ X ) ) ).
% unambiguous_star
thf(fact_30_combinable__instantiate__one,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,A: a,S: d > c,B: a,X: a,P: b,Q: b] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ A @ S @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ B @ S @ Delta @ A2 )
=> ( ( ( some_a @ X )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( ( ( sadd @ P @ Q )
= one )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ X @ S @ Delta @ A2 ) ) ) ) ) ) ).
% combinable_instantiate_one
thf(fact_31_combinable__instantiate,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,A: a,S: d > c,B: a,X: a,P: b,Q: b] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ A @ S @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ B @ S @ Delta @ A2 )
=> ( ( ( some_a @ X )
= ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ X @ S @ Delta @ ( mult_b_a_c_d @ ( sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ).
% combinable_instantiate
thf(fact_32_combinableI__old,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ! [A5: a,B4: a,P3: b,Q3: b,X4: a,Sigma: a,S2: d > c] :
( ( ( sat_a_b_d_c @ plus @ mult @ valid @ A5 @ S2 @ Delta @ A2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ B4 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma )
= ( plus @ ( mult @ P3 @ A5 ) @ ( mult @ Q3 @ B4 ) ) )
& ( Sigma
= ( mult @ ( sadd @ P3 @ Q3 ) @ X4 ) ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ X4 @ S2 @ Delta @ A2 ) )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 ) ) ).
% combinableI_old
thf(fact_33_sinv__inverse,axiom,
! [P: b] :
( ( smult @ P @ ( sinv @ P ) )
= one ) ).
% sinv_inverse
thf(fact_34_sat__wand,axiom,
! [S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,Sigma2: a,B2: assertion_a_b_c_d] :
( ! [A5: a,Sigma3: a] :
( ( ( sat_a_b_d_c @ plus @ mult @ valid @ A5 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma3 )
= ( plus @ Sigma2 @ A5 ) ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma3 @ S @ Delta @ B2 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) ) ) ).
% sat_wand
thf(fact_35_sat_Osimps_I3_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) )
= ( ! [A6: a,Sigma4: a] :
( ( ( sat_a_b_d_c @ plus @ mult @ valid @ A6 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma4 )
= ( plus @ Sigma2 @ A6 ) ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma4 @ S @ Delta @ B2 ) ) ) ) ).
% sat.simps(3)
thf(fact_36_sat_Osimps_I2_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) )
= ( ? [A6: a,B5: a] :
( ( ( some_a @ Sigma2 )
= ( plus @ A6 @ B5 ) )
& ( sat_a_b_d_c @ plus @ mult @ valid @ A6 @ S @ Delta @ A2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ B5 @ S @ Delta @ B2 ) ) ) ) ).
% sat.simps(2)
thf(fact_37_logic__axioms,axiom,
logic_a_b @ plus @ mult @ smult @ sadd @ sinv @ one @ valid ).
% logic_axioms
thf(fact_38_sat_Osimps_I7_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( and_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ A2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ).
% sat.simps(7)
thf(fact_39_smult__asso,axiom,
! [P: b,Q: b,R: b] :
( ( smult @ ( smult @ P @ Q ) @ R )
= ( smult @ P @ ( smult @ Q @ R ) ) ) ).
% smult_asso
thf(fact_40_smult__comm,axiom,
! [P: b,Q: b] :
( ( smult @ P @ Q )
= ( smult @ Q @ P ) ) ).
% smult_comm
thf(fact_41_double__mult,axiom,
! [P: b,Q: b,A: a] :
( ( mult @ P @ ( mult @ Q @ A ) )
= ( mult @ ( smult @ P @ Q ) @ A ) ) ).
% double_mult
thf(fact_42_smult__distrib,axiom,
! [P: b,Q: b,R: b] :
( ( smult @ P @ ( sadd @ Q @ R ) )
= ( sadd @ ( smult @ P @ Q ) @ ( smult @ P @ R ) ) ) ).
% smult_distrib
thf(fact_43_mem__Collect__eq,axiom,
! [A: a,P4: a > $o] :
( ( member_a @ A @ ( collect_a @ P4 ) )
= ( P4 @ A ) ) ).
% mem_Collect_eq
thf(fact_44_mem__Collect__eq,axiom,
! [A: b,P4: b > $o] :
( ( member_b @ A @ ( collect_b @ P4 ) )
= ( P4 @ A ) ) ).
% mem_Collect_eq
thf(fact_45_mem__Collect__eq,axiom,
! [A: option_a,P4: option_a > $o] :
( ( member_option_a @ A @ ( collect_option_a @ P4 ) )
= ( P4 @ A ) ) ).
% mem_Collect_eq
thf(fact_46_Collect__mem__eq,axiom,
! [A2: set_a] :
( ( collect_a
@ ^ [X5: a] : ( member_a @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_47_Collect__mem__eq,axiom,
! [A2: set_b] :
( ( collect_b
@ ^ [X5: b] : ( member_b @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_48_Collect__mem__eq,axiom,
! [A2: set_option_a] :
( ( collect_option_a
@ ^ [X5: option_a] : ( member_option_a @ X5 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_49_Collect__cong,axiom,
! [P4: option_a > $o,Q4: option_a > $o] :
( ! [X4: option_a] :
( ( P4 @ X4 )
= ( Q4 @ X4 ) )
=> ( ( collect_option_a @ P4 )
= ( collect_option_a @ Q4 ) ) ) ).
% Collect_cong
thf(fact_50_sone__neutral,axiom,
! [P: b] :
( ( smult @ one @ P )
= P ) ).
% sone_neutral
thf(fact_51_sat_Osimps_I1_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,P: b,A2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( mult_b_a_c_d @ P @ A2 ) )
= ( ? [A6: a] :
( ( Sigma2
= ( mult @ P @ A6 ) )
& ( sat_a_b_d_c @ plus @ mult @ valid @ A6 @ S @ Delta @ A2 ) ) ) ) ).
% sat.simps(1)
thf(fact_52_sat__mult,axiom,
! [Sigma2: a,P: b,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ! [A5: a] :
( ( Sigma2
= ( mult @ P @ A5 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ A5 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( mult_b_a_c_d @ P @ A2 ) ) ) ).
% sat_mult
thf(fact_53_entailsI,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ B2 ) )
=> ( entails_a_b_c_d @ plus @ mult @ valid @ A2 @ Delta @ B2 ) ) ).
% entailsI
thf(fact_54_entails__def,axiom,
! [A2: assertion_a_b_c_d,Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d] :
( ( entails_a_b_c_d @ plus @ mult @ valid @ A2 @ Delta @ B2 )
= ( ! [Sigma5: a,S3: d > c] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta @ B2 ) ) ) ) ).
% entails_def
thf(fact_55_pure__def,axiom,
! [A2: assertion_a_b_c_d] :
( ( pure_a_b_c_d @ plus @ mult @ valid @ A2 )
= ( ! [Sigma5: a,Sigma4: a,S3: d > c,Delta2: ( d > c ) > set_a,Delta3: ( d > c ) > set_a] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta2 @ A2 )
= ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 ) ) ) ) ).
% pure_def
thf(fact_56_equivalentI,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ B2 ) )
=> ( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ B2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ A2 ) )
=> ( equivalent_a_b_c_d @ plus @ mult @ valid @ A2 @ Delta @ B2 ) ) ) ).
% equivalentI
thf(fact_57_equivalent__def,axiom,
! [A2: assertion_a_b_c_d,Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d] :
( ( equivalent_a_b_c_d @ plus @ mult @ valid @ A2 @ Delta @ B2 )
= ( ( entails_a_b_c_d @ plus @ mult @ valid @ A2 @ Delta @ B2 )
& ( entails_a_b_c_d @ plus @ mult @ valid @ B2 @ Delta @ A2 ) ) ) ).
% equivalent_def
thf(fact_58_intuitionisticI,axiom,
! [S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ! [A5: a,B4: a] :
( ( ( pre_larger_a @ plus @ A5 @ B4 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ B4 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ A5 @ S @ Delta @ A2 ) )
=> ( intuit4720955538653295669_b_d_c @ plus @ mult @ valid @ S @ Delta @ A2 ) ) ).
% intuitionisticI
thf(fact_59_intuitionistic__def,axiom,
! [S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( intuit4720955538653295669_b_d_c @ plus @ mult @ valid @ S @ Delta @ A2 )
= ( ! [A6: a,B5: a] :
( ( ( pre_larger_a @ plus @ A6 @ B5 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ B5 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ A6 @ S @ Delta @ A2 ) ) ) ) ).
% intuitionistic_def
thf(fact_60_not__in__fv__def,axiom,
! [A2: assertion_a_b_c_d,S4: set_d] :
( ( not_in_fv_a_b_c_d @ plus @ mult @ valid @ A2 @ S4 )
= ( ! [Sigma5: a,S3: d > c,Delta2: ( d > c ) > set_a,S5: d > c] :
( ( equal_outside_d_c @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta2 @ A2 )
= ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S5 @ Delta2 @ A2 ) ) ) ) ) ).
% not_in_fv_def
thf(fact_61_logic_Ounambiguous_Ocong,axiom,
unambiguous_a_b_d_c = unambiguous_a_b_d_c ).
% logic.unambiguous.cong
thf(fact_62_logic_Ounambiguous__star,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_d_c @ Plus @ Mult @ Valid @ Delta @ A2 @ X )
=> ( unambiguous_a_b_d_c @ Plus @ Mult @ Valid @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) @ X ) ) ) ).
% logic.unambiguous_star
thf(fact_63_logic_Ocombinable__instantiate__one,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,A: a,S: d > c,B: a,X: a,P: b,Q: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A @ S @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B @ S @ Delta @ A2 )
=> ( ( ( some_a @ X )
= ( Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( ( ( Sadd @ P @ Q )
= One )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ X @ S @ Delta @ A2 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate_one
thf(fact_64_logic_OcombinableI__old,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,B4: a,P3: b,Q3: b,X4: a,Sigma: a,S2: d > c] :
( ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A5 @ S2 @ Delta @ A2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B4 @ S2 @ Delta @ A2 )
& ( ( some_a @ Sigma )
= ( Plus @ ( Mult @ P3 @ A5 ) @ ( Mult @ Q3 @ B4 ) ) )
& ( Sigma
= ( Mult @ ( Sadd @ P3 @ Q3 ) @ X4 ) ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ X4 @ S2 @ Delta @ A2 ) )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 ) ) ) ).
% logic.combinableI_old
thf(fact_65_logic_Ocombinable__instantiate,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,A: a,S: d > c,B: a,X: a,P: b,Q: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A @ S @ Delta @ A2 )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B @ S @ Delta @ A2 )
=> ( ( ( some_a @ X )
= ( Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ X @ S @ Delta @ ( mult_b_a_c_d @ ( Sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ) ).
% logic.combinable_instantiate
thf(fact_66_logic_Ocombinable__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
= ( ! [P2: b,Q2: b] : ( entails_a_b_c_d @ Plus @ Mult @ Valid @ ( star_a_b_c_d @ ( mult_b_a_c_d @ P2 @ A2 ) @ ( mult_b_a_c_d @ Q2 @ A2 ) ) @ Delta @ ( mult_b_a_c_d @ ( Sadd @ P2 @ Q2 ) @ A2 ) ) ) ) ) ).
% logic.combinable_def
thf(fact_67_logic_Ocombinable__mult,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,Pi: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( mult_b_a_c_d @ Pi @ A2 ) ) ) ) ).
% logic.combinable_mult
thf(fact_68_logic_Ocombinable__star,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) ) ) ) ) ).
% logic.combinable_star
thf(fact_69_logic_Ocombinable__wand,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) ) ) ) ).
% logic.combinable_wand
thf(fact_70_logic_Ocombinable__forall,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( forall_d_a_b_c @ X @ A2 ) ) ) ) ).
% logic.combinable_forall
thf(fact_71_logic_Ocombinable__and,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ B2 )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( and_a_b_c_d @ A2 @ B2 ) ) ) ) ) ).
% logic.combinable_and
thf(fact_72_unambiguousI,axiom,
! [X: d,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ! [Sigma_1: a,Sigma_2: a,V1: c,V2: c,S2: d > c] :
( ( ( pre_compatible_a @ plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma_1 @ ( fun_upd_d_c @ S2 @ X @ V1 ) @ Delta @ A2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma_2 @ ( fun_upd_d_c @ S2 @ X @ V2 ) @ Delta @ A2 ) )
=> ( V1 = V2 ) )
=> ( unambiguous_a_b_d_c @ plus @ mult @ valid @ Delta @ A2 @ X ) ) ).
% unambiguousI
thf(fact_73_unambiguous__def,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( unambiguous_a_b_d_c @ plus @ mult @ valid @ Delta @ A2 @ X )
= ( ! [Sigma_12: a,Sigma_22: a,V12: c,V22: c,S3: d > c] :
( ( ( pre_compatible_a @ plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma_12 @ ( fun_upd_d_c @ S3 @ X @ V12 ) @ Delta @ A2 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma_22 @ ( fun_upd_d_c @ S3 @ X @ V22 ) @ Delta @ A2 ) )
=> ( V12 = V22 ) ) ) ) ).
% unambiguous_def
thf(fact_74_combinable__exists,axiom,
! [Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ A2 )
=> ( ( unambiguous_a_b_d_c @ plus @ mult @ valid @ Delta @ A2 @ X )
=> ( combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ Delta @ ( exists_d_a_b_c @ X @ A2 ) ) ) ) ).
% combinable_exists
thf(fact_75_sat_Osimps_I9_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,X: d,A2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( forall_d_a_b_c @ X @ A2 ) )
= ( ! [V: c] : ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V ) @ Delta @ A2 ) ) ) ).
% sat.simps(9)
thf(fact_76_sat__forall,axiom,
! [Sigma2: a,S: d > c,X: d,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ! [V3: c] : ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( forall_d_a_b_c @ X @ A2 ) ) ) ).
% sat_forall
thf(fact_77_sat_Osimps_I10_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ pred_a_b_c_d )
= ( member_a @ Sigma2 @ ( Delta @ S ) ) ) ).
% sat.simps(10)
thf(fact_78_sat_Osimps_I12_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( wildcard_a_b_c_d @ A2 ) )
= ( ? [A6: a,P2: b] :
( ( Sigma2
= ( mult @ P2 @ A6 ) )
& ( sat_a_b_d_c @ plus @ mult @ valid @ A6 @ S @ Delta @ A2 ) ) ) ) ).
% sat.simps(12)
thf(fact_79_sat_Osimps_I6_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( or_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ A2 )
| ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ).
% sat.simps(6)
thf(fact_80_sat_Osimps_I5_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( imp_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ).
% sat.simps(5)
thf(fact_81_sat__imp,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ A2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ B2 ) )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( imp_a_b_c_d @ A2 @ B2 ) ) ) ).
% sat_imp
thf(fact_82_sat_Osimps_I11_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( bounded_a_b_c_d @ A2 ) )
= ( ( valid @ Sigma2 )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ A2 ) ) ) ).
% sat.simps(11)
thf(fact_83_sat_Osimps_I8_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,X: d,A2: assertion_a_b_c_d] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( exists_d_a_b_c @ X @ A2 ) )
= ( ? [V: c] : ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V ) @ Delta @ A2 ) ) ) ).
% sat.simps(8)
thf(fact_84_logic_Ocombinable__exists,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ A2 )
=> ( ( unambiguous_a_b_d_c @ Plus @ Mult @ Valid @ Delta @ A2 @ X )
=> ( combinable_a_b_d_c @ Plus @ Mult @ Sadd @ Valid @ Delta @ ( exists_d_a_b_c @ X @ A2 ) ) ) ) ) ).
% logic.combinable_exists
thf(fact_85_logic_Ounambiguous__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,X: d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( unambiguous_a_b_d_c @ Plus @ Mult @ Valid @ Delta @ A2 @ X )
= ( ! [Sigma_12: a,Sigma_22: a,V12: c,V22: c,S3: d > c] :
( ( ( pre_compatible_a @ Plus @ Sigma_12 @ Sigma_22 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma_12 @ ( fun_upd_d_c @ S3 @ X @ V12 ) @ Delta @ A2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma_22 @ ( fun_upd_d_c @ S3 @ X @ V22 ) @ Delta @ A2 ) )
=> ( V12 = V22 ) ) ) ) ) ).
% logic.unambiguous_def
thf(fact_86_logic_OunambiguousI,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: d,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma_1: a,Sigma_2: a,V1: c,V2: c,S2: d > c] :
( ( ( pre_compatible_a @ Plus @ Sigma_1 @ Sigma_2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma_1 @ ( fun_upd_d_c @ S2 @ X @ V1 ) @ Delta @ A2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma_2 @ ( fun_upd_d_c @ S2 @ X @ V2 ) @ Delta @ A2 ) )
=> ( V1 = V2 ) )
=> ( unambiguous_a_b_d_c @ Plus @ Mult @ Valid @ Delta @ A2 @ X ) ) ) ).
% logic.unambiguousI
thf(fact_87_hoare__triple__input,axiom,
! [P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ Q4 @ Delta )
= ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ ( bounded_a_b_c_d @ P4 ) @ C @ Q4 @ Delta ) ) ).
% hoare_triple_input
thf(fact_88_logic_Onot__in__fv__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_c_d,S4: set_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ S4 )
= ( ! [Sigma5: a,S3: d > c,Delta2: ( d > c ) > set_a,S5: d > c] :
( ( equal_outside_d_c @ S3 @ S5 @ S4 )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta2 @ A2 )
= ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S5 @ Delta2 @ A2 ) ) ) ) ) ) ).
% logic.not_in_fv_def
thf(fact_89_logic_Ointuitionistic__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( intuit4720955538653295669_b_d_c @ Plus @ Mult @ Valid @ S @ Delta @ A2 )
= ( ! [A6: a,B5: a] :
( ( ( pre_larger_a @ Plus @ A6 @ B5 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B5 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A6 @ S @ Delta @ A2 ) ) ) ) ) ).
% logic.intuitionistic_def
thf(fact_90_logic_OintuitionisticI,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,B4: a] :
( ( ( pre_larger_a @ Plus @ A5 @ B4 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B4 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A5 @ S @ Delta @ A2 ) )
=> ( intuit4720955538653295669_b_d_c @ Plus @ Mult @ Valid @ S @ Delta @ A2 ) ) ) ).
% logic.intuitionisticI
thf(fact_91_logic__def,axiom,
( logic_a_b
= ( ^ [Plus2: a > a > option_a,Mult2: b > a > a,Smult2: b > b > b,Sadd2: b > b > b,Sinv2: b > b,One2: b,Valid2: a > $o] :
( ! [A6: a,B5: a] :
( ( Plus2 @ A6 @ B5 )
= ( Plus2 @ B5 @ A6 ) )
& ! [A6: a,B5: a,Ab2: a,C2: a,Bc2: a] :
( ( ( ( Plus2 @ A6 @ B5 )
= ( some_a @ Ab2 ) )
& ( ( Plus2 @ B5 @ C2 )
= ( some_a @ Bc2 ) ) )
=> ( ( Plus2 @ Ab2 @ C2 )
= ( Plus2 @ A6 @ Bc2 ) ) )
& ! [A6: a,B5: a,Ab2: a,C2: a] :
( ( ( ( Plus2 @ A6 @ B5 )
= ( some_a @ Ab2 ) )
& ~ ( pre_compatible_a @ Plus2 @ B5 @ C2 ) )
=> ~ ( pre_compatible_a @ Plus2 @ Ab2 @ C2 ) )
& ! [P2: b] :
( ( Smult2 @ P2 @ ( Sinv2 @ P2 ) )
= One2 )
& ! [P2: b] :
( ( Smult2 @ One2 @ P2 )
= P2 )
& ! [P2: b,Q2: b] :
( ( Sadd2 @ P2 @ Q2 )
= ( Sadd2 @ Q2 @ P2 ) )
& ! [P2: b,Q2: b] :
( ( Smult2 @ P2 @ Q2 )
= ( Smult2 @ Q2 @ P2 ) )
& ! [P2: b,Q2: b,R2: b] :
( ( Smult2 @ P2 @ ( Sadd2 @ Q2 @ R2 ) )
= ( Sadd2 @ ( Smult2 @ P2 @ Q2 ) @ ( Smult2 @ P2 @ R2 ) ) )
& ! [P2: b,Q2: b,R2: b] :
( ( Smult2 @ ( Smult2 @ P2 @ Q2 ) @ R2 )
= ( Smult2 @ P2 @ ( Smult2 @ Q2 @ R2 ) ) )
& ! [P2: b,Q2: b,A6: a] :
( ( Mult2 @ P2 @ ( Mult2 @ Q2 @ A6 ) )
= ( Mult2 @ ( Smult2 @ P2 @ Q2 ) @ A6 ) )
& ! [A6: a,B5: a,C2: a,P2: b] :
( ( ( some_a @ A6 )
= ( Plus2 @ B5 @ C2 ) )
=> ( ( some_a @ ( Mult2 @ P2 @ A6 ) )
= ( Plus2 @ ( Mult2 @ P2 @ B5 ) @ ( Mult2 @ P2 @ C2 ) ) ) )
& ! [P2: b,Q2: b,X5: a] :
( ( some_a @ ( Mult2 @ ( Sadd2 @ P2 @ Q2 ) @ X5 ) )
= ( Plus2 @ ( Mult2 @ P2 @ X5 ) @ ( Mult2 @ Q2 @ X5 ) ) )
& ! [A6: a] :
( ( Mult2 @ One2 @ A6 )
= A6 )
& ! [A6: a,B5: a] :
( ( ( Valid2 @ A6 )
& ( pre_larger_a @ Plus2 @ A6 @ B5 ) )
=> ( Valid2 @ B5 ) ) ) ) ) ).
% logic_def
thf(fact_92_logic_Osat_Osimps_I8_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,X: d,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( exists_d_a_b_c @ X @ A2 ) )
= ( ? [V: c] : ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(8)
thf(fact_93_logic_Osat__forall,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,X: d,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [V3: c] : ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V3 ) @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( forall_d_a_b_c @ X @ A2 ) ) ) ) ).
% logic.sat_forall
thf(fact_94_logic_Osat_Osimps_I9_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,X: d,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( forall_d_a_b_c @ X @ A2 ) )
= ( ! [V: c] : ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ ( fun_upd_d_c @ S @ X @ V ) @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(9)
thf(fact_95_logic_Osat_Osimps_I3_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) )
= ( ! [A6: a,Sigma4: a] :
( ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A6 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma4 )
= ( Plus @ Sigma2 @ A6 ) ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma4 @ S @ Delta @ B2 ) ) ) ) ) ).
% logic.sat.simps(3)
thf(fact_96_logic_Osat__wand,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,Sigma2: a,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a,Sigma3: a] :
( ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A5 @ S @ Delta @ A2 )
& ( ( some_a @ Sigma3 )
= ( Plus @ Sigma2 @ A5 ) ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma3 @ S @ Delta @ B2 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( wand_a_b_c_d @ A2 @ B2 ) ) ) ) ).
% logic.sat_wand
thf(fact_97_assertion_Oinject_I2_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,Y21: b,Y22: assertion_a_b_c_d] :
( ( ( mult_b_a_c_d @ X21 @ X22 )
= ( mult_b_a_c_d @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% assertion.inject(2)
thf(fact_98_assertion_Oinject_I3_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d] :
( ( ( star_a_b_c_d @ X31 @ X32 )
= ( star_a_b_c_d @ Y31 @ Y32 ) )
= ( ( X31 = Y31 )
& ( X32 = Y32 ) ) ) ).
% assertion.inject(3)
thf(fact_99_assertion_Oinject_I4_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
( ( ( wand_a_b_c_d @ X41 @ X42 )
= ( wand_a_b_c_d @ Y41 @ Y42 ) )
= ( ( X41 = Y41 )
& ( X42 = Y42 ) ) ) ).
% assertion.inject(4)
thf(fact_100_assertion_Oinject_I9_J,axiom,
! [X91: d,X92: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
( ( ( forall_d_a_b_c @ X91 @ X92 )
= ( forall_d_a_b_c @ Y91 @ Y92 ) )
= ( ( X91 = Y91 )
& ( X92 = Y92 ) ) ) ).
% assertion.inject(9)
thf(fact_101_assertion_Oinject_I10_J,axiom,
! [X11: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
( ( ( bounded_a_b_c_d @ X11 )
= ( bounded_a_b_c_d @ Y11 ) )
= ( X11 = Y11 ) ) ).
% assertion.inject(10)
thf(fact_102_assertion_Oinject_I6_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
( ( ( and_a_b_c_d @ X61 @ X62 )
= ( and_a_b_c_d @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% assertion.inject(6)
thf(fact_103_assertion_Oinject_I7_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
( ( ( imp_a_b_c_d @ X71 @ X72 )
= ( imp_a_b_c_d @ Y71 @ Y72 ) )
= ( ( X71 = Y71 )
& ( X72 = Y72 ) ) ) ).
% assertion.inject(7)
thf(fact_104_assertion_Oinject_I8_J,axiom,
! [X81: d,X82: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
( ( ( exists_d_a_b_c @ X81 @ X82 )
= ( exists_d_a_b_c @ Y81 @ Y82 ) )
= ( ( X81 = Y81 )
& ( X82 = Y82 ) ) ) ).
% assertion.inject(8)
thf(fact_105_assertion_Oinject_I5_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
( ( ( or_a_b_c_d @ X51 @ X52 )
= ( or_a_b_c_d @ Y51 @ Y52 ) )
= ( ( X51 = Y51 )
& ( X52 = Y52 ) ) ) ).
% assertion.inject(5)
thf(fact_106_assertion_Oinject_I11_J,axiom,
! [X12: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
( ( ( wildcard_a_b_c_d @ X12 )
= ( wildcard_a_b_c_d @ Y12 ) )
= ( X12 = Y12 ) ) ).
% assertion.inject(11)
thf(fact_107_hoare__triple__output,axiom,
! [C: set_Pr7868159745199425715_a_d_c,P4: assertion_a_b_c_d,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( valid_command_a_d_c @ valid @ C )
=> ( ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ Q4 @ Delta )
= ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ ( bounded_a_b_c_d @ Q4 ) @ Delta ) ) ) ).
% hoare_triple_output
thf(fact_108_logic_Ohoare__triple__input,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ Q4 @ Delta )
= ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ ( bounded_a_b_c_d @ P4 ) @ C @ Q4 @ Delta ) ) ) ).
% logic.hoare_triple_input
thf(fact_109_logic_Osat_Ocong,axiom,
sat_a_b_d_c = sat_a_b_d_c ).
% logic.sat.cong
thf(fact_110_logic_Osmult__distrib,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sadd @ Q @ R ) )
= ( Sadd @ ( Smult @ P @ Q ) @ ( Smult @ P @ R ) ) ) ) ).
% logic.smult_distrib
thf(fact_111_logic_Osone__neutral,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ One @ P )
= P ) ) ).
% logic.sone_neutral
thf(fact_112_logic_Osinv__inverse,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ ( Sinv @ P ) )
= One ) ) ).
% logic.sinv_inverse
thf(fact_113_logic_Oone__neutral,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ One @ A )
= A ) ) ).
% logic.one_neutral
thf(fact_114_logic_Odouble__mult,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Mult @ P @ ( Mult @ Q @ A ) )
= ( Mult @ ( Smult @ P @ Q ) @ A ) ) ) ).
% logic.double_mult
thf(fact_115_logic_Ocommutative,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Plus @ A @ B )
= ( Plus @ B @ A ) ) ) ).
% logic.commutative
thf(fact_116_logic_Ounique__inv,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,P: b,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( A
= ( Mult @ P @ B ) )
= ( B
= ( Mult @ ( Sinv @ P ) @ A ) ) ) ) ).
% logic.unique_inv
thf(fact_117_logic_Osmult__comm,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ P @ Q )
= ( Smult @ Q @ P ) ) ) ).
% logic.smult_comm
thf(fact_118_logic_Osmult__asso,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Smult @ ( Smult @ P @ Q ) @ R )
= ( Smult @ P @ ( Smult @ Q @ R ) ) ) ) ).
% logic.smult_asso
thf(fact_119_logic_Ocan__divide,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( Mult @ P @ A )
= ( Mult @ P @ B ) )
=> ( A = B ) ) ) ).
% logic.can_divide
thf(fact_120_logic_Osadd__comm,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( Sadd @ P @ Q )
= ( Sadd @ Q @ P ) ) ) ).
% logic.sadd_comm
thf(fact_121_pre__logic_Ocompatible_Ocong,axiom,
pre_compatible_a = pre_compatible_a ).
% pre_logic.compatible.cong
thf(fact_122_pre__logic_Olarger_Ocong,axiom,
pre_larger_a = pre_larger_a ).
% pre_logic.larger.cong
thf(fact_123_logic_Oentails_Ocong,axiom,
entails_a_b_c_d = entails_a_b_c_d ).
% logic.entails.cong
thf(fact_124_logic_Opure_Ocong,axiom,
pure_a_b_c_d = pure_a_b_c_d ).
% logic.pure.cong
thf(fact_125_logic_Odistrib__mult,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,X: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( some_a @ ( Mult @ ( Sadd @ P @ Q ) @ X ) )
= ( Plus @ ( Mult @ P @ X ) @ ( Mult @ Q @ X ) ) ) ) ).
% logic.distrib_mult
thf(fact_126_logic_Oplus__mult,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus @ B @ C ) )
=> ( ( some_a @ ( Mult @ P @ A ) )
= ( Plus @ ( Mult @ P @ B ) @ ( Mult @ P @ C ) ) ) ) ) ).
% logic.plus_mult
thf(fact_127_logic_Omove__sum,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X1: a,X2: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ A )
= ( Plus @ A1 @ A22 ) )
=> ( ( ( some_a @ B )
= ( Plus @ B1 @ B22 ) )
=> ( ( ( some_a @ X )
= ( Plus @ A @ B ) )
=> ( ( ( some_a @ X1 )
= ( Plus @ A1 @ B1 ) )
=> ( ( ( some_a @ X2 )
= ( Plus @ A22 @ B22 ) )
=> ( ( some_a @ X )
= ( Plus @ X1 @ X2 ) ) ) ) ) ) ) ) ).
% logic.move_sum
thf(fact_128_logic_Oasso1,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a,Bc: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( ( Plus @ A @ B )
= ( some_a @ Ab ) )
& ( ( Plus @ B @ C )
= ( some_a @ Bc ) ) )
=> ( ( Plus @ Ab @ C )
= ( Plus @ A @ Bc ) ) ) ) ).
% logic.asso1
thf(fact_129_pre__logic_Olarger__def,axiom,
( pre_larger_a
= ( ^ [Plus2: a > a > option_a,A6: a,B5: a] :
? [C2: a] :
( ( some_a @ A6 )
= ( Plus2 @ B5 @ C2 ) ) ) ) ).
% pre_logic.larger_def
thf(fact_130_assertion_Odistinct_I23_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.distinct(23)
thf(fact_131_assertion_Odistinct_I25_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.distinct(25)
thf(fact_132_assertion_Odistinct_I35_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(35)
thf(fact_133_assertion_Odistinct_I39_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(39)
thf(fact_134_assertion_Odistinct_I43_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.distinct(43)
thf(fact_135_assertion_Odistinct_I29_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.distinct(29)
thf(fact_136_assertion_Odistinct_I31_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(31)
thf(fact_137_assertion_Odistinct_I53_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(53)
thf(fact_138_assertion_Odistinct_I57_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(57)
thf(fact_139_assertion_Odistinct_I33_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(33)
thf(fact_140_assertion_Odistinct_I47_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.distinct(47)
thf(fact_141_assertion_Odistinct_I49_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(49)
thf(fact_142_assertion_Odistinct_I27_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.distinct(27)
thf(fact_143_assertion_Odistinct_I51_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(51)
thf(fact_144_assertion_Odistinct_I41_J,axiom,
! [X21: b,X22: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(41)
thf(fact_145_assertion_Odistinct_I45_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.distinct(45)
thf(fact_146_assertion_Odistinct_I59_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(59)
thf(fact_147_assertion_Odistinct_I69_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(69)
thf(fact_148_assertion_Odistinct_I73_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(73)
thf(fact_149_assertion_Odistinct_I123_J,axiom,
! [X91: d,X92: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( forall_d_a_b_c @ X91 @ X92 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(123)
thf(fact_150_assertion_Odistinct_I63_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.distinct(63)
thf(fact_151_assertion_Odistinct_I65_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(65)
thf(fact_152_assertion_Odistinct_I95_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(95)
thf(fact_153_assertion_Odistinct_I99_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(99)
thf(fact_154_assertion_Odistinct_I105_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( imp_a_b_c_d @ X71 @ X72 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(105)
thf(fact_155_assertion_Odistinct_I109_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( imp_a_b_c_d @ X71 @ X72 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(109)
thf(fact_156_assertion_Odistinct_I67_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(67)
thf(fact_157_assertion_Odistinct_I91_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(91)
thf(fact_158_assertion_Odistinct_I113_J,axiom,
! [X81: d,X82: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( exists_d_a_b_c @ X81 @ X82 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(113)
thf(fact_159_assertion_Odistinct_I117_J,axiom,
! [X81: d,X82: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( exists_d_a_b_c @ X81 @ X82 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(117)
thf(fact_160_assertion_Odistinct_I61_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.distinct(61)
thf(fact_161_assertion_Odistinct_I93_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(93)
thf(fact_162_assertion_Odistinct_I103_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( imp_a_b_c_d @ X71 @ X72 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(103)
thf(fact_163_assertion_Odistinct_I83_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(83)
thf(fact_164_assertion_Odistinct_I87_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(87)
thf(fact_165_assertion_Odistinct_I75_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(75)
thf(fact_166_assertion_Odistinct_I77_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.distinct(77)
thf(fact_167_assertion_Odistinct_I79_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(79)
thf(fact_168_assertion_Odistinct_I125_J,axiom,
! [X91: d,X92: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( forall_d_a_b_c @ X91 @ X92 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(125)
thf(fact_169_assertion_Odistinct_I131_J,axiom,
! [X11: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( bounded_a_b_c_d @ X11 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(131)
thf(fact_170_assertion_Odistinct_I37_J,axiom,
! [X21: b,X22: assertion_a_b_c_d] :
( ( mult_b_a_c_d @ X21 @ X22 )
!= pred_a_b_c_d ) ).
% assertion.distinct(37)
thf(fact_171_assertion_Odistinct_I81_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(81)
thf(fact_172_assertion_Odistinct_I101_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(101)
thf(fact_173_assertion_Odistinct_I111_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( imp_a_b_c_d @ X71 @ X72 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(111)
thf(fact_174_assertion_Odistinct_I119_J,axiom,
! [X81: d,X82: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( exists_d_a_b_c @ X81 @ X82 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(119)
thf(fact_175_assertion_Odistinct_I55_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( star_a_b_c_d @ X31 @ X32 )
!= pred_a_b_c_d ) ).
% assertion.distinct(55)
thf(fact_176_assertion_Odistinct_I89_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,X12: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(89)
thf(fact_177_assertion_Odistinct_I71_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( wand_a_b_c_d @ X41 @ X42 )
!= pred_a_b_c_d ) ).
% assertion.distinct(71)
thf(fact_178_assertion_Odistinct_I121_J,axiom,
! [X91: d,X92: assertion_a_b_c_d] :
( ( forall_d_a_b_c @ X91 @ X92 )
!= pred_a_b_c_d ) ).
% assertion.distinct(121)
thf(fact_179_assertion_Odistinct_I127_J,axiom,
! [X11: assertion_a_b_c_d] :
( pred_a_b_c_d
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(127)
thf(fact_180_assertion_Odistinct_I97_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( and_a_b_c_d @ X61 @ X62 )
!= pred_a_b_c_d ) ).
% assertion.distinct(97)
thf(fact_181_assertion_Odistinct_I107_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( imp_a_b_c_d @ X71 @ X72 )
!= pred_a_b_c_d ) ).
% assertion.distinct(107)
thf(fact_182_assertion_Odistinct_I115_J,axiom,
! [X81: d,X82: assertion_a_b_c_d] :
( ( exists_d_a_b_c @ X81 @ X82 )
!= pred_a_b_c_d ) ).
% assertion.distinct(115)
thf(fact_183_logic_Ocompatible__multiples,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,Q: b,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) )
=> ( pre_compatible_a @ Plus @ A @ B ) ) ) ).
% logic.compatible_multiples
thf(fact_184_logic_Ocompatible__imp,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus @ A @ B )
=> ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.compatible_imp
thf(fact_185_logic_Ocompatible__iff,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_compatible_a @ Plus @ A @ B )
= ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.compatible_iff
thf(fact_186_assertion_Odistinct_I85_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( or_a_b_c_d @ X51 @ X52 )
!= pred_a_b_c_d ) ).
% assertion.distinct(85)
thf(fact_187_assertion_Odistinct_I129_J,axiom,
! [X12: assertion_a_b_c_d] :
( pred_a_b_c_d
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(129)
thf(fact_188_logic_Olarger__same,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus @ A @ B )
= ( pre_larger_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).
% logic.larger_same
thf(fact_189_logic_Ovalid__mono,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( Valid @ A )
& ( pre_larger_a @ Plus @ A @ B ) )
=> ( Valid @ B ) ) ) ).
% logic.valid_mono
thf(fact_190_logic_Osat_Osimps_I1_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,P: b,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( mult_b_a_c_d @ P @ A2 ) )
= ( ? [A6: a] :
( ( Sigma2
= ( Mult @ P @ A6 ) )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A6 @ S @ Delta @ A2 ) ) ) ) ) ).
% logic.sat.simps(1)
thf(fact_191_logic_Osat__mult,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,P: b,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [A5: a] :
( ( Sigma2
= ( Mult @ P @ A5 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A5 @ S @ Delta @ A2 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( mult_b_a_c_d @ P @ A2 ) ) ) ) ).
% logic.sat_mult
thf(fact_192_logic_Osat_Osimps_I11_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( bounded_a_b_c_d @ A2 ) )
= ( ( Valid @ Sigma2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ A2 ) ) ) ) ).
% logic.sat.simps(11)
thf(fact_193_logic_Osat_Osimps_I7_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( and_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ A2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ) ).
% logic.sat.simps(7)
thf(fact_194_logic_Osat__imp,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ B2 ) )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( imp_a_b_c_d @ A2 @ B2 ) ) ) ) ).
% logic.sat_imp
thf(fact_195_logic_Osat_Osimps_I5_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( imp_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ) ).
% logic.sat.simps(5)
thf(fact_196_logic_Osat_Osimps_I6_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( or_a_b_c_d @ A2 @ B2 ) )
= ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ A2 )
| ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ B2 ) ) ) ) ).
% logic.sat.simps(6)
thf(fact_197_logic_Osat_Osimps_I12_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( wildcard_a_b_c_d @ A2 ) )
= ( ? [A6: a,P2: b] :
( ( Sigma2
= ( Mult @ P2 @ A6 ) )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A6 @ S @ Delta @ A2 ) ) ) ) ) ).
% logic.sat.simps(12)
thf(fact_198_logic_Oasso3,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,Bc: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ~ ( pre_compatible_a @ Plus @ A @ B )
=> ( ( ( Plus @ B @ C )
= ( some_a @ Bc ) )
=> ~ ( pre_compatible_a @ Plus @ A @ Bc ) ) ) ) ).
% logic.asso3
thf(fact_199_logic_Oasso2,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( ( Plus @ A @ B )
= ( some_a @ Ab ) )
& ~ ( pre_compatible_a @ Plus @ B @ C ) )
=> ~ ( pre_compatible_a @ Plus @ Ab @ C ) ) ) ).
% logic.asso2
thf(fact_200_logic_Osat_Osimps_I10_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ pred_a_b_c_d )
= ( member_a @ Sigma2 @ ( Delta @ S ) ) ) ) ).
% logic.sat.simps(10)
thf(fact_201_logic_Olarger__first__sum,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Y: a,A: a,B: a,X: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ Y )
= ( Plus @ A @ B ) )
=> ( ( pre_larger_a @ Plus @ X @ Y )
=> ? [A4: a] :
( ( ( some_a @ X )
= ( Plus @ A4 @ B ) )
& ( pre_larger_a @ Plus @ A4 @ A ) ) ) ) ) ).
% logic.larger_first_sum
thf(fact_202_logic_Osum__both__larger,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X3: a,A3: a,B3: a,X: a,A: a,B: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( ( some_a @ X3 )
= ( Plus @ A3 @ B3 ) )
=> ( ( ( some_a @ X )
= ( Plus @ A @ B ) )
=> ( ( pre_larger_a @ Plus @ A3 @ A )
=> ( ( pre_larger_a @ Plus @ B3 @ B )
=> ( pre_larger_a @ Plus @ X3 @ X ) ) ) ) ) ) ).
% logic.sum_both_larger
thf(fact_203_logic_Olarger__implies__compatible,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: a,Y: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus @ X @ Y )
=> ( pre_compatible_a @ Plus @ X @ Y ) ) ) ).
% logic.larger_implies_compatible
thf(fact_204_logic_Ocompatible__smaller,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,X: a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pre_larger_a @ Plus @ A @ B )
=> ( ( pre_compatible_a @ Plus @ X @ A )
=> ( pre_compatible_a @ Plus @ X @ B ) ) ) ) ).
% logic.compatible_smaller
thf(fact_205_logic_Oentails__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_c_d,Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( entails_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ Delta @ B2 )
= ( ! [Sigma5: a,S3: d > c] :
( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta @ B2 ) ) ) ) ) ).
% logic.entails_def
thf(fact_206_logic_OentailsI,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ B2 ) )
=> ( entails_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ Delta @ B2 ) ) ) ).
% logic.entailsI
thf(fact_207_logic_OequivalentI,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ A2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ B2 ) )
=> ( ! [Sigma: a,S2: d > c] :
( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ B2 )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ A2 ) )
=> ( equivalent_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ Delta @ B2 ) ) ) ) ).
% logic.equivalentI
thf(fact_208_logic_Opure__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( pure_a_b_c_d @ Plus @ Mult @ Valid @ A2 )
= ( ! [Sigma5: a,Sigma4: a,S3: d > c,Delta2: ( d > c ) > set_a,Delta3: ( d > c ) > set_a] :
( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta2 @ A2 )
= ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 ) ) ) ) ) ).
% logic.pure_def
thf(fact_209_logic_Oequivalent__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_c_d,Delta: ( d > c ) > set_a,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( equivalent_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ Delta @ B2 )
= ( ( entails_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ Delta @ B2 )
& ( entails_a_b_c_d @ Plus @ Mult @ Valid @ B2 @ Delta @ A2 ) ) ) ) ).
% logic.equivalent_def
thf(fact_210_logic_Osat_Osimps_I2_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,A2: assertion_a_b_c_d,B2: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( star_a_b_c_d @ A2 @ B2 ) )
= ( ? [A6: a,B5: a] :
( ( ( some_a @ Sigma2 )
= ( Plus @ A6 @ B5 ) )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ A6 @ S @ Delta @ A2 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ B5 @ S @ Delta @ B2 ) ) ) ) ) ).
% logic.sat.simps(2)
thf(fact_211_sat_Osimps_I4_J,axiom,
! [Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,B: ( d > c ) > a > $o] :
( ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma2 @ S @ Delta @ ( sem_d_c_a_b @ B ) )
= ( B @ S @ Sigma2 ) ) ).
% sat.simps(4)
thf(fact_212_assertion_Oexhaust,axiom,
! [Y: assertion_a_b_c_d] :
( ! [X13: ( d > c ) > a > $o] :
( Y
!= ( sem_d_c_a_b @ X13 ) )
=> ( ! [X212: b,X222: assertion_a_b_c_d] :
( Y
!= ( mult_b_a_c_d @ X212 @ X222 ) )
=> ( ! [X312: assertion_a_b_c_d,X322: assertion_a_b_c_d] :
( Y
!= ( star_a_b_c_d @ X312 @ X322 ) )
=> ( ! [X412: assertion_a_b_c_d,X422: assertion_a_b_c_d] :
( Y
!= ( wand_a_b_c_d @ X412 @ X422 ) )
=> ( ! [X512: assertion_a_b_c_d,X522: assertion_a_b_c_d] :
( Y
!= ( or_a_b_c_d @ X512 @ X522 ) )
=> ( ! [X612: assertion_a_b_c_d,X622: assertion_a_b_c_d] :
( Y
!= ( and_a_b_c_d @ X612 @ X622 ) )
=> ( ! [X712: assertion_a_b_c_d,X722: assertion_a_b_c_d] :
( Y
!= ( imp_a_b_c_d @ X712 @ X722 ) )
=> ( ! [X812: d,X822: assertion_a_b_c_d] :
( Y
!= ( exists_d_a_b_c @ X812 @ X822 ) )
=> ( ! [X912: d,X922: assertion_a_b_c_d] :
( Y
!= ( forall_d_a_b_c @ X912 @ X922 ) )
=> ( ( Y != pred_a_b_c_d )
=> ( ! [X112: assertion_a_b_c_d] :
( Y
!= ( bounded_a_b_c_d @ X112 ) )
=> ~ ! [X122: assertion_a_b_c_d] :
( Y
!= ( wildcard_a_b_c_d @ X122 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% assertion.exhaust
thf(fact_213_fun__upd__apply,axiom,
( fun_upd_d_c
= ( ^ [F: d > c,X5: d,Y2: c,Z: d] : ( if_c @ ( Z = X5 ) @ Y2 @ ( F @ Z ) ) ) ) ).
% fun_upd_apply
thf(fact_214_fun__upd__triv,axiom,
! [F2: d > c,X: d] :
( ( fun_upd_d_c @ F2 @ X @ ( F2 @ X ) )
= F2 ) ).
% fun_upd_triv
thf(fact_215_fun__upd__upd,axiom,
! [F2: d > c,X: d,Y: c,Z2: c] :
( ( fun_upd_d_c @ ( fun_upd_d_c @ F2 @ X @ Y ) @ X @ Z2 )
= ( fun_upd_d_c @ F2 @ X @ Z2 ) ) ).
% fun_upd_upd
thf(fact_216_option_Oinject,axiom,
! [X2: a,Y23: a] :
( ( ( some_a @ X2 )
= ( some_a @ Y23 ) )
= ( X2 = Y23 ) ) ).
% option.inject
thf(fact_217_logic_Ohoare__triple__output,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr7868159745199425715_a_d_c,P4: assertion_a_b_c_d,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_d_c @ Valid @ C )
=> ( ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ Q4 @ Delta )
= ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ ( bounded_a_b_c_d @ Q4 ) @ Delta ) ) ) ) ).
% logic.hoare_triple_output
thf(fact_218_compatible__def,axiom,
! [A: a,B: a] :
( ( pre_compatible_a @ plus @ A @ B )
= ( ( plus @ A @ B )
!= none_a ) ) ).
% compatible_def
thf(fact_219_frame__rule,axiom,
! [C: set_Pr7868159745199425715_a_d_c,P4: assertion_a_b_c_d,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a,R3: assertion_a_b_c_d] :
( ( valid_command_a_d_c @ valid @ C )
=> ( ( safety7280469885071620222_a_d_c @ plus @ valid @ C )
=> ( ( frame_property_a_d_c @ plus @ valid @ C )
=> ( ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ Q4 @ Delta )
=> ( ( not_in_fv_a_b_c_d @ plus @ mult @ valid @ R3 @ ( modified_a_d_c @ C ) )
=> ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ ( star_a_b_c_d @ P4 @ R3 ) @ C @ ( star_a_b_c_d @ Q4 @ R3 ) @ Delta ) ) ) ) ) ) ).
% frame_rule
thf(fact_220_assertion_Oinject_I1_J,axiom,
! [X1: ( d > c ) > a > $o,Y1: ( d > c ) > a > $o] :
( ( ( sem_d_c_a_b @ X1 )
= ( sem_d_c_a_b @ Y1 ) )
= ( X1 = Y1 ) ) ).
% assertion.inject(1)
thf(fact_221_not__None__eq,axiom,
! [X: option_a] :
( ( X != none_a )
= ( ? [Y2: a] :
( X
= ( some_a @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_222_not__Some__eq,axiom,
! [X: option_a] :
( ( ! [Y2: a] :
( X
!= ( some_a @ Y2 ) ) )
= ( X = none_a ) ) ).
% not_Some_eq
thf(fact_223_option_Odistinct_I1_J,axiom,
! [X2: a] :
( none_a
!= ( some_a @ X2 ) ) ).
% option.distinct(1)
thf(fact_224_option_OdiscI,axiom,
! [Option: option_a,X2: a] :
( ( Option
= ( some_a @ X2 ) )
=> ( Option != none_a ) ) ).
% option.discI
thf(fact_225_option_Oexhaust,axiom,
! [Y: option_a] :
( ( Y != none_a )
=> ~ ! [X23: a] :
( Y
!= ( some_a @ X23 ) ) ) ).
% option.exhaust
thf(fact_226_split__option__ex,axiom,
( ( ^ [P5: option_a > $o] :
? [X6: option_a] : ( P5 @ X6 ) )
= ( ^ [P6: option_a > $o] :
( ( P6 @ none_a )
| ? [X5: a] : ( P6 @ ( some_a @ X5 ) ) ) ) ) ).
% split_option_ex
thf(fact_227_split__option__all,axiom,
( ( ^ [P5: option_a > $o] :
! [X6: option_a] : ( P5 @ X6 ) )
= ( ^ [P6: option_a > $o] :
( ( P6 @ none_a )
& ! [X5: a] : ( P6 @ ( some_a @ X5 ) ) ) ) ) ).
% split_option_all
thf(fact_228_combine__options__cases,axiom,
! [X: option_a,P4: option_a > option_a > $o,Y: option_a] :
( ( ( X = none_a )
=> ( P4 @ X @ Y ) )
=> ( ( ( Y = none_a )
=> ( P4 @ X @ Y ) )
=> ( ! [A5: a,B4: a] :
( ( X
= ( some_a @ A5 ) )
=> ( ( Y
= ( some_a @ B4 ) )
=> ( P4 @ X @ Y ) ) )
=> ( P4 @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_229_assertion_Odistinct_I1_J,axiom,
! [X1: ( d > c ) > a > $o,X21: b,X22: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.distinct(1)
thf(fact_230_assertion_Odistinct_I3_J,axiom,
! [X1: ( d > c ) > a > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.distinct(3)
thf(fact_231_assertion_Odistinct_I5_J,axiom,
! [X1: ( d > c ) > a > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.distinct(5)
thf(fact_232_assertion_Odistinct_I19_J,axiom,
! [X1: ( d > c ) > a > $o,X11: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.distinct(19)
thf(fact_233_assertion_Odistinct_I15_J,axiom,
! [X1: ( d > c ) > a > $o,X91: d,X92: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.distinct(15)
thf(fact_234_assertion_Odistinct_I11_J,axiom,
! [X1: ( d > c ) > a > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.distinct(11)
thf(fact_235_assertion_Odistinct_I9_J,axiom,
! [X1: ( d > c ) > a > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.distinct(9)
thf(fact_236_assertion_Odistinct_I13_J,axiom,
! [X1: ( d > c ) > a > $o,X81: d,X82: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.distinct(13)
thf(fact_237_assertion_Odistinct_I7_J,axiom,
! [X1: ( d > c ) > a > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.distinct(7)
thf(fact_238_assertion_Odistinct_I21_J,axiom,
! [X1: ( d > c ) > a > $o,X12: assertion_a_b_c_d] :
( ( sem_d_c_a_b @ X1 )
!= ( wildcard_a_b_c_d @ X12 ) ) ).
% assertion.distinct(21)
thf(fact_239_assertion_Odistinct_I17_J,axiom,
! [X1: ( d > c ) > a > $o] :
( ( sem_d_c_a_b @ X1 )
!= pred_a_b_c_d ) ).
% assertion.distinct(17)
thf(fact_240_pre__logic_Ocompatible__def,axiom,
( pre_compatible_a
= ( ^ [Plus2: a > a > option_a,A6: a,B5: a] :
( ( Plus2 @ A6 @ B5 )
!= none_a ) ) ) ).
% pre_logic.compatible_def
thf(fact_241_logic_Osat_Osimps_I4_J,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma2: a,S: d > c,Delta: ( d > c ) > set_a,B: ( d > c ) > a > $o] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta @ ( sem_d_c_a_b @ B ) )
= ( B @ S @ Sigma2 ) ) ) ).
% logic.sat.simps(4)
thf(fact_242_logic_Oframe__rule,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,C: set_Pr7868159745199425715_a_d_c,P4: assertion_a_b_c_d,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a,R3: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_command_a_d_c @ Valid @ C )
=> ( ( safety7280469885071620222_a_d_c @ Plus @ Valid @ C )
=> ( ( frame_property_a_d_c @ Plus @ Valid @ C )
=> ( ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ Q4 @ Delta )
=> ( ( not_in_fv_a_b_c_d @ Plus @ Mult @ Valid @ R3 @ ( modified_a_d_c @ C ) )
=> ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ ( star_a_b_c_d @ P4 @ R3 ) @ C @ ( star_a_b_c_d @ Q4 @ R3 ) @ Delta ) ) ) ) ) ) ) ).
% logic.frame_rule
thf(fact_243_fun__upd__def,axiom,
( fun_upd_d_c
= ( ^ [F: d > c,A6: d,B5: c,X5: d] : ( if_c @ ( X5 = A6 ) @ B5 @ ( F @ X5 ) ) ) ) ).
% fun_upd_def
thf(fact_244_fun__upd__eqD,axiom,
! [F2: d > c,X: d,Y: c,G: d > c,Z2: c] :
( ( ( fun_upd_d_c @ F2 @ X @ Y )
= ( fun_upd_d_c @ G @ X @ Z2 ) )
=> ( Y = Z2 ) ) ).
% fun_upd_eqD
thf(fact_245_fun__upd__idem,axiom,
! [F2: d > c,X: d,Y: c] :
( ( ( F2 @ X )
= Y )
=> ( ( fun_upd_d_c @ F2 @ X @ Y )
= F2 ) ) ).
% fun_upd_idem
thf(fact_246_fun__upd__same,axiom,
! [F2: d > c,X: d,Y: c] :
( ( fun_upd_d_c @ F2 @ X @ Y @ X )
= Y ) ).
% fun_upd_same
thf(fact_247_fun__upd__other,axiom,
! [Z2: d,X: d,F2: d > c,Y: c] :
( ( Z2 != X )
=> ( ( fun_upd_d_c @ F2 @ X @ Y @ Z2 )
= ( F2 @ Z2 ) ) ) ).
% fun_upd_other
thf(fact_248_fun__upd__twist,axiom,
! [A: d,C: d,M: d > c,B: c,D: c] :
( ( A != C )
=> ( ( fun_upd_d_c @ ( fun_upd_d_c @ M @ A @ B ) @ C @ D )
= ( fun_upd_d_c @ ( fun_upd_d_c @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_249_fun__upd__idem__iff,axiom,
! [F2: d > c,X: d,Y: c] :
( ( ( fun_upd_d_c @ F2 @ X @ Y )
= F2 )
= ( ( F2 @ X )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_250_not__in__fv__mod,axiom,
! [A2: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Sigma2: a,S: d > c,Sigma6: a,S6: d > c,X: a,Delta: ( d > c ) > set_a] :
( ( not_in_fv_a_b_c_d @ plus @ mult @ valid @ A2 @ ( modified_a_d_c @ C ) )
=> ( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma2 @ S ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_d_c @ plus @ mult @ valid @ X @ S @ Delta @ A2 )
= ( sat_a_b_d_c @ plus @ mult @ valid @ X @ S6 @ Delta @ A2 ) ) ) ) ).
% not_in_fv_mod
thf(fact_251_valid__hoare__triple__def,axiom,
! [P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ Q4 @ Delta )
= ( ! [Sigma5: a,S3: d > c] :
( ( ( valid @ Sigma5 )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta @ P4 ) )
=> ( ( safe_a_d_c @ C @ ( product_Pair_a_d_c @ Sigma5 @ S3 ) )
& ! [Sigma4: a,S5: d > c] :
( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma5 @ S3 ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma4 @ S5 ) ) ) @ C )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma4 @ S5 @ Delta @ Q4 ) ) ) ) ) ) ).
% valid_hoare_triple_def
thf(fact_252_valid__hoare__tripleI,axiom,
! [Delta: ( d > c ) > set_a,P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d] :
( ! [Sigma: a,S2: d > c] :
( ( ( valid @ Sigma )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ P4 ) )
=> ( safe_a_d_c @ C @ ( product_Pair_a_d_c @ Sigma @ S2 ) ) )
=> ( ! [Sigma: a,S2: d > c,Sigma3: a,S7: d > c] :
( ( ( valid @ Sigma )
& ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma @ S2 @ Delta @ P4 ) )
=> ( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma @ S2 ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma3 @ S7 ) ) ) @ C )
=> ( sat_a_b_d_c @ plus @ mult @ valid @ Sigma3 @ S7 @ Delta @ Q4 ) ) )
=> ( valid_8824771084768397689_b_c_d @ plus @ mult @ valid @ P4 @ C @ Q4 @ Delta ) ) ) ).
% valid_hoare_tripleI
thf(fact_253_logic_Ovalid__hoare__tripleI,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta: ( d > c ) > set_a,P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ! [Sigma: a,S2: d > c] :
( ( ( Valid @ Sigma )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ P4 ) )
=> ( safe_a_d_c @ C @ ( product_Pair_a_d_c @ Sigma @ S2 ) ) )
=> ( ! [Sigma: a,S2: d > c,Sigma3: a,S7: d > c] :
( ( ( Valid @ Sigma )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma @ S2 @ Delta @ P4 ) )
=> ( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma @ S2 ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma3 @ S7 ) ) ) @ C )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma3 @ S7 @ Delta @ Q4 ) ) )
=> ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ Q4 @ Delta ) ) ) ) ).
% logic.valid_hoare_tripleI
thf(fact_254_logic_Ovalid__hoare__triple__def,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P4: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Q4: assertion_a_b_c_d,Delta: ( d > c ) > set_a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( valid_8824771084768397689_b_c_d @ Plus @ Mult @ Valid @ P4 @ C @ Q4 @ Delta )
= ( ! [Sigma5: a,S3: d > c] :
( ( ( Valid @ Sigma5 )
& ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta @ P4 ) )
=> ( ( safe_a_d_c @ C @ ( product_Pair_a_d_c @ Sigma5 @ S3 ) )
& ! [Sigma4: a,S5: d > c] :
( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma5 @ S3 ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma4 @ S5 ) ) ) @ C )
=> ( sat_a_b_d_c @ Plus @ Mult @ Valid @ Sigma4 @ S5 @ Delta @ Q4 ) ) ) ) ) ) ) ).
% logic.valid_hoare_triple_def
thf(fact_255_logic_Onot__in__fv__mod,axiom,
! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_c_d,C: set_Pr7868159745199425715_a_d_c,Sigma2: a,S: d > c,Sigma6: a,S6: d > c,X: a,Delta: ( d > c ) > set_a] :
( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
=> ( ( not_in_fv_a_b_c_d @ Plus @ Mult @ Valid @ A2 @ ( modified_a_d_c @ C ) )
=> ( ( member2052822272342364412_a_d_c @ ( produc5208860900648697099_a_d_c @ ( product_Pair_a_d_c @ Sigma2 @ S ) @ ( some_P377817780860425132_a_d_c @ ( product_Pair_a_d_c @ Sigma6 @ S6 ) ) ) @ C )
=> ( ( sat_a_b_d_c @ Plus @ Mult @ Valid @ X @ S @ Delta @ A2 )
= ( sat_a_b_d_c @ Plus @ Mult @ Valid @ X @ S6 @ Delta @ A2 ) ) ) ) ) ).
% logic.not_in_fv_mod
thf(fact_256_option_Ocollapse,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( ( some_a @ ( the_a2 @ Option ) )
= Option ) ) ).
% option.collapse
thf(fact_257_option_Osel,axiom,
! [X2: a] :
( ( the_a2 @ ( some_a @ X2 ) )
= X2 ) ).
% option.sel
thf(fact_258_option_Oexpand,axiom,
! [Option: option_a,Option2: option_a] :
( ( ( Option = none_a )
= ( Option2 = none_a ) )
=> ( ( ( Option != none_a )
=> ( ( Option2 != none_a )
=> ( ( the_a2 @ Option )
= ( the_a2 @ Option2 ) ) ) )
=> ( Option = Option2 ) ) ) ).
% option.expand
thf(fact_259_option_Oexhaust__sel,axiom,
! [Option: option_a] :
( ( Option != none_a )
=> ( Option
= ( some_a @ ( the_a2 @ Option ) ) ) ) ).
% option.exhaust_sel
thf(fact_260_option_Osplit__sel,axiom,
! [P4: $o > $o,F1: $o,F22: a > $o,Option: option_a] :
( ( P4 @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P4 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
=> ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_261_option_Osplit__sel,axiom,
! [P4: option_a > $o,F1: option_a,F22: a > option_a,Option: option_a] :
( ( P4 @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P4 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
=> ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_262_option_Osplit__sel,axiom,
! [P4: a > $o,F1: a,F22: a > a,Option: option_a] :
( ( P4 @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( ( ( Option = none_a )
=> ( P4 @ F1 ) )
& ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
=> ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_263_option_Osplit__sel__asm,axiom,
! [P4: $o > $o,F1: $o,F22: a > $o,Option: option_a] :
( ( P4 @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P4 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
& ~ ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_264_option_Osplit__sel__asm,axiom,
! [P4: option_a > $o,F1: option_a,F22: a > option_a,Option: option_a] :
( ( P4 @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P4 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
& ~ ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_265_option_Osplit__sel__asm,axiom,
! [P4: a > $o,F1: a,F22: a > a,Option: option_a] :
( ( P4 @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( ~ ( ( ( Option = none_a )
& ~ ( P4 @ F1 ) )
| ( ( Option
= ( some_a @ ( the_a2 @ Option ) ) )
& ~ ( P4 @ ( F22 @ ( the_a2 @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_266_map__add__upd__left,axiom,
! [M: a,E2: a > option_a,E1: a > option_a,U1: a] :
( ~ ( member_a @ M @ ( dom_a_a @ E2 ) )
=> ( ( map_add_a_a @ ( fun_upd_a_option_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_upd_a_option_a @ ( map_add_a_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_267_map__add__upd__left,axiom,
! [M: option_a,E2: option_a > option_a,E1: option_a > option_a,U1: a] :
( ~ ( member_option_a @ M @ ( dom_option_a_a @ E2 ) )
=> ( ( map_add_option_a_a @ ( fun_up1079276522633388797tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_up1079276522633388797tion_a @ ( map_add_option_a_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_268_map__add__upd__left,axiom,
! [M: b,E2: b > option_a,E1: b > option_a,U1: a] :
( ~ ( member_b @ M @ ( dom_b_a @ E2 ) )
=> ( ( map_add_b_a @ ( fun_upd_b_option_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
= ( fun_upd_b_option_a @ ( map_add_b_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).
% map_add_upd_left
thf(fact_269_option_Ocase__eq__if,axiom,
( case_option_o_a
= ( ^ [F12: $o,F23: a > $o,Option3: option_a] :
( ( ( Option3 = none_a )
=> F12 )
& ( ( Option3 != none_a )
=> ( F23 @ ( the_a2 @ Option3 ) ) ) ) ) ) ).
% option.case_eq_if
thf(fact_270_option_Ocase__eq__if,axiom,
( case_o3148979394504432965on_a_a
= ( ^ [F12: option_a,F23: a > option_a,Option3: option_a] : ( if_option_a @ ( Option3 = none_a ) @ F12 @ ( F23 @ ( the_a2 @ Option3 ) ) ) ) ) ).
% option.case_eq_if
thf(fact_271_option_Ocase__eq__if,axiom,
( case_option_a_a
= ( ^ [F12: a,F23: a > a,Option3: option_a] : ( if_a @ ( Option3 = none_a ) @ F12 @ ( F23 @ ( the_a2 @ Option3 ) ) ) ) ) ).
% option.case_eq_if
thf(fact_272_option_Oset__sel,axiom,
! [A: option_option_a] :
( ( A != none_option_a )
=> ( member_option_a @ ( the_option_a2 @ A ) @ ( set_option_option_a2 @ A ) ) ) ).
% option.set_sel
thf(fact_273_option_Oset__sel,axiom,
! [A: option_b] :
( ( A != none_b )
=> ( member_b @ ( the_b2 @ A ) @ ( set_option_b2 @ A ) ) ) ).
% option.set_sel
thf(fact_274_option_Oset__sel,axiom,
! [A: option_a] :
( ( A != none_a )
=> ( member_a @ ( the_a2 @ A ) @ ( set_option_a2 @ A ) ) ) ).
% option.set_sel
thf(fact_275_bind__eq__None__conv,axiom,
! [A: option_a,F2: a > option_a] :
( ( ( bind_a_a @ A @ F2 )
= none_a )
= ( ( A = none_a )
| ( ( F2 @ ( the_a2 @ A ) )
= none_a ) ) ) ).
% bind_eq_None_conv
thf(fact_276_elem__set,axiom,
! [X: option_a,Xo: option_option_a] :
( ( member_option_a @ X @ ( set_option_option_a2 @ Xo ) )
= ( Xo
= ( some_option_a @ X ) ) ) ).
% elem_set
thf(fact_277_elem__set,axiom,
! [X: b,Xo: option_b] :
( ( member_b @ X @ ( set_option_b2 @ Xo ) )
= ( Xo
= ( some_b @ X ) ) ) ).
% elem_set
thf(fact_278_elem__set,axiom,
! [X: a,Xo: option_a] :
( ( member_a @ X @ ( set_option_a2 @ Xo ) )
= ( Xo
= ( some_a @ X ) ) ) ).
% elem_set
thf(fact_279_bind__runit,axiom,
! [X: option_a] :
( ( bind_a_a @ X @ some_a )
= X ) ).
% bind_runit
thf(fact_280_fun__upd__None__if__notin__dom,axiom,
! [K: a,M: a > option_a] :
( ~ ( member_a @ K @ ( dom_a_a @ M ) )
=> ( ( fun_upd_a_option_a @ M @ K @ none_a )
= M ) ) ).
% fun_upd_None_if_notin_dom
thf(fact_281_fun__upd__None__if__notin__dom,axiom,
! [K: option_a,M: option_a > option_a] :
( ~ ( member_option_a @ K @ ( dom_option_a_a @ M ) )
=> ( ( fun_up1079276522633388797tion_a @ M @ K @ none_a )
= M ) ) ).
% fun_upd_None_if_notin_dom
thf(fact_282_fun__upd__None__if__notin__dom,axiom,
! [K: b,M: b > option_a] :
( ~ ( member_b @ K @ ( dom_b_a @ M ) )
=> ( ( fun_upd_b_option_a @ M @ K @ none_a )
= M ) ) ).
% fun_upd_None_if_notin_dom
thf(fact_283_bind__option__cong,axiom,
! [X: option_a,Y: option_a,F2: a > option_a,G: a > option_a] :
( ( X = Y )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ Y ) )
=> ( ( F2 @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( bind_a_a @ X @ F2 )
= ( bind_a_a @ Y @ G ) ) ) ) ).
% bind_option_cong
thf(fact_284_bind__option__cong__code,axiom,
! [X: option_a,Y: option_a,F2: a > option_a] :
( ( X = Y )
=> ( ( bind_a_a @ X @ F2 )
= ( bind_a_a @ Y @ F2 ) ) ) ).
% bind_option_cong_code
thf(fact_285_domD,axiom,
! [A: a,M: a > option_a] :
( ( member_a @ A @ ( dom_a_a @ M ) )
=> ? [B4: a] :
( ( M @ A )
= ( some_a @ B4 ) ) ) ).
% domD
thf(fact_286_domD,axiom,
! [A: option_a,M: option_a > option_a] :
( ( member_option_a @ A @ ( dom_option_a_a @ M ) )
=> ? [B4: a] :
( ( M @ A )
= ( some_a @ B4 ) ) ) ).
% domD
thf(fact_287_domD,axiom,
! [A: b,M: b > option_a] :
( ( member_b @ A @ ( dom_b_a @ M ) )
=> ? [B4: a] :
( ( M @ A )
= ( some_a @ B4 ) ) ) ).
% domD
thf(fact_288_domI,axiom,
! [M: a > option_a,A: a,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_a @ A @ ( dom_a_a @ M ) ) ) ).
% domI
thf(fact_289_domI,axiom,
! [M: option_a > option_a,A: option_a,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_option_a @ A @ ( dom_option_a_a @ M ) ) ) ).
% domI
thf(fact_290_domI,axiom,
! [M: b > option_a,A: b,B: a] :
( ( ( M @ A )
= ( some_a @ B ) )
=> ( member_b @ A @ ( dom_b_a @ M ) ) ) ).
% domI
thf(fact_291_domIff,axiom,
! [A: a,M: a > option_a] :
( ( member_a @ A @ ( dom_a_a @ M ) )
= ( ( M @ A )
!= none_a ) ) ).
% domIff
thf(fact_292_domIff,axiom,
! [A: option_a,M: option_a > option_a] :
( ( member_option_a @ A @ ( dom_option_a_a @ M ) )
= ( ( M @ A )
!= none_a ) ) ).
% domIff
thf(fact_293_domIff,axiom,
! [A: b,M: b > option_a] :
( ( member_b @ A @ ( dom_b_a @ M ) )
= ( ( M @ A )
!= none_a ) ) ).
% domIff
thf(fact_294_bind__eq__Some__conv,axiom,
! [F2: option_a,G: a > option_a,X: a] :
( ( ( bind_a_a @ F2 @ G )
= ( some_a @ X ) )
= ( ? [Y2: a] :
( ( F2
= ( some_a @ Y2 ) )
& ( ( G @ Y2 )
= ( some_a @ X ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_295_Option_Obind__cong,axiom,
! [X: option_a,Y: option_a,F2: a > option_a,G: a > option_a] :
( ( X = Y )
=> ( ! [A5: a] :
( ( Y
= ( some_a @ A5 ) )
=> ( ( F2 @ A5 )
= ( G @ A5 ) ) )
=> ( ( bind_a_a @ X @ F2 )
= ( bind_a_a @ Y @ G ) ) ) ) ).
% Option.bind_cong
thf(fact_296_bind_Obind__lunit,axiom,
! [X: a,F2: a > option_a] :
( ( bind_a_a @ ( some_a @ X ) @ F2 )
= ( F2 @ X ) ) ).
% bind.bind_lunit
thf(fact_297_bind_Obind__lzero,axiom,
! [F2: a > option_a] :
( ( bind_a_a @ none_a @ F2 )
= none_a ) ).
% bind.bind_lzero
thf(fact_298_ospec,axiom,
! [A2: option_a,P4: a > $o,X: a] :
( ! [X4: a] :
( ( member_a @ X4 @ ( set_option_a2 @ A2 ) )
=> ( P4 @ X4 ) )
=> ( ( A2
= ( some_a @ X ) )
=> ( P4 @ X ) ) ) ).
% ospec
thf(fact_299_option_Oset__intros,axiom,
! [X2: option_a] : ( member_option_a @ X2 @ ( set_option_option_a2 @ ( some_option_a @ X2 ) ) ) ).
% option.set_intros
thf(fact_300_option_Oset__intros,axiom,
! [X2: b] : ( member_b @ X2 @ ( set_option_b2 @ ( some_b @ X2 ) ) ) ).
% option.set_intros
thf(fact_301_option_Oset__intros,axiom,
! [X2: a] : ( member_a @ X2 @ ( set_option_a2 @ ( some_a @ X2 ) ) ) ).
% option.set_intros
thf(fact_302_option_Oset__cases,axiom,
! [E: option_a,A: option_option_a] :
( ( member_option_a @ E @ ( set_option_option_a2 @ A ) )
=> ( A
= ( some_option_a @ E ) ) ) ).
% option.set_cases
thf(fact_303_option_Oset__cases,axiom,
! [E: b,A: option_b] :
( ( member_b @ E @ ( set_option_b2 @ A ) )
=> ( A
= ( some_b @ E ) ) ) ).
% option.set_cases
thf(fact_304_option_Oset__cases,axiom,
! [E: a,A: option_a] :
( ( member_a @ E @ ( set_option_a2 @ A ) )
=> ( A
= ( some_a @ E ) ) ) ).
% option.set_cases
thf(fact_305_option_Osimps_I5_J,axiom,
! [F1: $o,F22: a > $o,X2: a] :
( ( case_option_o_a @ F1 @ F22 @ ( some_a @ X2 ) )
= ( F22 @ X2 ) ) ).
% option.simps(5)
thf(fact_306_option_Osimps_I5_J,axiom,
! [F1: option_a,F22: a > option_a,X2: a] :
( ( case_o3148979394504432965on_a_a @ F1 @ F22 @ ( some_a @ X2 ) )
= ( F22 @ X2 ) ) ).
% option.simps(5)
thf(fact_307_option_Osimps_I5_J,axiom,
! [F1: a,F22: a > a,X2: a] :
( ( case_option_a_a @ F1 @ F22 @ ( some_a @ X2 ) )
= ( F22 @ X2 ) ) ).
% option.simps(5)
thf(fact_308_option_Osimps_I4_J,axiom,
! [F1: $o,F22: a > $o] :
( ( case_option_o_a @ F1 @ F22 @ none_a )
= F1 ) ).
% option.simps(4)
thf(fact_309_option_Osimps_I4_J,axiom,
! [F1: option_a,F22: a > option_a] :
( ( case_o3148979394504432965on_a_a @ F1 @ F22 @ none_a )
= F1 ) ).
% option.simps(4)
thf(fact_310_option_Osimps_I4_J,axiom,
! [F1: a,F22: a > a] :
( ( case_option_a_a @ F1 @ F22 @ none_a )
= F1 ) ).
% option.simps(4)
thf(fact_311_bind__split__asm,axiom,
! [P4: option_a > $o,M: option_a,F2: a > option_a] :
( ( P4 @ ( bind_a_a @ M @ F2 ) )
= ( ~ ( ( ( M = none_a )
& ~ ( P4 @ none_a ) )
| ? [X5: a] :
( ( M
= ( some_a @ X5 ) )
& ~ ( P4 @ ( F2 @ X5 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_312_bind__split,axiom,
! [P4: option_a > $o,M: option_a,F2: a > option_a] :
( ( P4 @ ( bind_a_a @ M @ F2 ) )
= ( ( ( M = none_a )
=> ( P4 @ none_a ) )
& ! [V: a] :
( ( M
= ( some_a @ V ) )
=> ( P4 @ ( F2 @ V ) ) ) ) ) ).
% bind_split
thf(fact_313_is__none__bind,axiom,
! [F2: option_a,G: a > option_a] :
( ( is_none_a @ ( bind_a_a @ F2 @ G ) )
= ( ( is_none_a @ F2 )
| ( is_none_a @ ( G @ ( the_a2 @ F2 ) ) ) ) ) ).
% is_none_bind
thf(fact_314_set__empty__eq,axiom,
! [Xo: option_option_a] :
( ( ( set_option_option_a2 @ Xo )
= bot_bot_set_option_a )
= ( Xo = none_option_a ) ) ).
% set_empty_eq
thf(fact_315_set__empty__eq,axiom,
! [Xo: option_a] :
( ( ( set_option_a2 @ Xo )
= bot_bot_set_a )
= ( Xo = none_a ) ) ).
% set_empty_eq
thf(fact_316_dom__eq__empty__conv,axiom,
! [F2: a > option_a] :
( ( ( dom_a_a @ F2 )
= bot_bot_set_a )
= ( F2
= ( ^ [X5: a] : none_a ) ) ) ).
% dom_eq_empty_conv
thf(fact_317_dom__eq__empty__conv,axiom,
! [F2: option_a > option_a] :
( ( ( dom_option_a_a @ F2 )
= bot_bot_set_option_a )
= ( F2
= ( ^ [X5: option_a] : none_a ) ) ) ).
% dom_eq_empty_conv
thf(fact_318_is__none__code_I2_J,axiom,
! [X: a] :
~ ( is_none_a @ ( some_a @ X ) ) ).
% is_none_code(2)
thf(fact_319_is__none__code_I1_J,axiom,
is_none_a @ none_a ).
% is_none_code(1)
thf(fact_320_is__none__simps_I2_J,axiom,
! [X: a] :
~ ( is_none_a @ ( some_a @ X ) ) ).
% is_none_simps(2)
thf(fact_321_is__none__simps_I1_J,axiom,
is_none_a @ none_a ).
% is_none_simps(1)
thf(fact_322_Option_Ois__none__def,axiom,
( is_none_a
= ( ^ [X5: option_a] : ( X5 = none_a ) ) ) ).
% Option.is_none_def
thf(fact_323_option_Osimps_I14_J,axiom,
( ( set_option_option_a2 @ none_option_a )
= bot_bot_set_option_a ) ).
% option.simps(14)
thf(fact_324_option_Osimps_I14_J,axiom,
( ( set_option_a2 @ none_a )
= bot_bot_set_a ) ).
% option.simps(14)
thf(fact_325_option_Osimps_I15_J,axiom,
! [X2: option_a] :
( ( set_option_option_a2 @ ( some_option_a @ X2 ) )
= ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ).
% option.simps(15)
thf(fact_326_option_Osimps_I15_J,axiom,
! [X2: a] :
( ( set_option_a2 @ ( some_a @ X2 ) )
= ( insert_a @ X2 @ bot_bot_set_a ) ) ).
% option.simps(15)
thf(fact_327_restrict__map__to__empty,axiom,
! [M: a > option_a] :
( ( restrict_map_a_a @ M @ bot_bot_set_a )
= ( ^ [X5: a] : none_a ) ) ).
% restrict_map_to_empty
thf(fact_328_restrict__map__to__empty,axiom,
! [M: option_a > option_a] :
( ( restri3984065703976872170on_a_a @ M @ bot_bot_set_option_a )
= ( ^ [X5: option_a] : none_a ) ) ).
% restrict_map_to_empty
thf(fact_329_these__empty,axiom,
( ( these_option_a @ bot_bo4163488203964334806tion_a )
= bot_bot_set_option_a ) ).
% these_empty
thf(fact_330_these__empty,axiom,
( ( these_a @ bot_bot_set_option_a )
= bot_bot_set_a ) ).
% these_empty
thf(fact_331_restrict__out,axiom,
! [X: a,A2: set_a,M: a > option_a] :
( ~ ( member_a @ X @ A2 )
=> ( ( restrict_map_a_a @ M @ A2 @ X )
= none_a ) ) ).
% restrict_out
thf(fact_332_restrict__out,axiom,
! [X: option_a,A2: set_option_a,M: option_a > option_a] :
( ~ ( member_option_a @ X @ A2 )
=> ( ( restri3984065703976872170on_a_a @ M @ A2 @ X )
= none_a ) ) ).
% restrict_out
thf(fact_333_restrict__out,axiom,
! [X: b,A2: set_b,M: b > option_a] :
( ~ ( member_b @ X @ A2 )
=> ( ( restrict_map_b_a @ M @ A2 @ X )
= none_a ) ) ).
% restrict_out
thf(fact_334_these__insert__None,axiom,
! [A2: set_option_a] :
( ( these_a @ ( insert_option_a @ none_a @ A2 ) )
= ( these_a @ A2 ) ) ).
% these_insert_None
thf(fact_335_these__insert__Some,axiom,
! [X: option_a,A2: set_option_option_a] :
( ( these_option_a @ ( insert605063979879581146tion_a @ ( some_option_a @ X ) @ A2 ) )
= ( insert_option_a @ X @ ( these_option_a @ A2 ) ) ) ).
% these_insert_Some
thf(fact_336_these__insert__Some,axiom,
! [X: a,A2: set_option_a] :
( ( these_a @ ( insert_option_a @ ( some_a @ X ) @ A2 ) )
= ( insert_a @ X @ ( these_a @ A2 ) ) ) ).
% these_insert_Some
thf(fact_337_override__on__insert,axiom,
! [F2: d > c,G: d > c,X: d,X7: set_d] :
( ( override_on_d_c @ F2 @ G @ ( insert_d @ X @ X7 ) )
= ( fun_upd_d_c @ ( override_on_d_c @ F2 @ G @ X7 ) @ X @ ( G @ X ) ) ) ).
% override_on_insert
thf(fact_338_override__on__insert_H,axiom,
! [F2: d > c,G: d > c,X: d,X7: set_d] :
( ( override_on_d_c @ F2 @ G @ ( insert_d @ X @ X7 ) )
= ( override_on_d_c @ ( fun_upd_d_c @ F2 @ X @ ( G @ X ) ) @ G @ X7 ) ) ).
% override_on_insert'
thf(fact_339_these__empty__eq,axiom,
! [B2: set_option_option_a] :
( ( ( these_option_a @ B2 )
= bot_bot_set_option_a )
= ( ( B2 = bot_bo4163488203964334806tion_a )
| ( B2
= ( insert605063979879581146tion_a @ none_option_a @ bot_bo4163488203964334806tion_a ) ) ) ) ).
% these_empty_eq
thf(fact_340_these__empty__eq,axiom,
! [B2: set_option_a] :
( ( ( these_a @ B2 )
= bot_bot_set_a )
= ( ( B2 = bot_bot_set_option_a )
| ( B2
= ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% these_empty_eq
thf(fact_341_these__not__empty__eq,axiom,
! [B2: set_option_option_a] :
( ( ( these_option_a @ B2 )
!= bot_bot_set_option_a )
= ( ( B2 != bot_bo4163488203964334806tion_a )
& ( B2
!= ( insert605063979879581146tion_a @ none_option_a @ bot_bo4163488203964334806tion_a ) ) ) ) ).
% these_not_empty_eq
thf(fact_342_these__not__empty__eq,axiom,
! [B2: set_option_a] :
( ( ( these_a @ B2 )
!= bot_bot_set_a )
= ( ( B2 != bot_bot_set_option_a )
& ( B2
!= ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% these_not_empty_eq
thf(fact_343_restrict__map__def,axiom,
( restrict_map_a_a
= ( ^ [M2: a > option_a,A7: set_a,X5: a] : ( if_option_a @ ( member_a @ X5 @ A7 ) @ ( M2 @ X5 ) @ none_a ) ) ) ).
% restrict_map_def
thf(fact_344_restrict__map__def,axiom,
( restri3984065703976872170on_a_a
= ( ^ [M2: option_a > option_a,A7: set_option_a,X5: option_a] : ( if_option_a @ ( member_option_a @ X5 @ A7 ) @ ( M2 @ X5 ) @ none_a ) ) ) ).
% restrict_map_def
thf(fact_345_restrict__map__def,axiom,
( restrict_map_b_a
= ( ^ [M2: b > option_a,A7: set_b,X5: b] : ( if_option_a @ ( member_b @ X5 @ A7 ) @ ( M2 @ X5 ) @ none_a ) ) ) ).
% restrict_map_def
thf(fact_346_in__these__eq,axiom,
! [X: option_a,A2: set_option_option_a] :
( ( member_option_a @ X @ ( these_option_a @ A2 ) )
= ( member5113800082084363315tion_a @ ( some_option_a @ X ) @ A2 ) ) ).
% in_these_eq
thf(fact_347_in__these__eq,axiom,
! [X: b,A2: set_option_b] :
( ( member_b @ X @ ( these_b @ A2 ) )
= ( member_option_b @ ( some_b @ X ) @ A2 ) ) ).
% in_these_eq
thf(fact_348_in__these__eq,axiom,
! [X: a,A2: set_option_a] :
( ( member_a @ X @ ( these_a @ A2 ) )
= ( member_option_a @ ( some_a @ X ) @ A2 ) ) ).
% in_these_eq
thf(fact_349_insert__dom,axiom,
! [F2: a > option_a,X: a,Y: a] :
( ( ( F2 @ X )
= ( some_a @ Y ) )
=> ( ( insert_a @ X @ ( dom_a_a @ F2 ) )
= ( dom_a_a @ F2 ) ) ) ).
% insert_dom
thf(fact_350_insert__dom,axiom,
! [F2: option_a > option_a,X: option_a,Y: a] :
( ( ( F2 @ X )
= ( some_a @ Y ) )
=> ( ( insert_option_a @ X @ ( dom_option_a_a @ F2 ) )
= ( dom_option_a_a @ F2 ) ) ) ).
% insert_dom
thf(fact_351_restrict__upd__same,axiom,
! [M: a > option_a,X: a,Y: a] :
( ( restrict_map_a_a @ ( fun_upd_a_option_a @ M @ X @ ( some_a @ Y ) ) @ ( uminus_uminus_set_a @ ( insert_a @ X @ bot_bot_set_a ) ) )
= ( restrict_map_a_a @ M @ ( uminus_uminus_set_a @ ( insert_a @ X @ bot_bot_set_a ) ) ) ) ).
% restrict_upd_same
thf(fact_352_restrict__upd__same,axiom,
! [M: option_a > option_a,X: option_a,Y: a] :
( ( restri3984065703976872170on_a_a @ ( fun_up1079276522633388797tion_a @ M @ X @ ( some_a @ Y ) ) @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) )
= ( restri3984065703976872170on_a_a @ M @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) ) ) ).
% restrict_upd_same
thf(fact_353_fun__upd__None__restrict,axiom,
! [X: b,D2: set_b,M: b > option_a] :
( ( ( member_b @ X @ D2 )
=> ( ( fun_upd_b_option_a @ ( restrict_map_b_a @ M @ D2 ) @ X @ none_a )
= ( restrict_map_b_a @ M @ ( minus_minus_set_b @ D2 @ ( insert_b @ X @ bot_bot_set_b ) ) ) ) )
& ( ~ ( member_b @ X @ D2 )
=> ( ( fun_upd_b_option_a @ ( restrict_map_b_a @ M @ D2 ) @ X @ none_a )
= ( restrict_map_b_a @ M @ D2 ) ) ) ) ).
% fun_upd_None_restrict
thf(fact_354_fun__upd__None__restrict,axiom,
! [X: a,D2: set_a,M: a > option_a] :
( ( ( member_a @ X @ D2 )
=> ( ( fun_upd_a_option_a @ ( restrict_map_a_a @ M @ D2 ) @ X @ none_a )
= ( restrict_map_a_a @ M @ ( minus_minus_set_a @ D2 @ ( insert_a @ X @ bot_bot_set_a ) ) ) ) )
& ( ~ ( member_a @ X @ D2 )
=> ( ( fun_upd_a_option_a @ ( restrict_map_a_a @ M @ D2 ) @ X @ none_a )
= ( restrict_map_a_a @ M @ D2 ) ) ) ) ).
% fun_upd_None_restrict
thf(fact_355_fun__upd__None__restrict,axiom,
! [X: option_a,D2: set_option_a,M: option_a > option_a] :
( ( ( member_option_a @ X @ D2 )
=> ( ( fun_up1079276522633388797tion_a @ ( restri3984065703976872170on_a_a @ M @ D2 ) @ X @ none_a )
= ( restri3984065703976872170on_a_a @ M @ ( minus_1574173051537231627tion_a @ D2 @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) ) ) )
& ( ~ ( member_option_a @ X @ D2 )
=> ( ( fun_up1079276522633388797tion_a @ ( restri3984065703976872170on_a_a @ M @ D2 ) @ X @ none_a )
= ( restri3984065703976872170on_a_a @ M @ D2 ) ) ) ) ).
% fun_upd_None_restrict
thf(fact_356_dom__fun__upd,axiom,
! [Y: option_a,F2: a > option_a,X: a] :
( ( ( Y = none_a )
=> ( ( dom_a_a @ ( fun_upd_a_option_a @ F2 @ X @ Y ) )
= ( minus_minus_set_a @ ( dom_a_a @ F2 ) @ ( insert_a @ X @ bot_bot_set_a ) ) ) )
& ( ( Y != none_a )
=> ( ( dom_a_a @ ( fun_upd_a_option_a @ F2 @ X @ Y ) )
= ( insert_a @ X @ ( dom_a_a @ F2 ) ) ) ) ) ).
% dom_fun_upd
thf(fact_357_dom__fun__upd,axiom,
! [Y: option_a,F2: option_a > option_a,X: option_a] :
( ( ( Y = none_a )
=> ( ( dom_option_a_a @ ( fun_up1079276522633388797tion_a @ F2 @ X @ Y ) )
= ( minus_1574173051537231627tion_a @ ( dom_option_a_a @ F2 ) @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) ) )
& ( ( Y != none_a )
=> ( ( dom_option_a_a @ ( fun_up1079276522633388797tion_a @ F2 @ X @ Y ) )
= ( insert_option_a @ X @ ( dom_option_a_a @ F2 ) ) ) ) ) ).
% dom_fun_upd
thf(fact_358_restrict__complement__singleton__eq,axiom,
! [F2: a > option_a,X: a] :
( ( restrict_map_a_a @ F2 @ ( uminus_uminus_set_a @ ( insert_a @ X @ bot_bot_set_a ) ) )
= ( fun_upd_a_option_a @ F2 @ X @ none_a ) ) ).
% restrict_complement_singleton_eq
thf(fact_359_restrict__complement__singleton__eq,axiom,
! [F2: option_a > option_a,X: option_a] :
( ( restri3984065703976872170on_a_a @ F2 @ ( uminus6205308855922866075tion_a @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) )
= ( fun_up1079276522633388797tion_a @ F2 @ X @ none_a ) ) ).
% restrict_complement_singleton_eq
thf(fact_360_dom__minus,axiom,
! [F2: a > option_a,X: a,A2: set_a] :
( ( ( F2 @ X )
= none_a )
=> ( ( minus_minus_set_a @ ( dom_a_a @ F2 ) @ ( insert_a @ X @ A2 ) )
= ( minus_minus_set_a @ ( dom_a_a @ F2 ) @ A2 ) ) ) ).
% dom_minus
thf(fact_361_dom__minus,axiom,
! [F2: option_a > option_a,X: option_a,A2: set_option_a] :
( ( ( F2 @ X )
= none_a )
=> ( ( minus_1574173051537231627tion_a @ ( dom_option_a_a @ F2 ) @ ( insert_option_a @ X @ A2 ) )
= ( minus_1574173051537231627tion_a @ ( dom_option_a_a @ F2 ) @ A2 ) ) ) ).
% dom_minus
thf(fact_362_fun__upd__image,axiom,
! [X: b,A2: set_b,F2: b > a,Y: a] :
( ( ( member_b @ X @ A2 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F2 @ X @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_b_a @ F2 @ ( minus_minus_set_b @ A2 @ ( insert_b @ X @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X @ A2 )
=> ( ( image_b_a @ ( fun_upd_b_a @ F2 @ X @ Y ) @ A2 )
= ( image_b_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_363_fun__upd__image,axiom,
! [X: b,A2: set_b,F2: b > option_a,Y: option_a] :
( ( ( member_b @ X @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F2 @ X @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_b_option_a @ F2 @ ( minus_minus_set_b @ A2 @ ( insert_b @ X @ bot_bot_set_b ) ) ) ) ) )
& ( ~ ( member_b @ X @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ F2 @ X @ Y ) @ A2 )
= ( image_b_option_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_364_fun__upd__image,axiom,
! [X: d,A2: set_d,F2: d > c,Y: c] :
( ( ( member_d @ X @ A2 )
=> ( ( image_d_c @ ( fun_upd_d_c @ F2 @ X @ Y ) @ A2 )
= ( insert_c @ Y @ ( image_d_c @ F2 @ ( minus_minus_set_d @ A2 @ ( insert_d @ X @ bot_bot_set_d ) ) ) ) ) )
& ( ~ ( member_d @ X @ A2 )
=> ( ( image_d_c @ ( fun_upd_d_c @ F2 @ X @ Y ) @ A2 )
= ( image_d_c @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_365_fun__upd__image,axiom,
! [X: a,A2: set_a,F2: a > a,Y: a] :
( ( ( member_a @ X @ A2 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F2 @ X @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_a_a @ F2 @ ( minus_minus_set_a @ A2 @ ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X @ A2 )
=> ( ( image_a_a @ ( fun_upd_a_a @ F2 @ X @ Y ) @ A2 )
= ( image_a_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_366_fun__upd__image,axiom,
! [X: a,A2: set_a,F2: a > option_a,Y: option_a] :
( ( ( member_a @ X @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ X @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) )
& ( ~ ( member_a @ X @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ X @ Y ) @ A2 )
= ( image_a_option_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_367_fun__upd__image,axiom,
! [X: option_a,A2: set_option_a,F2: option_a > a,Y: a] :
( ( ( member_option_a @ X @ A2 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F2 @ X @ Y ) @ A2 )
= ( insert_a @ Y @ ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X @ A2 )
=> ( ( image_option_a_a @ ( fun_upd_option_a_a @ F2 @ X @ Y ) @ A2 )
= ( image_option_a_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_368_fun__upd__image,axiom,
! [X: option_a,A2: set_option_a,F2: option_a > option_a,Y: option_a] :
( ( ( member_option_a @ X @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ X @ Y ) @ A2 )
= ( insert_option_a @ Y @ ( image_7439109396645324421tion_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ X @ bot_bot_set_option_a ) ) ) ) ) )
& ( ~ ( member_option_a @ X @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ X @ Y ) @ A2 )
= ( image_7439109396645324421tion_a @ F2 @ A2 ) ) ) ) ).
% fun_upd_image
thf(fact_369_ran__map__upd__Some,axiom,
! [M: a > option_a,X: a,Y: a,Z2: a] :
( ( ( M @ X )
= ( some_a @ Y ) )
=> ( ( inj_on_a_option_a @ M @ ( dom_a_a @ M ) )
=> ( ~ ( member_a @ Z2 @ ( ran_a_a @ M ) )
=> ( ( ran_a_a @ ( fun_upd_a_option_a @ M @ X @ ( some_a @ Z2 ) ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( ran_a_a @ M ) @ ( insert_a @ Y @ bot_bot_set_a ) ) @ ( insert_a @ Z2 @ bot_bot_set_a ) ) ) ) ) ) ).
% ran_map_upd_Some
thf(fact_370_these__image__Some__eq,axiom,
! [A2: set_a] :
( ( these_a @ ( image_a_option_a @ some_a @ A2 ) )
= A2 ) ).
% these_image_Some_eq
thf(fact_371_dom__eq__singleton__conv,axiom,
! [F2: a > option_a,X: a] :
( ( ( dom_a_a @ F2 )
= ( insert_a @ X @ bot_bot_set_a ) )
= ( ? [V: a] :
( F2
= ( fun_upd_a_option_a
@ ^ [X5: a] : none_a
@ X
@ ( some_a @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_372_dom__eq__singleton__conv,axiom,
! [F2: option_a > option_a,X: option_a] :
( ( ( dom_option_a_a @ F2 )
= ( insert_option_a @ X @ bot_bot_set_option_a ) )
= ( ? [V: a] :
( F2
= ( fun_up1079276522633388797tion_a
@ ^ [X5: option_a] : none_a
@ X
@ ( some_a @ V ) ) ) ) ) ).
% dom_eq_singleton_conv
thf(fact_373_image__map__upd,axiom,
! [X: a,A2: set_a,M: a > option_a,Y: a] :
( ~ ( member_a @ X @ A2 )
=> ( ( image_a_option_a @ ( fun_upd_a_option_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
= ( image_a_option_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_374_image__map__upd,axiom,
! [X: option_a,A2: set_option_a,M: option_a > option_a,Y: a] :
( ~ ( member_option_a @ X @ A2 )
=> ( ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
= ( image_7439109396645324421tion_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_375_image__map__upd,axiom,
! [X: b,A2: set_b,M: b > option_a,Y: a] :
( ~ ( member_b @ X @ A2 )
=> ( ( image_b_option_a @ ( fun_upd_b_option_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
= ( image_b_option_a @ M @ A2 ) ) ) ).
% image_map_upd
thf(fact_376_assertion_Osimps_I325_J,axiom,
! [X21: b,X22: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( mult_b_a_c_d @ X21 @ X22 ) )
= ( insert_b @ X21 @ ( set_as796765862704242958_b_c_d @ X22 ) ) ) ).
% assertion.simps(325)
thf(fact_377_bind__assoc,axiom,
! [X: option_a,F2: a > option_a,G: a > option_a] :
( ( bind_a_a @ ( bind_a_a @ X @ F2 ) @ G )
= ( bind_a_a @ X
@ ^ [Y2: a] : ( bind_a_a @ ( F2 @ Y2 ) @ G ) ) ) ).
% bind_assoc
thf(fact_378_inj__on__empty,axiom,
! [F2: a > option_a] : ( inj_on_a_option_a @ F2 @ bot_bot_set_a ) ).
% inj_on_empty
thf(fact_379_bind__rzero,axiom,
! [X: option_a] :
( ( bind_a_a @ X
@ ^ [X5: a] : none_a )
= none_a ) ).
% bind_rzero
thf(fact_380_dom__empty,axiom,
( ( dom_a_a
@ ^ [X5: a] : none_a )
= bot_bot_set_a ) ).
% dom_empty
thf(fact_381_dom__empty,axiom,
( ( dom_option_a_a
@ ^ [X5: option_a] : none_a )
= bot_bot_set_option_a ) ).
% dom_empty
thf(fact_382_inj__on__insert,axiom,
! [F2: a > a,A: a,A2: set_a] :
( ( inj_on_a_a @ F2 @ ( insert_a @ A @ A2 ) )
= ( ( inj_on_a_a @ F2 @ A2 )
& ~ ( member_a @ ( F2 @ A ) @ ( image_a_a @ F2 @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_383_inj__on__insert,axiom,
! [F2: a > option_a,A: a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ ( insert_a @ A @ A2 ) )
= ( ( inj_on_a_option_a @ F2 @ A2 )
& ~ ( member_option_a @ ( F2 @ A ) @ ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_384_inj__on__insert,axiom,
! [F2: a > b,A: a,A2: set_a] :
( ( inj_on_a_b @ F2 @ ( insert_a @ A @ A2 ) )
= ( ( inj_on_a_b @ F2 @ A2 )
& ~ ( member_b @ ( F2 @ A ) @ ( image_a_b @ F2 @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_385_inj__on__insert,axiom,
! [F2: option_a > a,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ ( insert_option_a @ A @ A2 ) )
= ( ( inj_on_option_a_a @ F2 @ A2 )
& ~ ( member_a @ ( F2 @ A ) @ ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_386_inj__on__insert,axiom,
! [F2: option_a > option_a,A: option_a,A2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ ( insert_option_a @ A @ A2 ) )
= ( ( inj_on8559383841115902449tion_a @ F2 @ A2 )
& ~ ( member_option_a @ ( F2 @ A ) @ ( image_7439109396645324421tion_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_387_inj__on__insert,axiom,
! [F2: option_a > b,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_b @ F2 @ ( insert_option_a @ A @ A2 ) )
= ( ( inj_on_option_a_b @ F2 @ A2 )
& ~ ( member_b @ ( F2 @ A ) @ ( image_option_a_b @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) ) ) ) ) ).
% inj_on_insert
thf(fact_388_inj__img__insertE,axiom,
! [F2: a > a,A2: set_a,X: a,B2: set_a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ~ ( member_a @ X @ B2 )
=> ( ( ( insert_a @ X @ B2 )
= ( image_a_a @ F2 @ A2 ) )
=> ~ ! [X8: a,A8: set_a] :
( ~ ( member_a @ X8 @ A8 )
=> ( ( A2
= ( insert_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_a_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_389_inj__img__insertE,axiom,
! [F2: option_a > a,A2: set_option_a,X: a,B2: set_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ~ ( member_a @ X @ B2 )
=> ( ( ( insert_a @ X @ B2 )
= ( image_option_a_a @ F2 @ A2 ) )
=> ~ ! [X8: option_a,A8: set_option_a] :
( ~ ( member_option_a @ X8 @ A8 )
=> ( ( A2
= ( insert_option_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_option_a_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_390_inj__img__insertE,axiom,
! [F2: b > a,A2: set_b,X: a,B2: set_a] :
( ( inj_on_b_a @ F2 @ A2 )
=> ( ~ ( member_a @ X @ B2 )
=> ( ( ( insert_a @ X @ B2 )
= ( image_b_a @ F2 @ A2 ) )
=> ~ ! [X8: b,A8: set_b] :
( ~ ( member_b @ X8 @ A8 )
=> ( ( A2
= ( insert_b @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_b_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_391_inj__img__insertE,axiom,
! [F2: a > option_a,A2: set_a,X: option_a,B2: set_option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ~ ( member_option_a @ X @ B2 )
=> ( ( ( insert_option_a @ X @ B2 )
= ( image_a_option_a @ F2 @ A2 ) )
=> ~ ! [X8: a,A8: set_a] :
( ~ ( member_a @ X8 @ A8 )
=> ( ( A2
= ( insert_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_a_option_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_392_inj__img__insertE,axiom,
! [F2: option_a > option_a,A2: set_option_a,X: option_a,B2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ A2 )
=> ( ~ ( member_option_a @ X @ B2 )
=> ( ( ( insert_option_a @ X @ B2 )
= ( image_7439109396645324421tion_a @ F2 @ A2 ) )
=> ~ ! [X8: option_a,A8: set_option_a] :
( ~ ( member_option_a @ X8 @ A8 )
=> ( ( A2
= ( insert_option_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_7439109396645324421tion_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_393_inj__img__insertE,axiom,
! [F2: b > option_a,A2: set_b,X: option_a,B2: set_option_a] :
( ( inj_on_b_option_a @ F2 @ A2 )
=> ( ~ ( member_option_a @ X @ B2 )
=> ( ( ( insert_option_a @ X @ B2 )
= ( image_b_option_a @ F2 @ A2 ) )
=> ~ ! [X8: b,A8: set_b] :
( ~ ( member_b @ X8 @ A8 )
=> ( ( A2
= ( insert_b @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_b_option_a @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_394_inj__img__insertE,axiom,
! [F2: a > b,A2: set_a,X: b,B2: set_b] :
( ( inj_on_a_b @ F2 @ A2 )
=> ( ~ ( member_b @ X @ B2 )
=> ( ( ( insert_b @ X @ B2 )
= ( image_a_b @ F2 @ A2 ) )
=> ~ ! [X8: a,A8: set_a] :
( ~ ( member_a @ X8 @ A8 )
=> ( ( A2
= ( insert_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_a_b @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_395_inj__img__insertE,axiom,
! [F2: option_a > b,A2: set_option_a,X: b,B2: set_b] :
( ( inj_on_option_a_b @ F2 @ A2 )
=> ( ~ ( member_b @ X @ B2 )
=> ( ( ( insert_b @ X @ B2 )
= ( image_option_a_b @ F2 @ A2 ) )
=> ~ ! [X8: option_a,A8: set_option_a] :
( ~ ( member_option_a @ X8 @ A8 )
=> ( ( A2
= ( insert_option_a @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_option_a_b @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_396_inj__img__insertE,axiom,
! [F2: b > b,A2: set_b,X: b,B2: set_b] :
( ( inj_on_b_b @ F2 @ A2 )
=> ( ~ ( member_b @ X @ B2 )
=> ( ( ( insert_b @ X @ B2 )
= ( image_b_b @ F2 @ A2 ) )
=> ~ ! [X8: b,A8: set_b] :
( ~ ( member_b @ X8 @ A8 )
=> ( ( A2
= ( insert_b @ X8 @ A8 ) )
=> ( ( X
= ( F2 @ X8 ) )
=> ( B2
!= ( image_b_b @ F2 @ A8 ) ) ) ) ) ) ) ) ).
% inj_img_insertE
thf(fact_397_Option_Othese__def,axiom,
( these_a
= ( ^ [A7: set_option_a] :
( image_option_a_a @ the_a2
@ ( collect_option_a
@ ^ [X5: option_a] :
( ( member_option_a @ X5 @ A7 )
& ( X5 != none_a ) ) ) ) ) ) ).
% Option.these_def
thf(fact_398_dom__def,axiom,
( dom_option_a_a
= ( ^ [M2: option_a > option_a] :
( collect_option_a
@ ^ [A6: option_a] :
( ( M2 @ A6 )
!= none_a ) ) ) ) ).
% dom_def
thf(fact_399_inj__onD,axiom,
! [F2: a > option_a,A2: set_a,X: a,Y: a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( ( F2 @ X )
= ( F2 @ Y ) )
=> ( ( member_a @ X @ A2 )
=> ( ( member_a @ Y @ A2 )
=> ( X = Y ) ) ) ) ) ).
% inj_onD
thf(fact_400_inj__onI,axiom,
! [A2: set_a,F2: a > option_a] :
( ! [X4: a,Y3: a] :
( ( member_a @ X4 @ A2 )
=> ( ( member_a @ Y3 @ A2 )
=> ( ( ( F2 @ X4 )
= ( F2 @ Y3 ) )
=> ( X4 = Y3 ) ) ) )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ).
% inj_onI
thf(fact_401_inj__on__def,axiom,
( inj_on_a_option_a
= ( ^ [F: a > option_a,A7: set_a] :
! [X5: a] :
( ( member_a @ X5 @ A7 )
=> ! [Y2: a] :
( ( member_a @ Y2 @ A7 )
=> ( ( ( F @ X5 )
= ( F @ Y2 ) )
=> ( X5 = Y2 ) ) ) ) ) ) ).
% inj_on_def
thf(fact_402_inj__on__cong,axiom,
! [A2: set_a,F2: a > option_a,G: a > option_a] :
( ! [A5: a] :
( ( member_a @ A5 @ A2 )
=> ( ( F2 @ A5 )
= ( G @ A5 ) ) )
=> ( ( inj_on_a_option_a @ F2 @ A2 )
= ( inj_on_a_option_a @ G @ A2 ) ) ) ).
% inj_on_cong
thf(fact_403_inj__on__eq__iff,axiom,
! [F2: a > option_a,A2: set_a,X: a,Y: a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( member_a @ X @ A2 )
=> ( ( member_a @ Y @ A2 )
=> ( ( ( F2 @ X )
= ( F2 @ Y ) )
= ( X = Y ) ) ) ) ) ).
% inj_on_eq_iff
thf(fact_404_inj__on__contraD,axiom,
! [F2: a > option_a,A2: set_a,X: a,Y: a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( X != Y )
=> ( ( member_a @ X @ A2 )
=> ( ( member_a @ Y @ A2 )
=> ( ( F2 @ X )
!= ( F2 @ Y ) ) ) ) ) ) ).
% inj_on_contraD
thf(fact_405_inj__on__inverseI,axiom,
! [A2: set_a,G: option_a > a,F2: a > option_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ( ( G @ ( F2 @ X4 ) )
= X4 ) )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ).
% inj_on_inverseI
thf(fact_406_inj__on__image__iff,axiom,
! [A2: set_a,G: a > option_a,F2: a > a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ! [Xa: a] :
( ( member_a @ Xa @ A2 )
=> ( ( ( G @ ( F2 @ X4 ) )
= ( G @ ( F2 @ Xa ) ) )
= ( ( G @ X4 )
= ( G @ Xa ) ) ) ) )
=> ( ( inj_on_a_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ G @ ( image_a_a @ F2 @ A2 ) )
= ( inj_on_a_option_a @ G @ A2 ) ) ) ) ).
% inj_on_image_iff
thf(fact_407_inj__on__Un__image__eq__iff,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ ( sup_sup_set_option_a @ A2 @ B2 ) )
=> ( ( ( image_option_a_a @ F2 @ A2 )
= ( image_option_a_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ).
% inj_on_Un_image_eq_iff
thf(fact_408_inj__on__Un__image__eq__iff,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ ( sup_sup_set_a @ A2 @ B2 ) )
=> ( ( ( image_a_option_a @ F2 @ A2 )
= ( image_a_option_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ).
% inj_on_Un_image_eq_iff
thf(fact_409_assertion_Osimps_I326_J,axiom,
! [X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( star_a_b_c_d @ X31 @ X32 ) )
= ( sup_sup_set_b @ ( set_as796765862704242958_b_c_d @ X31 ) @ ( set_as796765862704242958_b_c_d @ X32 ) ) ) ).
% assertion.simps(326)
thf(fact_410_assertion_Osimps_I327_J,axiom,
! [X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( wand_a_b_c_d @ X41 @ X42 ) )
= ( sup_sup_set_b @ ( set_as796765862704242958_b_c_d @ X41 ) @ ( set_as796765862704242958_b_c_d @ X42 ) ) ) ).
% assertion.simps(327)
thf(fact_411_assertion_Osimps_I329_J,axiom,
! [X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( and_a_b_c_d @ X61 @ X62 ) )
= ( sup_sup_set_b @ ( set_as796765862704242958_b_c_d @ X61 ) @ ( set_as796765862704242958_b_c_d @ X62 ) ) ) ).
% assertion.simps(329)
thf(fact_412_assertion_Osimps_I330_J,axiom,
! [X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( imp_a_b_c_d @ X71 @ X72 ) )
= ( sup_sup_set_b @ ( set_as796765862704242958_b_c_d @ X71 ) @ ( set_as796765862704242958_b_c_d @ X72 ) ) ) ).
% assertion.simps(330)
thf(fact_413_assertion_Osimps_I328_J,axiom,
! [X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( or_a_b_c_d @ X51 @ X52 ) )
= ( sup_sup_set_b @ ( set_as796765862704242958_b_c_d @ X51 ) @ ( set_as796765862704242958_b_c_d @ X52 ) ) ) ).
% assertion.simps(328)
thf(fact_414_inj__on__fun__updI,axiom,
! [F2: option_a > a,A2: set_option_a,Y: a,X: option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ~ ( member_a @ Y @ ( image_option_a_a @ F2 @ A2 ) )
=> ( inj_on_option_a_a @ ( fun_upd_option_a_a @ F2 @ X @ Y ) @ A2 ) ) ) ).
% inj_on_fun_updI
thf(fact_415_inj__on__fun__updI,axiom,
! [F2: a > option_a,A2: set_a,Y: option_a,X: a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ~ ( member_option_a @ Y @ ( image_a_option_a @ F2 @ A2 ) )
=> ( inj_on_a_option_a @ ( fun_upd_a_option_a @ F2 @ X @ Y ) @ A2 ) ) ) ).
% inj_on_fun_updI
thf(fact_416_inj__on__fun__updI,axiom,
! [F2: d > c,A2: set_d,Y: c,X: d] :
( ( inj_on_d_c @ F2 @ A2 )
=> ( ~ ( member_c @ Y @ ( image_d_c @ F2 @ A2 ) )
=> ( inj_on_d_c @ ( fun_upd_d_c @ F2 @ X @ Y ) @ A2 ) ) ) ).
% inj_on_fun_updI
thf(fact_417_option_Ocase__distrib,axiom,
! [H: $o > $o,F1: $o,F22: a > $o,Option: option_a] :
( ( H @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( case_option_o_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_418_option_Ocase__distrib,axiom,
! [H: $o > option_a,F1: $o,F22: a > $o,Option: option_a] :
( ( H @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( case_o3148979394504432965on_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_419_option_Ocase__distrib,axiom,
! [H: $o > a,F1: $o,F22: a > $o,Option: option_a] :
( ( H @ ( case_option_o_a @ F1 @ F22 @ Option ) )
= ( case_option_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_420_option_Ocase__distrib,axiom,
! [H: option_a > $o,F1: option_a,F22: a > option_a,Option: option_a] :
( ( H @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( case_option_o_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_421_option_Ocase__distrib,axiom,
! [H: option_a > option_a,F1: option_a,F22: a > option_a,Option: option_a] :
( ( H @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( case_o3148979394504432965on_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_422_option_Ocase__distrib,axiom,
! [H: option_a > a,F1: option_a,F22: a > option_a,Option: option_a] :
( ( H @ ( case_o3148979394504432965on_a_a @ F1 @ F22 @ Option ) )
= ( case_option_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_423_option_Ocase__distrib,axiom,
! [H: a > $o,F1: a,F22: a > a,Option: option_a] :
( ( H @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( case_option_o_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_424_option_Ocase__distrib,axiom,
! [H: a > option_a,F1: a,F22: a > a,Option: option_a] :
( ( H @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( case_o3148979394504432965on_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_425_option_Ocase__distrib,axiom,
! [H: a > a,F1: a,F22: a > a,Option: option_a] :
( ( H @ ( case_option_a_a @ F1 @ F22 @ Option ) )
= ( case_option_a_a @ ( H @ F1 )
@ ^ [X5: a] : ( H @ ( F22 @ X5 ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_426_case__optionE,axiom,
! [P4: $o,Q4: a > $o,X: option_a] :
( ( case_option_o_a @ P4 @ Q4 @ X )
=> ( ( ( X = none_a )
=> ~ P4 )
=> ~ ! [Y3: a] :
( ( X
= ( some_a @ Y3 ) )
=> ~ ( Q4 @ Y3 ) ) ) ) ).
% case_optionE
thf(fact_427_option_Odisc__eq__case_I1_J,axiom,
! [Option: option_a] :
( ( Option = none_a )
= ( case_option_o_a @ $true
@ ^ [Uu: a] : $false
@ Option ) ) ).
% option.disc_eq_case(1)
thf(fact_428_option_Odisc__eq__case_I2_J,axiom,
! [Option: option_a] :
( ( Option != none_a )
= ( case_option_o_a @ $false
@ ^ [Uu: a] : $true
@ Option ) ) ).
% option.disc_eq_case(2)
thf(fact_429_Some__image__these__eq,axiom,
! [A2: set_option_a] :
( ( image_a_option_a @ some_a @ ( these_a @ A2 ) )
= ( collect_option_a
@ ^ [X5: option_a] :
( ( member_option_a @ X5 @ A2 )
& ( X5 != none_a ) ) ) ) ).
% Some_image_these_eq
thf(fact_430_inj__on__diff,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( inj_on_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% inj_on_diff
thf(fact_431_inj__Some,axiom,
! [A2: set_a] : ( inj_on_a_option_a @ some_a @ A2 ) ).
% inj_Some
thf(fact_432_assertion_Oset__intros_I1_J,axiom,
! [X21: b,X22: assertion_a_b_c_d] : ( member_b @ X21 @ ( set_as796765862704242958_b_c_d @ ( mult_b_a_c_d @ X21 @ X22 ) ) ) ).
% assertion.set_intros(1)
thf(fact_433_assertion_Oset__intros_I2_J,axiom,
! [Yb: b,X22: assertion_a_b_c_d,X21: b] :
( ( member_b @ Yb @ ( set_as796765862704242958_b_c_d @ X22 ) )
=> ( member_b @ Yb @ ( set_as796765862704242958_b_c_d @ ( mult_b_a_c_d @ X21 @ X22 ) ) ) ) ).
% assertion.set_intros(2)
thf(fact_434_assertion_Oset__intros_I3_J,axiom,
! [Yc: b,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( member_b @ Yc @ ( set_as796765862704242958_b_c_d @ X31 ) )
=> ( member_b @ Yc @ ( set_as796765862704242958_b_c_d @ ( star_a_b_c_d @ X31 @ X32 ) ) ) ) ).
% assertion.set_intros(3)
thf(fact_435_assertion_Oset__intros_I4_J,axiom,
! [Yd: b,X32: assertion_a_b_c_d,X31: assertion_a_b_c_d] :
( ( member_b @ Yd @ ( set_as796765862704242958_b_c_d @ X32 ) )
=> ( member_b @ Yd @ ( set_as796765862704242958_b_c_d @ ( star_a_b_c_d @ X31 @ X32 ) ) ) ) ).
% assertion.set_intros(4)
thf(fact_436_assertion_Oset__intros_I5_J,axiom,
! [Ye: b,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( member_b @ Ye @ ( set_as796765862704242958_b_c_d @ X41 ) )
=> ( member_b @ Ye @ ( set_as796765862704242958_b_c_d @ ( wand_a_b_c_d @ X41 @ X42 ) ) ) ) ).
% assertion.set_intros(5)
thf(fact_437_assertion_Oset__intros_I6_J,axiom,
! [Yf: b,X42: assertion_a_b_c_d,X41: assertion_a_b_c_d] :
( ( member_b @ Yf @ ( set_as796765862704242958_b_c_d @ X42 ) )
=> ( member_b @ Yf @ ( set_as796765862704242958_b_c_d @ ( wand_a_b_c_d @ X41 @ X42 ) ) ) ) ).
% assertion.set_intros(6)
thf(fact_438_assertion_Oset__intros_I14_J,axiom,
! [Yn: b,X92: assertion_a_b_c_d,X91: d] :
( ( member_b @ Yn @ ( set_as796765862704242958_b_c_d @ X92 ) )
=> ( member_b @ Yn @ ( set_as796765862704242958_b_c_d @ ( forall_d_a_b_c @ X91 @ X92 ) ) ) ) ).
% assertion.set_intros(14)
thf(fact_439_assertion_Osimps_I332_J,axiom,
! [X91: d,X92: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( forall_d_a_b_c @ X91 @ X92 ) )
= ( set_as796765862704242958_b_c_d @ X92 ) ) ).
% assertion.simps(332)
thf(fact_440_assertion_Oset__intros_I15_J,axiom,
! [Yo: b,X11: assertion_a_b_c_d] :
( ( member_b @ Yo @ ( set_as796765862704242958_b_c_d @ X11 ) )
=> ( member_b @ Yo @ ( set_as796765862704242958_b_c_d @ ( bounded_a_b_c_d @ X11 ) ) ) ) ).
% assertion.set_intros(15)
thf(fact_441_assertion_Osimps_I334_J,axiom,
! [X11: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( bounded_a_b_c_d @ X11 ) )
= ( set_as796765862704242958_b_c_d @ X11 ) ) ).
% assertion.simps(334)
thf(fact_442_assertion_Oset__intros_I9_J,axiom,
! [Yi: b,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( member_b @ Yi @ ( set_as796765862704242958_b_c_d @ X61 ) )
=> ( member_b @ Yi @ ( set_as796765862704242958_b_c_d @ ( and_a_b_c_d @ X61 @ X62 ) ) ) ) ).
% assertion.set_intros(9)
thf(fact_443_assertion_Oset__intros_I10_J,axiom,
! [Yj: b,X62: assertion_a_b_c_d,X61: assertion_a_b_c_d] :
( ( member_b @ Yj @ ( set_as796765862704242958_b_c_d @ X62 ) )
=> ( member_b @ Yj @ ( set_as796765862704242958_b_c_d @ ( and_a_b_c_d @ X61 @ X62 ) ) ) ) ).
% assertion.set_intros(10)
thf(fact_444_assertion_Oset__intros_I11_J,axiom,
! [Yk: b,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( member_b @ Yk @ ( set_as796765862704242958_b_c_d @ X71 ) )
=> ( member_b @ Yk @ ( set_as796765862704242958_b_c_d @ ( imp_a_b_c_d @ X71 @ X72 ) ) ) ) ).
% assertion.set_intros(11)
thf(fact_445_assertion_Oset__intros_I12_J,axiom,
! [Yl: b,X72: assertion_a_b_c_d,X71: assertion_a_b_c_d] :
( ( member_b @ Yl @ ( set_as796765862704242958_b_c_d @ X72 ) )
=> ( member_b @ Yl @ ( set_as796765862704242958_b_c_d @ ( imp_a_b_c_d @ X71 @ X72 ) ) ) ) ).
% assertion.set_intros(12)
thf(fact_446_assertion_Oset__intros_I13_J,axiom,
! [Ym: b,X82: assertion_a_b_c_d,X81: d] :
( ( member_b @ Ym @ ( set_as796765862704242958_b_c_d @ X82 ) )
=> ( member_b @ Ym @ ( set_as796765862704242958_b_c_d @ ( exists_d_a_b_c @ X81 @ X82 ) ) ) ) ).
% assertion.set_intros(13)
thf(fact_447_assertion_Osimps_I331_J,axiom,
! [X81: d,X82: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( exists_d_a_b_c @ X81 @ X82 ) )
= ( set_as796765862704242958_b_c_d @ X82 ) ) ).
% assertion.simps(331)
thf(fact_448_assertion_Oset__intros_I7_J,axiom,
! [Yg: b,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( member_b @ Yg @ ( set_as796765862704242958_b_c_d @ X51 ) )
=> ( member_b @ Yg @ ( set_as796765862704242958_b_c_d @ ( or_a_b_c_d @ X51 @ X52 ) ) ) ) ).
% assertion.set_intros(7)
thf(fact_449_assertion_Oset__intros_I8_J,axiom,
! [Yh: b,X52: assertion_a_b_c_d,X51: assertion_a_b_c_d] :
( ( member_b @ Yh @ ( set_as796765862704242958_b_c_d @ X52 ) )
=> ( member_b @ Yh @ ( set_as796765862704242958_b_c_d @ ( or_a_b_c_d @ X51 @ X52 ) ) ) ) ).
% assertion.set_intros(8)
thf(fact_450_assertion_Oset__intros_I16_J,axiom,
! [Yp: b,X12: assertion_a_b_c_d] :
( ( member_b @ Yp @ ( set_as796765862704242958_b_c_d @ X12 ) )
=> ( member_b @ Yp @ ( set_as796765862704242958_b_c_d @ ( wildcard_a_b_c_d @ X12 ) ) ) ) ).
% assertion.set_intros(16)
thf(fact_451_assertion_Osimps_I335_J,axiom,
! [X12: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( wildcard_a_b_c_d @ X12 ) )
= ( set_as796765862704242958_b_c_d @ X12 ) ) ).
% assertion.simps(335)
thf(fact_452_None__notin__image__Some,axiom,
! [A2: set_a] :
~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A2 ) ) ).
% None_notin_image_Some
thf(fact_453_assertion_Osimps_I324_J,axiom,
! [X1: ( d > c ) > a > $o] :
( ( set_as796765862704242958_b_c_d @ ( sem_d_c_a_b @ X1 ) )
= bot_bot_set_b ) ).
% assertion.simps(324)
thf(fact_454_assertion_Osimps_I333_J,axiom,
( ( set_as796765862704242958_b_c_d @ pred_a_b_c_d )
= bot_bot_set_b ) ).
% assertion.simps(333)
thf(fact_455_inj__on__Un,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ ( sup_sup_set_option_a @ A2 @ B2 ) )
= ( ( inj_on_option_a_a @ F2 @ A2 )
& ( inj_on_option_a_a @ F2 @ B2 )
& ( ( inf_inf_set_a @ ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ B2 ) ) @ ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ B2 @ A2 ) ) )
= bot_bot_set_a ) ) ) ).
% inj_on_Un
thf(fact_456_inj__on__Un,axiom,
! [F2: b > a,A2: set_b,B2: set_b] :
( ( inj_on_b_a @ F2 @ ( sup_sup_set_b @ A2 @ B2 ) )
= ( ( inj_on_b_a @ F2 @ A2 )
& ( inj_on_b_a @ F2 @ B2 )
& ( ( inf_inf_set_a @ ( image_b_a @ F2 @ ( minus_minus_set_b @ A2 @ B2 ) ) @ ( image_b_a @ F2 @ ( minus_minus_set_b @ B2 @ A2 ) ) )
= bot_bot_set_a ) ) ) ).
% inj_on_Un
thf(fact_457_inj__on__Un,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ ( sup_sup_set_a @ A2 @ B2 ) )
= ( ( inj_on_a_option_a @ F2 @ A2 )
& ( inj_on_a_option_a @ F2 @ B2 )
& ( ( inf_inf_set_option_a @ ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ B2 ) ) @ ( image_a_option_a @ F2 @ ( minus_minus_set_a @ B2 @ A2 ) ) )
= bot_bot_set_option_a ) ) ) ).
% inj_on_Un
thf(fact_458_inj__on__Un,axiom,
! [F2: b > option_a,A2: set_b,B2: set_b] :
( ( inj_on_b_option_a @ F2 @ ( sup_sup_set_b @ A2 @ B2 ) )
= ( ( inj_on_b_option_a @ F2 @ A2 )
& ( inj_on_b_option_a @ F2 @ B2 )
& ( ( inf_inf_set_option_a @ ( image_b_option_a @ F2 @ ( minus_minus_set_b @ A2 @ B2 ) ) @ ( image_b_option_a @ F2 @ ( minus_minus_set_b @ B2 @ A2 ) ) )
= bot_bot_set_option_a ) ) ) ).
% inj_on_Un
thf(fact_459_finite__Map__induct,axiom,
! [M: b > option_a,P4: ( b > option_a ) > $o] :
( ( finite_finite_b @ ( dom_b_a @ M ) )
=> ( ( P4
@ ^ [X5: b] : none_a )
=> ( ! [K2: b,V3: a,M3: b > option_a] :
( ( finite_finite_b @ ( dom_b_a @ M3 ) )
=> ( ~ ( member_b @ K2 @ ( dom_b_a @ M3 ) )
=> ( ( P4 @ M3 )
=> ( P4 @ ( fun_upd_b_option_a @ M3 @ K2 @ ( some_a @ V3 ) ) ) ) ) )
=> ( P4 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_460_finite__Map__induct,axiom,
! [M: option_a > option_a,P4: ( option_a > option_a ) > $o] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ M ) )
=> ( ( P4
@ ^ [X5: option_a] : none_a )
=> ( ! [K2: option_a,V3: a,M3: option_a > option_a] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ M3 ) )
=> ( ~ ( member_option_a @ K2 @ ( dom_option_a_a @ M3 ) )
=> ( ( P4 @ M3 )
=> ( P4 @ ( fun_up1079276522633388797tion_a @ M3 @ K2 @ ( some_a @ V3 ) ) ) ) ) )
=> ( P4 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_461_finite__Map__induct,axiom,
! [M: a > option_a,P4: ( a > option_a ) > $o] :
( ( finite_finite_a @ ( dom_a_a @ M ) )
=> ( ( P4
@ ^ [X5: a] : none_a )
=> ( ! [K2: a,V3: a,M3: a > option_a] :
( ( finite_finite_a @ ( dom_a_a @ M3 ) )
=> ( ~ ( member_a @ K2 @ ( dom_a_a @ M3 ) )
=> ( ( P4 @ M3 )
=> ( P4 @ ( fun_upd_a_option_a @ M3 @ K2 @ ( some_a @ V3 ) ) ) ) ) )
=> ( P4 @ M ) ) ) ) ).
% finite_Map_induct
thf(fact_462_inj__on__disjoint__Un,axiom,
! [F2: a > a,A2: set_a,G: a > a,B2: set_a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ( inj_on_a_a @ G @ B2 )
=> ( ( ( inf_inf_set_a @ ( image_a_a @ F2 @ A2 ) @ ( image_a_a @ G @ B2 ) )
= bot_bot_set_a )
=> ( inj_on_a_a
@ ^ [X5: a] : ( if_a @ ( member_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_463_inj__on__disjoint__Un,axiom,
! [F2: option_a > a,A2: set_option_a,G: option_a > a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( inj_on_option_a_a @ G @ B2 )
=> ( ( ( inf_inf_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ G @ B2 ) )
= bot_bot_set_a )
=> ( inj_on_option_a_a
@ ^ [X5: option_a] : ( if_a @ ( member_option_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_option_a @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_464_inj__on__disjoint__Un,axiom,
! [F2: b > a,A2: set_b,G: b > a,B2: set_b] :
( ( inj_on_b_a @ F2 @ A2 )
=> ( ( inj_on_b_a @ G @ B2 )
=> ( ( ( inf_inf_set_a @ ( image_b_a @ F2 @ A2 ) @ ( image_b_a @ G @ B2 ) )
= bot_bot_set_a )
=> ( inj_on_b_a
@ ^ [X5: b] : ( if_a @ ( member_b @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_b @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_465_inj__on__disjoint__Un,axiom,
! [F2: a > option_a,A2: set_a,G: a > option_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ G @ B2 )
=> ( ( ( inf_inf_set_option_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ G @ B2 ) )
= bot_bot_set_option_a )
=> ( inj_on_a_option_a
@ ^ [X5: a] : ( if_option_a @ ( member_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_466_inj__on__disjoint__Un,axiom,
! [F2: option_a > option_a,A2: set_option_a,G: option_a > option_a,B2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ A2 )
=> ( ( inj_on8559383841115902449tion_a @ G @ B2 )
=> ( ( ( inf_inf_set_option_a @ ( image_7439109396645324421tion_a @ F2 @ A2 ) @ ( image_7439109396645324421tion_a @ G @ B2 ) )
= bot_bot_set_option_a )
=> ( inj_on8559383841115902449tion_a
@ ^ [X5: option_a] : ( if_option_a @ ( member_option_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_option_a @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_467_inj__on__disjoint__Un,axiom,
! [F2: b > option_a,A2: set_b,G: b > option_a,B2: set_b] :
( ( inj_on_b_option_a @ F2 @ A2 )
=> ( ( inj_on_b_option_a @ G @ B2 )
=> ( ( ( inf_inf_set_option_a @ ( image_b_option_a @ F2 @ A2 ) @ ( image_b_option_a @ G @ B2 ) )
= bot_bot_set_option_a )
=> ( inj_on_b_option_a
@ ^ [X5: b] : ( if_option_a @ ( member_b @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_b @ A2 @ B2 ) ) ) ) ) ).
% inj_on_disjoint_Un
thf(fact_468_the__inv__into__onto,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( image_a_option_a @ ( the_in1757154643552616557on_a_a @ A2 @ F2 ) @ ( image_option_a_a @ F2 @ A2 ) )
= A2 ) ) ).
% the_inv_into_onto
thf(fact_469_the__inv__into__onto,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( image_option_a_a @ ( the_in8758012798868597241tion_a @ A2 @ F2 ) @ ( image_a_option_a @ F2 @ A2 ) )
= A2 ) ) ).
% the_inv_into_onto
thf(fact_470_notin__range__Some,axiom,
! [X: option_option_a] :
( ( ~ ( member5113800082084363315tion_a @ X @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) ) )
= ( X = none_option_a ) ) ).
% notin_range_Some
thf(fact_471_notin__range__Some,axiom,
! [X: option_a] :
( ( ~ ( member_option_a @ X @ ( image_a_option_a @ some_a @ top_top_set_a ) ) )
= ( X = none_a ) ) ).
% notin_range_Some
thf(fact_472_finite__option__UNIV,axiom,
( ( finite8114217219359860531tion_a @ top_to1659475022456381882tion_a )
= ( finite1674126218327898605tion_a @ top_top_set_option_a ) ) ).
% finite_option_UNIV
thf(fact_473_finite__option__UNIV,axiom,
( ( finite1674126218327898605tion_a @ top_top_set_option_a )
= ( finite_finite_a @ top_top_set_a ) ) ).
% finite_option_UNIV
thf(fact_474_dom__const,axiom,
! [F2: a > a] :
( ( dom_a_a
@ ^ [X5: a] : ( some_a @ ( F2 @ X5 ) ) )
= top_top_set_a ) ).
% dom_const
thf(fact_475_dom__const,axiom,
! [F2: option_a > a] :
( ( dom_option_a_a
@ ^ [X5: option_a] : ( some_a @ ( F2 @ X5 ) ) )
= top_top_set_option_a ) ).
% dom_const
thf(fact_476_finite__range__Some,axiom,
( ( finite8114217219359860531tion_a @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) )
= ( finite1674126218327898605tion_a @ top_top_set_option_a ) ) ).
% finite_range_Some
thf(fact_477_finite__range__Some,axiom,
( ( finite1674126218327898605tion_a @ ( image_a_option_a @ some_a @ top_top_set_a ) )
= ( finite_finite_a @ top_top_set_a ) ) ).
% finite_range_Some
thf(fact_478_image__Int,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( image_a_option_a @ F2 @ ( inf_inf_set_a @ A2 @ B2 ) )
= ( inf_inf_set_option_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) ) ) ) ).
% image_Int
thf(fact_479_image__Int,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( image_option_a_a @ F2 @ ( inf_inf_set_option_a @ A2 @ B2 ) )
= ( inf_inf_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) ) ) ) ).
% image_Int
thf(fact_480_the__inv__f__f,axiom,
! [F2: a > option_a,X: a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( the_in8758012798868597241tion_a @ top_top_set_a @ F2 @ ( F2 @ X ) )
= X ) ) ).
% the_inv_f_f
thf(fact_481_finite__map__freshness,axiom,
! [F2: a > option_a] :
( ( finite_finite_a @ ( dom_a_a @ F2 ) )
=> ( ~ ( finite_finite_a @ top_top_set_a )
=> ? [X4: a] :
( ( F2 @ X4 )
= none_a ) ) ) ).
% finite_map_freshness
thf(fact_482_finite__map__freshness,axiom,
! [F2: option_a > option_a] :
( ( finite1674126218327898605tion_a @ ( dom_option_a_a @ F2 ) )
=> ( ~ ( finite1674126218327898605tion_a @ top_top_set_option_a )
=> ? [X4: option_a] :
( ( F2 @ X4 )
= none_a ) ) ) ).
% finite_map_freshness
thf(fact_483_inj__on__Int,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( ( inj_on_a_option_a @ F2 @ A2 )
| ( inj_on_a_option_a @ F2 @ B2 ) )
=> ( inj_on_a_option_a @ F2 @ ( inf_inf_set_a @ A2 @ B2 ) ) ) ).
% inj_on_Int
thf(fact_484_surj__def,axiom,
! [F2: a > a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
= ( ! [Y2: a] :
? [X5: a] :
( Y2
= ( F2 @ X5 ) ) ) ) ).
% surj_def
thf(fact_485_surj__def,axiom,
! [F2: a > option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
= ( ! [Y2: option_a] :
? [X5: a] :
( Y2
= ( F2 @ X5 ) ) ) ) ).
% surj_def
thf(fact_486_surj__def,axiom,
! [F2: option_a > a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
= ( ! [Y2: a] :
? [X5: option_a] :
( Y2
= ( F2 @ X5 ) ) ) ) ).
% surj_def
thf(fact_487_surj__def,axiom,
! [F2: option_a > option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
= ( ! [Y2: option_a] :
? [X5: option_a] :
( Y2
= ( F2 @ X5 ) ) ) ) ).
% surj_def
thf(fact_488_surjI,axiom,
! [G: a > a,F2: a > a] :
( ! [X4: a] :
( ( G @ ( F2 @ X4 ) )
= X4 )
=> ( ( image_a_a @ G @ top_top_set_a )
= top_top_set_a ) ) ).
% surjI
thf(fact_489_surjI,axiom,
! [G: a > option_a,F2: option_a > a] :
( ! [X4: option_a] :
( ( G @ ( F2 @ X4 ) )
= X4 )
=> ( ( image_a_option_a @ G @ top_top_set_a )
= top_top_set_option_a ) ) ).
% surjI
thf(fact_490_surjI,axiom,
! [G: option_a > a,F2: a > option_a] :
( ! [X4: a] :
( ( G @ ( F2 @ X4 ) )
= X4 )
=> ( ( image_option_a_a @ G @ top_top_set_option_a )
= top_top_set_a ) ) ).
% surjI
thf(fact_491_surjI,axiom,
! [G: option_a > option_a,F2: option_a > option_a] :
( ! [X4: option_a] :
( ( G @ ( F2 @ X4 ) )
= X4 )
=> ( ( image_7439109396645324421tion_a @ G @ top_top_set_option_a )
= top_top_set_option_a ) ) ).
% surjI
thf(fact_492_surjE,axiom,
! [F2: a > a,Y: a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ~ ! [X4: a] :
( Y
!= ( F2 @ X4 ) ) ) ).
% surjE
thf(fact_493_surjE,axiom,
! [F2: a > option_a,Y: option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ~ ! [X4: a] :
( Y
!= ( F2 @ X4 ) ) ) ).
% surjE
thf(fact_494_surjE,axiom,
! [F2: option_a > a,Y: a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ~ ! [X4: option_a] :
( Y
!= ( F2 @ X4 ) ) ) ).
% surjE
thf(fact_495_surjE,axiom,
! [F2: option_a > option_a,Y: option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ~ ! [X4: option_a] :
( Y
!= ( F2 @ X4 ) ) ) ).
% surjE
thf(fact_496_surjD,axiom,
! [F2: a > a,Y: a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ? [X4: a] :
( Y
= ( F2 @ X4 ) ) ) ).
% surjD
thf(fact_497_surjD,axiom,
! [F2: a > option_a,Y: option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ? [X4: a] :
( Y
= ( F2 @ X4 ) ) ) ).
% surjD
thf(fact_498_surjD,axiom,
! [F2: option_a > a,Y: a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ? [X4: option_a] :
( Y
= ( F2 @ X4 ) ) ) ).
% surjD
thf(fact_499_surjD,axiom,
! [F2: option_a > option_a,Y: option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ? [X4: option_a] :
( Y
= ( F2 @ X4 ) ) ) ).
% surjD
thf(fact_500_inj__def,axiom,
! [F2: a > option_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
= ( ! [X5: a,Y2: a] :
( ( ( F2 @ X5 )
= ( F2 @ Y2 ) )
=> ( X5 = Y2 ) ) ) ) ).
% inj_def
thf(fact_501_inj__eq,axiom,
! [F2: a > option_a,X: a,Y: a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ( F2 @ X )
= ( F2 @ Y ) )
= ( X = Y ) ) ) ).
% inj_eq
thf(fact_502_injI,axiom,
! [F2: a > option_a] :
( ! [X4: a,Y3: a] :
( ( ( F2 @ X4 )
= ( F2 @ Y3 ) )
=> ( X4 = Y3 ) )
=> ( inj_on_a_option_a @ F2 @ top_top_set_a ) ) ).
% injI
thf(fact_503_injD,axiom,
! [F2: a > option_a,X: a,Y: a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ( F2 @ X )
= ( F2 @ Y ) )
=> ( X = Y ) ) ) ).
% injD
thf(fact_504_the__inv__into__f__eq,axiom,
! [F2: a > option_a,A2: set_a,X: a,Y: option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( ( F2 @ X )
= Y )
=> ( ( member_a @ X @ A2 )
=> ( ( the_in8758012798868597241tion_a @ A2 @ F2 @ Y )
= X ) ) ) ) ).
% the_inv_into_f_eq
thf(fact_505_the__inv__into__f__f,axiom,
! [F2: a > option_a,A2: set_a,X: a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( member_a @ X @ A2 )
=> ( ( the_in8758012798868597241tion_a @ A2 @ F2 @ ( F2 @ X ) )
= X ) ) ) ).
% the_inv_into_f_f
thf(fact_506_finite__range__updI,axiom,
! [F2: a > option_a,A: a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_a_option_a @ F2 @ top_top_set_a ) )
=> ( finite1674126218327898605tion_a @ ( image_a_option_a @ ( fun_upd_a_option_a @ F2 @ A @ ( some_a @ B ) ) @ top_top_set_a ) ) ) ).
% finite_range_updI
thf(fact_507_finite__range__updI,axiom,
! [F2: option_a > option_a,A: option_a,B: a] :
( ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a ) )
=> ( finite1674126218327898605tion_a @ ( image_7439109396645324421tion_a @ ( fun_up1079276522633388797tion_a @ F2 @ A @ ( some_a @ B ) ) @ top_top_set_option_a ) ) ) ).
% finite_range_updI
thf(fact_508_inj__singleton,axiom,
! [A2: set_a] :
( inj_on_a_set_a
@ ^ [X5: a] : ( insert_a @ X5 @ bot_bot_set_a )
@ A2 ) ).
% inj_singleton
thf(fact_509_inj__singleton,axiom,
! [A2: set_option_a] :
( inj_on7881382345526841553tion_a
@ ^ [X5: option_a] : ( insert_option_a @ X5 @ bot_bot_set_option_a )
@ A2 ) ).
% inj_singleton
thf(fact_510_inj__image__mem__iff,axiom,
! [F2: b > a,A: b,A2: set_b] :
( ( inj_on_b_a @ F2 @ top_top_set_b )
=> ( ( member_a @ ( F2 @ A ) @ ( image_b_a @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_511_inj__image__mem__iff,axiom,
! [F2: b > option_a,A: b,A2: set_b] :
( ( inj_on_b_option_a @ F2 @ top_top_set_b )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_b_option_a @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_512_inj__image__mem__iff,axiom,
! [F2: b > b,A: b,A2: set_b] :
( ( inj_on_b_b @ F2 @ top_top_set_b )
=> ( ( member_b @ ( F2 @ A ) @ ( image_b_b @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_513_inj__image__mem__iff,axiom,
! [F2: a > a,A: a,A2: set_a] :
( ( inj_on_a_a @ F2 @ top_top_set_a )
=> ( ( member_a @ ( F2 @ A ) @ ( image_a_a @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_514_inj__image__mem__iff,axiom,
! [F2: a > option_a,A: a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_a_option_a @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_515_inj__image__mem__iff,axiom,
! [F2: a > b,A: a,A2: set_a] :
( ( inj_on_a_b @ F2 @ top_top_set_a )
=> ( ( member_b @ ( F2 @ A ) @ ( image_a_b @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_516_inj__image__mem__iff,axiom,
! [F2: option_a > a,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( member_a @ ( F2 @ A ) @ ( image_option_a_a @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_517_inj__image__mem__iff,axiom,
! [F2: option_a > option_a,A: option_a,A2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_7439109396645324421tion_a @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_518_inj__image__mem__iff,axiom,
! [F2: option_a > b,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_b @ F2 @ top_top_set_option_a )
=> ( ( member_b @ ( F2 @ A ) @ ( image_option_a_b @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ).
% inj_image_mem_iff
thf(fact_519_inj__image__eq__iff,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ( image_a_option_a @ F2 @ A2 )
= ( image_a_option_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ).
% inj_image_eq_iff
thf(fact_520_inj__image__eq__iff,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( ( image_option_a_a @ F2 @ A2 )
= ( image_option_a_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ).
% inj_image_eq_iff
thf(fact_521_range__ex1__eq,axiom,
! [F2: a > a,B: a] :
( ( inj_on_a_a @ F2 @ top_top_set_a )
=> ( ( member_a @ B @ ( image_a_a @ F2 @ top_top_set_a ) )
= ( ? [X5: a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_522_range__ex1__eq,axiom,
! [F2: a > option_a,B: option_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( member_option_a @ B @ ( image_a_option_a @ F2 @ top_top_set_a ) )
= ( ? [X5: a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_523_range__ex1__eq,axiom,
! [F2: a > b,B: b] :
( ( inj_on_a_b @ F2 @ top_top_set_a )
=> ( ( member_b @ B @ ( image_a_b @ F2 @ top_top_set_a ) )
= ( ? [X5: a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_524_range__ex1__eq,axiom,
! [F2: option_a > a,B: a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( member_a @ B @ ( image_option_a_a @ F2 @ top_top_set_option_a ) )
= ( ? [X5: option_a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: option_a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_525_range__ex1__eq,axiom,
! [F2: option_a > option_a,B: option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
=> ( ( member_option_a @ B @ ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a ) )
= ( ? [X5: option_a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: option_a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_526_range__ex1__eq,axiom,
! [F2: option_a > b,B: b] :
( ( inj_on_option_a_b @ F2 @ top_top_set_option_a )
=> ( ( member_b @ B @ ( image_option_a_b @ F2 @ top_top_set_option_a ) )
= ( ? [X5: option_a] :
( ( B
= ( F2 @ X5 ) )
& ! [Y2: option_a] :
( ( B
= ( F2 @ Y2 ) )
=> ( Y2 = X5 ) ) ) ) ) ) ).
% range_ex1_eq
thf(fact_527_UNIV__option__conv,axiom,
( top_to1659475022456381882tion_a
= ( insert605063979879581146tion_a @ none_option_a @ ( image_2132136900116418507tion_a @ some_option_a @ top_top_set_option_a ) ) ) ).
% UNIV_option_conv
thf(fact_528_UNIV__option__conv,axiom,
( top_top_set_option_a
= ( insert_option_a @ none_a @ ( image_a_option_a @ some_a @ top_top_set_a ) ) ) ).
% UNIV_option_conv
thf(fact_529_inj__on__the__inv__into,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( inj_on_a_option_a @ ( the_in1757154643552616557on_a_a @ A2 @ F2 ) @ ( image_option_a_a @ F2 @ A2 ) ) ) ).
% inj_on_the_inv_into
thf(fact_530_inj__on__the__inv__into,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( inj_on_option_a_a @ ( the_in8758012798868597241tion_a @ A2 @ F2 ) @ ( image_a_option_a @ F2 @ A2 ) ) ) ).
% inj_on_the_inv_into
thf(fact_531_f__the__inv__into__f,axiom,
! [F2: option_a > a,A2: set_option_a,Y: a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( member_a @ Y @ ( image_option_a_a @ F2 @ A2 ) )
=> ( ( F2 @ ( the_in1757154643552616557on_a_a @ A2 @ F2 @ Y ) )
= Y ) ) ) ).
% f_the_inv_into_f
thf(fact_532_f__the__inv__into__f,axiom,
! [F2: a > option_a,A2: set_a,Y: option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( member_option_a @ Y @ ( image_a_option_a @ F2 @ A2 ) )
=> ( ( F2 @ ( the_in8758012798868597241tion_a @ A2 @ F2 @ Y ) )
= Y ) ) ) ).
% f_the_inv_into_f
thf(fact_533_image__set__diff,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ B2 ) )
= ( minus_1574173051537231627tion_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) ) ) ) ).
% image_set_diff
thf(fact_534_image__set__diff,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ B2 ) )
= ( minus_minus_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) ) ) ) ).
% image_set_diff
thf(fact_535_finite__update__induct,axiom,
! [F2: d > c,C: c,P4: ( d > c ) > $o] :
( ( finite_finite_d
@ ( collect_d
@ ^ [A6: d] :
( ( F2 @ A6 )
!= C ) ) )
=> ( ( P4
@ ^ [A6: d] : C )
=> ( ! [A5: d,B4: c,F3: d > c] :
( ( finite_finite_d
@ ( collect_d
@ ^ [C2: d] :
( ( F3 @ C2 )
!= C ) ) )
=> ( ( ( F3 @ A5 )
= C )
=> ( ( B4 != C )
=> ( ( P4 @ F3 )
=> ( P4 @ ( fun_upd_d_c @ F3 @ A5 @ B4 ) ) ) ) ) )
=> ( P4 @ F2 ) ) ) ) ).
% finite_update_induct
thf(fact_536_inj__image__Compl__subset,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ F2 @ ( uminus_uminus_set_a @ A2 ) ) @ ( uminus6205308855922866075tion_a @ ( image_a_option_a @ F2 @ A2 ) ) ) ) ).
% inj_image_Compl_subset
thf(fact_537_inj__image__Compl__subset,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ord_less_eq_set_a @ ( image_option_a_a @ F2 @ ( uminus6205308855922866075tion_a @ A2 ) ) @ ( uminus_uminus_set_a @ ( image_option_a_a @ F2 @ A2 ) ) ) ) ).
% inj_image_Compl_subset
thf(fact_538_combine__options__def,axiom,
( combine_options_a
= ( ^ [F: a > a > a,X5: option_a,Y2: option_a] :
( case_o3148979394504432965on_a_a @ Y2
@ ^ [Z: a] :
( case_o3148979394504432965on_a_a @ ( some_a @ Z )
@ ^ [Aa: a] : ( some_a @ ( F @ Z @ Aa ) )
@ Y2 )
@ X5 ) ) ) ).
% combine_options_def
thf(fact_539_map__option__case,axiom,
( map_option_a_a
= ( ^ [F: a > a] :
( case_o3148979394504432965on_a_a @ none_a
@ ^ [X5: a] : ( some_a @ ( F @ X5 ) ) ) ) ) ).
% map_option_case
thf(fact_540_map__option__eq__Some,axiom,
! [F2: a > a,Xo: option_a,Y: a] :
( ( ( map_option_a_a @ F2 @ Xo )
= ( some_a @ Y ) )
= ( ? [Z: a] :
( ( Xo
= ( some_a @ Z ) )
& ( ( F2 @ Z )
= Y ) ) ) ) ).
% map_option_eq_Some
thf(fact_541_None__eq__map__option__iff,axiom,
! [F2: a > a,X: option_a] :
( ( none_a
= ( map_option_a_a @ F2 @ X ) )
= ( X = none_a ) ) ).
% None_eq_map_option_iff
thf(fact_542_map__option__is__None,axiom,
! [F2: a > a,Opt: option_a] :
( ( ( map_option_a_a @ F2 @ Opt )
= none_a )
= ( Opt = none_a ) ) ).
% map_option_is_None
thf(fact_543_option_Omap__disc__iff,axiom,
! [F2: a > a,A: option_a] :
( ( ( map_option_a_a @ F2 @ A )
= none_a )
= ( A = none_a ) ) ).
% option.map_disc_iff
thf(fact_544_combine__options__simps_I3_J,axiom,
! [F2: a > a > a,A: a,B: a] :
( ( combine_options_a @ F2 @ ( some_a @ A ) @ ( some_a @ B ) )
= ( some_a @ ( F2 @ A @ B ) ) ) ).
% combine_options_simps(3)
thf(fact_545_combine__options__simps_I1_J,axiom,
! [F2: a > a > a,Y: option_a] :
( ( combine_options_a @ F2 @ none_a @ Y )
= Y ) ).
% combine_options_simps(1)
thf(fact_546_combine__options__simps_I2_J,axiom,
! [F2: a > a > a,X: option_a] :
( ( combine_options_a @ F2 @ X @ none_a )
= X ) ).
% combine_options_simps(2)
thf(fact_547_is__none__map__option,axiom,
! [F2: a > a,X: option_a] :
( ( is_none_a @ ( map_option_a_a @ F2 @ X ) )
= ( is_none_a @ X ) ) ).
% is_none_map_option
thf(fact_548_option_Osimps_I9_J,axiom,
! [F2: a > a,X2: a] :
( ( map_option_a_a @ F2 @ ( some_a @ X2 ) )
= ( some_a @ ( F2 @ X2 ) ) ) ).
% option.simps(9)
thf(fact_549_map__option__cong,axiom,
! [X: option_a,Y: option_a,F2: a > a,G: a > a] :
( ( X = Y )
=> ( ! [A5: a] :
( ( Y
= ( some_a @ A5 ) )
=> ( ( F2 @ A5 )
= ( G @ A5 ) ) )
=> ( ( map_option_a_a @ F2 @ X )
= ( map_option_a_a @ G @ Y ) ) ) ) ).
% map_option_cong
thf(fact_550_option_Osimps_I8_J,axiom,
! [F2: a > a] :
( ( map_option_a_a @ F2 @ none_a )
= none_a ) ).
% option.simps(8)
thf(fact_551_subset__inj__on,axiom,
! [F2: a > option_a,B2: set_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ) ).
% subset_inj_on
thf(fact_552_inj__on__subset,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( ord_less_eq_set_a @ B2 @ A2 )
=> ( inj_on_a_option_a @ F2 @ B2 ) ) ) ).
% inj_on_subset
thf(fact_553_combine__options__assoc,axiom,
! [F2: a > a > a,X: option_a,Y: option_a,Z2: option_a] :
( ! [X4: a,Y3: a,Z3: a] :
( ( F2 @ ( F2 @ X4 @ Y3 ) @ Z3 )
= ( F2 @ X4 @ ( F2 @ Y3 @ Z3 ) ) )
=> ( ( combine_options_a @ F2 @ ( combine_options_a @ F2 @ X @ Y ) @ Z2 )
= ( combine_options_a @ F2 @ X @ ( combine_options_a @ F2 @ Y @ Z2 ) ) ) ) ).
% combine_options_assoc
thf(fact_554_combine__options__commute,axiom,
! [F2: a > a > a,X: option_a,Y: option_a] :
( ! [X4: a,Y3: a] :
( ( F2 @ X4 @ Y3 )
= ( F2 @ Y3 @ X4 ) )
=> ( ( combine_options_a @ F2 @ X @ Y )
= ( combine_options_a @ F2 @ Y @ X ) ) ) ).
% combine_options_commute
thf(fact_555_combine__options__left__commute,axiom,
! [F2: a > a > a,Y: option_a,X: option_a,Z2: option_a] :
( ! [X4: a,Y3: a] :
( ( F2 @ X4 @ Y3 )
= ( F2 @ Y3 @ X4 ) )
=> ( ! [X4: a,Y3: a,Z3: a] :
( ( F2 @ ( F2 @ X4 @ Y3 ) @ Z3 )
= ( F2 @ X4 @ ( F2 @ Y3 @ Z3 ) ) )
=> ( ( combine_options_a @ F2 @ Y @ ( combine_options_a @ F2 @ X @ Z2 ) )
= ( combine_options_a @ F2 @ X @ ( combine_options_a @ F2 @ Y @ Z2 ) ) ) ) ) ).
% combine_options_left_commute
thf(fact_556_option_Omap__ident,axiom,
! [T: option_a] :
( ( map_option_a_a
@ ^ [X5: a] : X5
@ T )
= T ) ).
% option.map_ident
thf(fact_557_option_Omap__cong,axiom,
! [X: option_a,Ya: option_a,F2: a > a,G: a > a] :
( ( X = Ya )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ Ya ) )
=> ( ( F2 @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( map_option_a_a @ F2 @ X )
= ( map_option_a_a @ G @ Ya ) ) ) ) ).
% option.map_cong
thf(fact_558_option_Omap__cong0,axiom,
! [X: option_a,F2: a > a,G: a > a] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( F2 @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( map_option_a_a @ F2 @ X )
= ( map_option_a_a @ G @ X ) ) ) ).
% option.map_cong0
thf(fact_559_option_Oinj__map__strong,axiom,
! [X: option_a,Xa2: option_a,F2: a > a,Fa: a > a] :
( ! [Z3: a,Za: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( member_a @ Za @ ( set_option_a2 @ Xa2 ) )
=> ( ( ( F2 @ Z3 )
= ( Fa @ Za ) )
=> ( Z3 = Za ) ) ) )
=> ( ( ( map_option_a_a @ F2 @ X )
= ( map_option_a_a @ Fa @ Xa2 ) )
=> ( X = Xa2 ) ) ) ).
% option.inj_map_strong
thf(fact_560_option_Omap__ident__strong,axiom,
! [T: option_option_a,F2: option_a > option_a] :
( ! [Z3: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ T ) )
=> ( ( F2 @ Z3 )
= Z3 ) )
=> ( ( map_op788413144570152203tion_a @ F2 @ T )
= T ) ) ).
% option.map_ident_strong
thf(fact_561_option_Omap__ident__strong,axiom,
! [T: option_b,F2: b > b] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ T ) )
=> ( ( F2 @ Z3 )
= Z3 ) )
=> ( ( map_option_b_b @ F2 @ T )
= T ) ) ).
% option.map_ident_strong
thf(fact_562_option_Omap__ident__strong,axiom,
! [T: option_a,F2: a > a] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ T ) )
=> ( ( F2 @ Z3 )
= Z3 ) )
=> ( ( map_option_a_a @ F2 @ T )
= T ) ) ).
% option.map_ident_strong
thf(fact_563_map__option__idI,axiom,
! [X: option_option_a,F2: option_a > option_a] :
( ! [Y3: option_a] :
( ( member_option_a @ Y3 @ ( set_option_option_a2 @ X ) )
=> ( ( F2 @ Y3 )
= Y3 ) )
=> ( ( map_op788413144570152203tion_a @ F2 @ X )
= X ) ) ).
% map_option_idI
thf(fact_564_map__option__idI,axiom,
! [X: option_b,F2: b > b] :
( ! [Y3: b] :
( ( member_b @ Y3 @ ( set_option_b2 @ X ) )
=> ( ( F2 @ Y3 )
= Y3 ) )
=> ( ( map_option_b_b @ F2 @ X )
= X ) ) ).
% map_option_idI
thf(fact_565_map__option__idI,axiom,
! [X: option_a,F2: a > a] :
( ! [Y3: a] :
( ( member_a @ Y3 @ ( set_option_a2 @ X ) )
=> ( ( F2 @ Y3 )
= Y3 ) )
=> ( ( map_option_a_a @ F2 @ X )
= X ) ) ).
% map_option_idI
thf(fact_566_option_Oinj__map,axiom,
! [F2: a > option_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( inj_on2224753519991154999tion_a @ ( map_op2340691886215429841tion_a @ F2 ) @ top_top_set_option_a ) ) ).
% option.inj_map
thf(fact_567_option_Oinj__map,axiom,
! [F2: a > a] :
( ( inj_on_a_a @ F2 @ top_top_set_a )
=> ( inj_on8559383841115902449tion_a @ ( map_option_a_a @ F2 ) @ top_top_set_option_a ) ) ).
% option.inj_map
thf(fact_568_option_Oset__map,axiom,
! [F2: a > option_a,V4: option_a] :
( ( set_option_option_a2 @ ( map_op2340691886215429841tion_a @ F2 @ V4 ) )
= ( image_a_option_a @ F2 @ ( set_option_a2 @ V4 ) ) ) ).
% option.set_map
thf(fact_569_option_Oset__map,axiom,
! [F2: option_a > a,V4: option_option_a] :
( ( set_option_a2 @ ( map_op4563205767754224965on_a_a @ F2 @ V4 ) )
= ( image_option_a_a @ F2 @ ( set_option_option_a2 @ V4 ) ) ) ).
% option.set_map
thf(fact_570_option_Oset__map,axiom,
! [F2: a > a,V4: option_a] :
( ( set_option_a2 @ ( map_option_a_a @ F2 @ V4 ) )
= ( image_a_a @ F2 @ ( set_option_a2 @ V4 ) ) ) ).
% option.set_map
thf(fact_571_inj__on__image__eq__iff,axiom,
! [F2: option_a > a,C3: set_option_a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ B2 @ C3 )
=> ( ( ( image_option_a_a @ F2 @ A2 )
= ( image_option_a_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ) ) ).
% inj_on_image_eq_iff
thf(fact_572_inj__on__image__eq__iff,axiom,
! [F2: a > option_a,C3: set_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ C3 )
=> ( ( ord_less_eq_set_a @ A2 @ C3 )
=> ( ( ord_less_eq_set_a @ B2 @ C3 )
=> ( ( ( image_a_option_a @ F2 @ A2 )
= ( image_a_option_a @ F2 @ B2 ) )
= ( A2 = B2 ) ) ) ) ) ).
% inj_on_image_eq_iff
thf(fact_573_inj__on__image__mem__iff,axiom,
! [F2: a > a,B2: set_a,A: a,A2: set_a] :
( ( inj_on_a_a @ F2 @ B2 )
=> ( ( member_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_a @ ( F2 @ A ) @ ( image_a_a @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_574_inj__on__image__mem__iff,axiom,
! [F2: a > option_a,B2: set_a,A: a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ B2 )
=> ( ( member_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_a_option_a @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_575_inj__on__image__mem__iff,axiom,
! [F2: a > b,B2: set_a,A: a,A2: set_a] :
( ( inj_on_a_b @ F2 @ B2 )
=> ( ( member_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( ( member_b @ ( F2 @ A ) @ ( image_a_b @ F2 @ A2 ) )
= ( member_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_576_inj__on__image__mem__iff,axiom,
! [F2: option_a > a,B2: set_option_a,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ B2 )
=> ( ( member_option_a @ A @ B2 )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( ( member_a @ ( F2 @ A ) @ ( image_option_a_a @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_577_inj__on__image__mem__iff,axiom,
! [F2: option_a > option_a,B2: set_option_a,A: option_a,A2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ B2 )
=> ( ( member_option_a @ A @ B2 )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_7439109396645324421tion_a @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_578_inj__on__image__mem__iff,axiom,
! [F2: option_a > b,B2: set_option_a,A: option_a,A2: set_option_a] :
( ( inj_on_option_a_b @ F2 @ B2 )
=> ( ( member_option_a @ A @ B2 )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( ( member_b @ ( F2 @ A ) @ ( image_option_a_b @ F2 @ A2 ) )
= ( member_option_a @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_579_inj__on__image__mem__iff,axiom,
! [F2: b > a,B2: set_b,A: b,A2: set_b] :
( ( inj_on_b_a @ F2 @ B2 )
=> ( ( member_b @ A @ B2 )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( ( member_a @ ( F2 @ A ) @ ( image_b_a @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_580_inj__on__image__mem__iff,axiom,
! [F2: b > option_a,B2: set_b,A: b,A2: set_b] :
( ( inj_on_b_option_a @ F2 @ B2 )
=> ( ( member_b @ A @ B2 )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( ( member_option_a @ ( F2 @ A ) @ ( image_b_option_a @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_581_inj__on__image__mem__iff,axiom,
! [F2: b > b,B2: set_b,A: b,A2: set_b] :
( ( inj_on_b_b @ F2 @ B2 )
=> ( ( member_b @ A @ B2 )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( ( member_b @ ( F2 @ A ) @ ( image_b_b @ F2 @ A2 ) )
= ( member_b @ A @ A2 ) ) ) ) ) ).
% inj_on_image_mem_iff
thf(fact_582_option_Omap__sel,axiom,
! [A: option_a,F2: a > a] :
( ( A != none_a )
=> ( ( the_a2 @ ( map_option_a_a @ F2 @ A ) )
= ( F2 @ ( the_a2 @ A ) ) ) ) ).
% option.map_sel
thf(fact_583_the__map__option,axiom,
! [X: option_a,F2: a > a] :
( ~ ( is_none_a @ X )
=> ( ( the_a2 @ ( map_option_a_a @ F2 @ X ) )
= ( F2 @ ( the_a2 @ X ) ) ) ) ).
% the_map_option
thf(fact_584_inj__image__subset__iff,axiom,
! [F2: a > option_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) )
= ( ord_less_eq_set_a @ A2 @ B2 ) ) ) ).
% inj_image_subset_iff
thf(fact_585_inj__image__subset__iff,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( ord_less_eq_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) )
= ( ord_le1955136853071979460tion_a @ A2 @ B2 ) ) ) ).
% inj_image_subset_iff
thf(fact_586_inj__on__image__Int,axiom,
! [F2: option_a > a,C3: set_option_a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ B2 @ C3 )
=> ( ( image_option_a_a @ F2 @ ( inf_inf_set_option_a @ A2 @ B2 ) )
= ( inf_inf_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) ) ) ) ) ) ).
% inj_on_image_Int
thf(fact_587_inj__on__image__Int,axiom,
! [F2: a > option_a,C3: set_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ C3 )
=> ( ( ord_less_eq_set_a @ A2 @ C3 )
=> ( ( ord_less_eq_set_a @ B2 @ C3 )
=> ( ( image_a_option_a @ F2 @ ( inf_inf_set_a @ A2 @ B2 ) )
= ( inf_inf_set_option_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) ) ) ) ) ) ).
% inj_on_image_Int
thf(fact_588_inj__on__image__set__diff,axiom,
! [F2: option_a > a,C3: set_option_a,A2: set_option_a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ ( minus_1574173051537231627tion_a @ A2 @ B2 ) @ C3 )
=> ( ( ord_le1955136853071979460tion_a @ B2 @ C3 )
=> ( ( image_option_a_a @ F2 @ ( minus_1574173051537231627tion_a @ A2 @ B2 ) )
= ( minus_minus_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) ) ) ) ) ) ).
% inj_on_image_set_diff
thf(fact_589_inj__on__image__set__diff,axiom,
! [F2: a > option_a,C3: set_a,A2: set_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ C3 )
=> ( ( ord_less_eq_set_a @ ( minus_minus_set_a @ A2 @ B2 ) @ C3 )
=> ( ( ord_less_eq_set_a @ B2 @ C3 )
=> ( ( image_a_option_a @ F2 @ ( minus_minus_set_a @ A2 @ B2 ) )
= ( minus_1574173051537231627tion_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) ) ) ) ) ) ).
% inj_on_image_set_diff
thf(fact_590_surj__Compl__image__subset,axiom,
! [F2: a > a,A2: set_a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ ( image_a_a @ F2 @ A2 ) ) @ ( image_a_a @ F2 @ ( uminus_uminus_set_a @ A2 ) ) ) ) ).
% surj_Compl_image_subset
thf(fact_591_surj__Compl__image__subset,axiom,
! [F2: a > option_a,A2: set_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ord_le1955136853071979460tion_a @ ( uminus6205308855922866075tion_a @ ( image_a_option_a @ F2 @ A2 ) ) @ ( image_a_option_a @ F2 @ ( uminus_uminus_set_a @ A2 ) ) ) ) ).
% surj_Compl_image_subset
thf(fact_592_surj__Compl__image__subset,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ ( image_option_a_a @ F2 @ A2 ) ) @ ( image_option_a_a @ F2 @ ( uminus6205308855922866075tion_a @ A2 ) ) ) ) ).
% surj_Compl_image_subset
thf(fact_593_surj__Compl__image__subset,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ord_le1955136853071979460tion_a @ ( uminus6205308855922866075tion_a @ ( image_7439109396645324421tion_a @ F2 @ A2 ) ) @ ( image_7439109396645324421tion_a @ F2 @ ( uminus6205308855922866075tion_a @ A2 ) ) ) ) ).
% surj_Compl_image_subset
thf(fact_594_the__inv__into__into,axiom,
! [F2: a > a,A2: set_a,X: a,B2: set_a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ( member_a @ X @ ( image_a_a @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( member_a @ ( the_inv_into_a_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_595_the__inv__into__into,axiom,
! [F2: option_a > a,A2: set_option_a,X: a,B2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( member_a @ X @ ( image_option_a_a @ F2 @ A2 ) )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( member_option_a @ ( the_in1757154643552616557on_a_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_596_the__inv__into__into,axiom,
! [F2: b > a,A2: set_b,X: a,B2: set_b] :
( ( inj_on_b_a @ F2 @ A2 )
=> ( ( member_a @ X @ ( image_b_a @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( member_b @ ( the_inv_into_b_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_597_the__inv__into__into,axiom,
! [F2: a > option_a,A2: set_a,X: option_a,B2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( member_option_a @ X @ ( image_a_option_a @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( member_a @ ( the_in8758012798868597241tion_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_598_the__inv__into__into,axiom,
! [F2: option_a > option_a,A2: set_option_a,X: option_a,B2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ A2 )
=> ( ( member_option_a @ X @ ( image_7439109396645324421tion_a @ F2 @ A2 ) )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( member_option_a @ ( the_in2538339130118444083tion_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_599_the__inv__into__into,axiom,
! [F2: b > option_a,A2: set_b,X: option_a,B2: set_b] :
( ( inj_on_b_option_a @ F2 @ A2 )
=> ( ( member_option_a @ X @ ( image_b_option_a @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( member_b @ ( the_in5672256556878602680tion_a @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_600_the__inv__into__into,axiom,
! [F2: a > b,A2: set_a,X: b,B2: set_a] :
( ( inj_on_a_b @ F2 @ A2 )
=> ( ( member_b @ X @ ( image_a_b @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_a @ A2 @ B2 )
=> ( member_a @ ( the_inv_into_a_b @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_601_the__inv__into__into,axiom,
! [F2: option_a > b,A2: set_option_a,X: b,B2: set_option_a] :
( ( inj_on_option_a_b @ F2 @ A2 )
=> ( ( member_b @ X @ ( image_option_a_b @ F2 @ A2 ) )
=> ( ( ord_le1955136853071979460tion_a @ A2 @ B2 )
=> ( member_option_a @ ( the_in1757154643552616558on_a_b @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_602_the__inv__into__into,axiom,
! [F2: b > b,A2: set_b,X: b,B2: set_b] :
( ( inj_on_b_b @ F2 @ A2 )
=> ( ( member_b @ X @ ( image_b_b @ F2 @ A2 ) )
=> ( ( ord_less_eq_set_b @ A2 @ B2 )
=> ( member_b @ ( the_inv_into_b_b @ A2 @ F2 @ X ) @ B2 ) ) ) ) ).
% the_inv_into_into
thf(fact_603_vimage__subsetI,axiom,
! [F2: a > option_a,B2: set_option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ord_le1955136853071979460tion_a @ B2 @ ( image_a_option_a @ F2 @ A2 ) )
=> ( ord_less_eq_set_a @ ( vimage_a_option_a @ F2 @ B2 ) @ A2 ) ) ) ).
% vimage_subsetI
thf(fact_604_vimage__subsetI,axiom,
! [F2: option_a > a,B2: set_a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( ord_less_eq_set_a @ B2 @ ( image_option_a_a @ F2 @ A2 ) )
=> ( ord_le1955136853071979460tion_a @ ( vimage_option_a_a @ F2 @ B2 ) @ A2 ) ) ) ).
% vimage_subsetI
thf(fact_605_option_Othe__def,axiom,
( the_a2
= ( case_option_a_a @ undefined_a
@ ^ [X24: a] : X24 ) ) ).
% option.the_def
thf(fact_606_comp__apply,axiom,
( comp_option_a_a_a
= ( ^ [F: option_a > a,G2: a > option_a,X5: a] : ( F @ ( G2 @ X5 ) ) ) ) ).
% comp_apply
thf(fact_607_case__map__option,axiom,
! [G: a,H: option_a > a,F2: a > option_a,X: option_a] :
( ( case_o926465512965637841tion_a @ G @ H @ ( map_op2340691886215429841tion_a @ F2 @ X ) )
= ( case_option_a_a @ G @ ( comp_option_a_a_a @ H @ F2 ) @ X ) ) ).
% case_map_option
thf(fact_608_case__map__option,axiom,
! [G: $o,H: a > $o,F2: a > a,X: option_a] :
( ( case_option_o_a @ G @ H @ ( map_option_a_a @ F2 @ X ) )
= ( case_option_o_a @ G @ ( comp_a_o_a @ H @ F2 ) @ X ) ) ).
% case_map_option
thf(fact_609_case__map__option,axiom,
! [G: option_a,H: a > option_a,F2: a > a,X: option_a] :
( ( case_o3148979394504432965on_a_a @ G @ H @ ( map_option_a_a @ F2 @ X ) )
= ( case_o3148979394504432965on_a_a @ G @ ( comp_a_option_a_a @ H @ F2 ) @ X ) ) ).
% case_map_option
thf(fact_610_case__map__option,axiom,
! [G: a,H: a > a,F2: a > a,X: option_a] :
( ( case_option_a_a @ G @ H @ ( map_option_a_a @ F2 @ X ) )
= ( case_option_a_a @ G @ ( comp_a_a_a @ H @ F2 ) @ X ) ) ).
% case_map_option
thf(fact_611_inj__on__imageI2,axiom,
! [F4: option_a > a,F2: a > option_a,A2: set_a] :
( ( inj_on_a_a @ ( comp_option_a_a_a @ F4 @ F2 ) @ A2 )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ).
% inj_on_imageI2
thf(fact_612_inj__on__imageI2,axiom,
! [F4: option_a > option_a,F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ ( comp_o6087033147929006299on_a_a @ F4 @ F2 ) @ A2 )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ).
% inj_on_imageI2
thf(fact_613_map__option_Ocomp,axiom,
! [F2: option_a > a,G: a > option_a] :
( ( comp_o1254687777855551975tion_a @ ( map_op4563205767754224965on_a_a @ F2 ) @ ( map_op2340691886215429841tion_a @ G ) )
= ( map_option_a_a @ ( comp_option_a_a_a @ F2 @ G ) ) ) ).
% map_option.comp
thf(fact_614_map__option_Ocomp,axiom,
! [F2: a > a,G: a > a] :
( ( comp_o3154387707078715297tion_a @ ( map_option_a_a @ F2 ) @ ( map_option_a_a @ G ) )
= ( map_option_a_a @ ( comp_a_a_a @ F2 @ G ) ) ) ).
% map_option.comp
thf(fact_615_option_Omap__comp,axiom,
! [G: option_a > a,F2: a > option_a,V4: option_a] :
( ( map_op4563205767754224965on_a_a @ G @ ( map_op2340691886215429841tion_a @ F2 @ V4 ) )
= ( map_option_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ V4 ) ) ).
% option.map_comp
thf(fact_616_option_Omap__comp,axiom,
! [G: a > a,F2: a > a,V4: option_a] :
( ( map_option_a_a @ G @ ( map_option_a_a @ F2 @ V4 ) )
= ( map_option_a_a @ ( comp_a_a_a @ G @ F2 ) @ V4 ) ) ).
% option.map_comp
thf(fact_617_map__option_Ocompositionality,axiom,
! [F2: option_a > a,G: a > option_a,Option: option_a] :
( ( map_op4563205767754224965on_a_a @ F2 @ ( map_op2340691886215429841tion_a @ G @ Option ) )
= ( map_option_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ Option ) ) ).
% map_option.compositionality
thf(fact_618_map__option_Ocompositionality,axiom,
! [F2: a > a,G: a > a,Option: option_a] :
( ( map_option_a_a @ F2 @ ( map_option_a_a @ G @ Option ) )
= ( map_option_a_a @ ( comp_a_a_a @ F2 @ G ) @ Option ) ) ).
% map_option.compositionality
thf(fact_619_comp__eq__dest__lhs,axiom,
! [A: option_a > a,B: a > option_a,C: a > a,V4: a] :
( ( ( comp_option_a_a_a @ A @ B )
= C )
=> ( ( A @ ( B @ V4 ) )
= ( C @ V4 ) ) ) ).
% comp_eq_dest_lhs
thf(fact_620_comp__eq__elim,axiom,
! [A: option_a > a,B: a > option_a,C: option_a > a,D: a > option_a] :
( ( ( comp_option_a_a_a @ A @ B )
= ( comp_option_a_a_a @ C @ D ) )
=> ! [V5: a] :
( ( A @ ( B @ V5 ) )
= ( C @ ( D @ V5 ) ) ) ) ).
% comp_eq_elim
thf(fact_621_comp__eq__dest,axiom,
! [A: option_a > a,B: a > option_a,C: option_a > a,D: a > option_a,V4: a] :
( ( ( comp_option_a_a_a @ A @ B )
= ( comp_option_a_a_a @ C @ D ) )
=> ( ( A @ ( B @ V4 ) )
= ( C @ ( D @ V4 ) ) ) ) ).
% comp_eq_dest
thf(fact_622_vimage__comp,axiom,
! [F2: a > option_a,G: option_a > a,X: set_a] :
( ( vimage_a_option_a @ F2 @ ( vimage_option_a_a @ G @ X ) )
= ( vimage_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ X ) ) ).
% vimage_comp
thf(fact_623_comp__assoc,axiom,
! [F2: option_a > a,G: a > option_a,H: a > a] :
( ( comp_a_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ H )
= ( comp_option_a_a_a @ F2 @ ( comp_a_option_a_a @ G @ H ) ) ) ).
% comp_assoc
thf(fact_624_comp__assoc,axiom,
! [F2: a > a,G: option_a > a,H: a > option_a] :
( ( comp_option_a_a_a @ ( comp_a_a_option_a @ F2 @ G ) @ H )
= ( comp_a_a_a @ F2 @ ( comp_option_a_a_a @ G @ H ) ) ) ).
% comp_assoc
thf(fact_625_comp__assoc,axiom,
! [F2: option_a > a,G: option_a > option_a,H: a > option_a] :
( ( comp_option_a_a_a @ ( comp_o3864519266390211175tion_a @ F2 @ G ) @ H )
= ( comp_option_a_a_a @ F2 @ ( comp_o6087033147929006299on_a_a @ G @ H ) ) ) ).
% comp_assoc
thf(fact_626_comp__def,axiom,
( comp_option_a_a_a
= ( ^ [F: option_a > a,G2: a > option_a,X5: a] : ( F @ ( G2 @ X5 ) ) ) ) ).
% comp_def
thf(fact_627_set_Ocompositionality,axiom,
! [F2: a > option_a,G: option_a > a,Set: set_a] :
( ( vimage_a_option_a @ F2 @ ( vimage_option_a_a @ G @ Set ) )
= ( vimage_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ Set ) ) ).
% set.compositionality
thf(fact_628_set_Ocomp,axiom,
! [F2: a > option_a,G: option_a > a] :
( ( comp_s1419921648917501825_set_a @ ( vimage_a_option_a @ F2 ) @ ( vimage_option_a_a @ G ) )
= ( vimage_a_a @ ( comp_option_a_a_a @ G @ F2 ) ) ) ).
% set.comp
thf(fact_629_fun__upd__comp,axiom,
! [F2: option_a > a,G: a > option_a,X: a,Y: option_a] :
( ( comp_option_a_a_a @ F2 @ ( fun_upd_a_option_a @ G @ X @ Y ) )
= ( fun_upd_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ X @ ( F2 @ Y ) ) ) ).
% fun_upd_comp
thf(fact_630_fun__upd__comp,axiom,
! [F2: c > c,G: d > c,X: d,Y: c] :
( ( comp_c_c_d @ F2 @ ( fun_upd_d_c @ G @ X @ Y ) )
= ( fun_upd_d_c @ ( comp_c_c_d @ F2 @ G ) @ X @ ( F2 @ Y ) ) ) ).
% fun_upd_comp
thf(fact_631_image__eq__imp__comp,axiom,
! [F2: option_a > option_a,A2: set_option_a,G: a > option_a,B2: set_a,H: option_a > a] :
( ( ( image_7439109396645324421tion_a @ F2 @ A2 )
= ( image_a_option_a @ G @ B2 ) )
=> ( ( image_option_a_a @ ( comp_o3864519266390211175tion_a @ H @ F2 ) @ A2 )
= ( image_a_a @ ( comp_option_a_a_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_632_image__eq__imp__comp,axiom,
! [F2: a > a,A2: set_a,G: option_a > a,B2: set_option_a,H: a > option_a] :
( ( ( image_a_a @ F2 @ A2 )
= ( image_option_a_a @ G @ B2 ) )
=> ( ( image_a_option_a @ ( comp_a_option_a_a @ H @ F2 ) @ A2 )
= ( image_7439109396645324421tion_a @ ( comp_a6249931511552232923tion_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_633_image__eq__imp__comp,axiom,
! [F2: a > option_a,A2: set_a,G: option_a > option_a,B2: set_option_a,H: option_a > a] :
( ( ( image_a_option_a @ F2 @ A2 )
= ( image_7439109396645324421tion_a @ G @ B2 ) )
=> ( ( image_a_a @ ( comp_option_a_a_a @ H @ F2 ) @ A2 )
= ( image_option_a_a @ ( comp_o3864519266390211175tion_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_634_image__eq__imp__comp,axiom,
! [F2: a > option_a,A2: set_a,G: a > option_a,B2: set_a,H: option_a > a] :
( ( ( image_a_option_a @ F2 @ A2 )
= ( image_a_option_a @ G @ B2 ) )
=> ( ( image_a_a @ ( comp_option_a_a_a @ H @ F2 ) @ A2 )
= ( image_a_a @ ( comp_option_a_a_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_635_image__eq__imp__comp,axiom,
! [F2: a > option_a,A2: set_a,G: a > option_a,B2: set_a,H: option_a > option_a] :
( ( ( image_a_option_a @ F2 @ A2 )
= ( image_a_option_a @ G @ B2 ) )
=> ( ( image_a_option_a @ ( comp_o6087033147929006299on_a_a @ H @ F2 ) @ A2 )
= ( image_a_option_a @ ( comp_o6087033147929006299on_a_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_636_image__eq__imp__comp,axiom,
! [F2: option_a > a,A2: set_option_a,G: a > a,B2: set_a,H: a > option_a] :
( ( ( image_option_a_a @ F2 @ A2 )
= ( image_a_a @ G @ B2 ) )
=> ( ( image_7439109396645324421tion_a @ ( comp_a6249931511552232923tion_a @ H @ F2 ) @ A2 )
= ( image_a_option_a @ ( comp_a_option_a_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_637_image__eq__imp__comp,axiom,
! [F2: option_a > a,A2: set_option_a,G: option_a > a,B2: set_option_a,H: a > a] :
( ( ( image_option_a_a @ F2 @ A2 )
= ( image_option_a_a @ G @ B2 ) )
=> ( ( image_option_a_a @ ( comp_a_a_option_a @ H @ F2 ) @ A2 )
= ( image_option_a_a @ ( comp_a_a_option_a @ H @ G ) @ B2 ) ) ) ).
% image_eq_imp_comp
thf(fact_638_image__comp,axiom,
! [F2: option_a > option_a,G: a > option_a,R: set_a] :
( ( image_7439109396645324421tion_a @ F2 @ ( image_a_option_a @ G @ R ) )
= ( image_a_option_a @ ( comp_o6087033147929006299on_a_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_639_image__comp,axiom,
! [F2: a > a,G: option_a > a,R: set_option_a] :
( ( image_a_a @ F2 @ ( image_option_a_a @ G @ R ) )
= ( image_option_a_a @ ( comp_a_a_option_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_640_image__comp,axiom,
! [F2: a > option_a,G: a > a,R: set_a] :
( ( image_a_option_a @ F2 @ ( image_a_a @ G @ R ) )
= ( image_a_option_a @ ( comp_a_option_a_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_641_image__comp,axiom,
! [F2: a > option_a,G: option_a > a,R: set_option_a] :
( ( image_a_option_a @ F2 @ ( image_option_a_a @ G @ R ) )
= ( image_7439109396645324421tion_a @ ( comp_a6249931511552232923tion_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_642_image__comp,axiom,
! [F2: option_a > a,G: option_a > option_a,R: set_option_a] :
( ( image_option_a_a @ F2 @ ( image_7439109396645324421tion_a @ G @ R ) )
= ( image_option_a_a @ ( comp_o3864519266390211175tion_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_643_image__comp,axiom,
! [F2: option_a > a,G: a > option_a,R: set_a] :
( ( image_option_a_a @ F2 @ ( image_a_option_a @ G @ R ) )
= ( image_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ R ) ) ).
% image_comp
thf(fact_644_surj__image__vimage__eq,axiom,
! [F2: a > a,A2: set_a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ( image_a_a @ F2 @ ( vimage_a_a @ F2 @ A2 ) )
= A2 ) ) ).
% surj_image_vimage_eq
thf(fact_645_surj__image__vimage__eq,axiom,
! [F2: a > option_a,A2: set_option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ( image_a_option_a @ F2 @ ( vimage_a_option_a @ F2 @ A2 ) )
= A2 ) ) ).
% surj_image_vimage_eq
thf(fact_646_surj__image__vimage__eq,axiom,
! [F2: option_a > a,A2: set_a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ( image_option_a_a @ F2 @ ( vimage_option_a_a @ F2 @ A2 ) )
= A2 ) ) ).
% surj_image_vimage_eq
thf(fact_647_surj__image__vimage__eq,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ F2 @ ( vimage1562710927270423099tion_a @ F2 @ A2 ) )
= A2 ) ) ).
% surj_image_vimage_eq
thf(fact_648_comp__surj,axiom,
! [F2: a > a,G: a > a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ( ( image_a_a @ G @ top_top_set_a )
= top_top_set_a )
=> ( ( image_a_a @ ( comp_a_a_a @ G @ F2 ) @ top_top_set_a )
= top_top_set_a ) ) ) ).
% comp_surj
thf(fact_649_comp__surj,axiom,
! [F2: a > a,G: a > option_a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ( ( image_a_option_a @ G @ top_top_set_a )
= top_top_set_option_a )
=> ( ( image_a_option_a @ ( comp_a_option_a_a @ G @ F2 ) @ top_top_set_a )
= top_top_set_option_a ) ) ) ).
% comp_surj
thf(fact_650_comp__surj,axiom,
! [F2: a > option_a,G: option_a > a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ( ( image_option_a_a @ G @ top_top_set_option_a )
= top_top_set_a )
=> ( ( image_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ top_top_set_a )
= top_top_set_a ) ) ) ).
% comp_surj
thf(fact_651_comp__surj,axiom,
! [F2: a > option_a,G: option_a > option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ( ( image_7439109396645324421tion_a @ G @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( image_a_option_a @ ( comp_o6087033147929006299on_a_a @ G @ F2 ) @ top_top_set_a )
= top_top_set_option_a ) ) ) ).
% comp_surj
thf(fact_652_comp__surj,axiom,
! [F2: option_a > a,G: a > a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ( ( image_a_a @ G @ top_top_set_a )
= top_top_set_a )
=> ( ( image_option_a_a @ ( comp_a_a_option_a @ G @ F2 ) @ top_top_set_option_a )
= top_top_set_a ) ) ) ).
% comp_surj
thf(fact_653_comp__surj,axiom,
! [F2: option_a > a,G: a > option_a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ( ( image_a_option_a @ G @ top_top_set_a )
= top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ ( comp_a6249931511552232923tion_a @ G @ F2 ) @ top_top_set_option_a )
= top_top_set_option_a ) ) ) ).
% comp_surj
thf(fact_654_comp__surj,axiom,
! [F2: option_a > option_a,G: option_a > a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( ( image_option_a_a @ G @ top_top_set_option_a )
= top_top_set_a )
=> ( ( image_option_a_a @ ( comp_o3864519266390211175tion_a @ G @ F2 ) @ top_top_set_option_a )
= top_top_set_a ) ) ) ).
% comp_surj
thf(fact_655_comp__surj,axiom,
! [F2: option_a > option_a,G: option_a > option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( ( image_7439109396645324421tion_a @ G @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ ( comp_o3154387707078715297tion_a @ G @ F2 ) @ top_top_set_option_a )
= top_top_set_option_a ) ) ) ).
% comp_surj
thf(fact_656_comp__inj__on__iff,axiom,
! [F2: option_a > a,A2: set_option_a,F4: a > option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ F4 @ ( image_option_a_a @ F2 @ A2 ) )
= ( inj_on8559383841115902449tion_a @ ( comp_a6249931511552232923tion_a @ F4 @ F2 ) @ A2 ) ) ) ).
% comp_inj_on_iff
thf(fact_657_comp__inj__on__iff,axiom,
! [F2: a > a,A2: set_a,F4: a > option_a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ F4 @ ( image_a_a @ F2 @ A2 ) )
= ( inj_on_a_option_a @ ( comp_a_option_a_a @ F4 @ F2 ) @ A2 ) ) ) ).
% comp_inj_on_iff
thf(fact_658_comp__inj__on__iff,axiom,
! [F2: a > option_a,A2: set_a,F4: option_a > a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( inj_on_option_a_a @ F4 @ ( image_a_option_a @ F2 @ A2 ) )
= ( inj_on_a_a @ ( comp_option_a_a_a @ F4 @ F2 ) @ A2 ) ) ) ).
% comp_inj_on_iff
thf(fact_659_comp__inj__on__iff,axiom,
! [F2: a > option_a,A2: set_a,F4: option_a > option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( inj_on8559383841115902449tion_a @ F4 @ ( image_a_option_a @ F2 @ A2 ) )
= ( inj_on_a_option_a @ ( comp_o6087033147929006299on_a_a @ F4 @ F2 ) @ A2 ) ) ) ).
% comp_inj_on_iff
thf(fact_660_inj__on__imageI,axiom,
! [G: option_a > a,F2: a > option_a,A2: set_a] :
( ( inj_on_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ A2 )
=> ( inj_on_option_a_a @ G @ ( image_a_option_a @ F2 @ A2 ) ) ) ).
% inj_on_imageI
thf(fact_661_inj__on__imageI,axiom,
! [G: a > option_a,F2: option_a > a,A2: set_option_a] :
( ( inj_on8559383841115902449tion_a @ ( comp_a6249931511552232923tion_a @ G @ F2 ) @ A2 )
=> ( inj_on_a_option_a @ G @ ( image_option_a_a @ F2 @ A2 ) ) ) ).
% inj_on_imageI
thf(fact_662_inj__on__imageI,axiom,
! [G: option_a > option_a,F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ ( comp_o6087033147929006299on_a_a @ G @ F2 ) @ A2 )
=> ( inj_on8559383841115902449tion_a @ G @ ( image_a_option_a @ F2 @ A2 ) ) ) ).
% inj_on_imageI
thf(fact_663_inj__on__imageI,axiom,
! [G: a > option_a,F2: a > a,A2: set_a] :
( ( inj_on_a_option_a @ ( comp_a_option_a_a @ G @ F2 ) @ A2 )
=> ( inj_on_a_option_a @ G @ ( image_a_a @ F2 @ A2 ) ) ) ).
% inj_on_imageI
thf(fact_664_comp__inj__on,axiom,
! [F2: option_a > a,A2: set_option_a,G: a > option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ G @ ( image_option_a_a @ F2 @ A2 ) )
=> ( inj_on8559383841115902449tion_a @ ( comp_a6249931511552232923tion_a @ G @ F2 ) @ A2 ) ) ) ).
% comp_inj_on
thf(fact_665_comp__inj__on,axiom,
! [F2: a > a,A2: set_a,G: a > option_a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ( inj_on_a_option_a @ G @ ( image_a_a @ F2 @ A2 ) )
=> ( inj_on_a_option_a @ ( comp_a_option_a_a @ G @ F2 ) @ A2 ) ) ) ).
% comp_inj_on
thf(fact_666_comp__inj__on,axiom,
! [F2: a > option_a,A2: set_a,G: option_a > a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( inj_on_option_a_a @ G @ ( image_a_option_a @ F2 @ A2 ) )
=> ( inj_on_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ A2 ) ) ) ).
% comp_inj_on
thf(fact_667_comp__inj__on,axiom,
! [F2: a > option_a,A2: set_a,G: option_a > option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( inj_on8559383841115902449tion_a @ G @ ( image_a_option_a @ F2 @ A2 ) )
=> ( inj_on_a_option_a @ ( comp_o6087033147929006299on_a_a @ G @ F2 ) @ A2 ) ) ) ).
% comp_inj_on
thf(fact_668_inj__compose,axiom,
! [F2: a > option_a,G: a > a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( inj_on_a_a @ G @ top_top_set_a )
=> ( inj_on_a_option_a @ ( comp_a_option_a_a @ F2 @ G ) @ top_top_set_a ) ) ) ).
% inj_compose
thf(fact_669_inj__compose,axiom,
! [F2: a > option_a,G: option_a > a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( inj_on_option_a_a @ G @ top_top_set_option_a )
=> ( inj_on8559383841115902449tion_a @ ( comp_a6249931511552232923tion_a @ F2 @ G ) @ top_top_set_option_a ) ) ) ).
% inj_compose
thf(fact_670_inj__compose,axiom,
! [F2: option_a > a,G: a > option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( inj_on_a_option_a @ G @ top_top_set_a )
=> ( inj_on_a_a @ ( comp_option_a_a_a @ F2 @ G ) @ top_top_set_a ) ) ) ).
% inj_compose
thf(fact_671_inj__compose,axiom,
! [F2: option_a > option_a,G: a > option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
=> ( ( inj_on_a_option_a @ G @ top_top_set_a )
=> ( inj_on_a_option_a @ ( comp_o6087033147929006299on_a_a @ F2 @ G ) @ top_top_set_a ) ) ) ).
% inj_compose
thf(fact_672_bind__map__option,axiom,
! [F2: a > a,X: option_a,G: a > option_a] :
( ( bind_a_a @ ( map_option_a_a @ F2 @ X ) @ G )
= ( bind_a_a @ X @ ( comp_a_option_a_a @ G @ F2 ) ) ) ).
% bind_map_option
thf(fact_673_map__option__bind,axiom,
! [F2: a > a,X: option_a,G: a > option_a] :
( ( map_option_a_a @ F2 @ ( bind_a_a @ X @ G ) )
= ( bind_a_a @ X @ ( comp_o6087033147929006299on_a_a @ ( map_option_a_a @ F2 ) @ G ) ) ) ).
% map_option_bind
thf(fact_674_surj__vimage__empty,axiom,
! [F2: a > a,A2: set_a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ( ( vimage_a_a @ F2 @ A2 )
= bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) ) ).
% surj_vimage_empty
thf(fact_675_surj__vimage__empty,axiom,
! [F2: a > option_a,A2: set_option_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ( ( vimage_a_option_a @ F2 @ A2 )
= bot_bot_set_a )
= ( A2 = bot_bot_set_option_a ) ) ) ).
% surj_vimage_empty
thf(fact_676_surj__vimage__empty,axiom,
! [F2: option_a > a,A2: set_a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ( ( vimage_option_a_a @ F2 @ A2 )
= bot_bot_set_option_a )
= ( A2 = bot_bot_set_a ) ) ) ).
% surj_vimage_empty
thf(fact_677_surj__vimage__empty,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( ( vimage1562710927270423099tion_a @ F2 @ A2 )
= bot_bot_set_option_a )
= ( A2 = bot_bot_set_option_a ) ) ) ).
% surj_vimage_empty
thf(fact_678_vimage__subsetD,axiom,
! [F2: a > a,B2: set_a,A2: set_a] :
( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( ( ord_less_eq_set_a @ ( vimage_a_a @ F2 @ B2 ) @ A2 )
=> ( ord_less_eq_set_a @ B2 @ ( image_a_a @ F2 @ A2 ) ) ) ) ).
% vimage_subsetD
thf(fact_679_vimage__subsetD,axiom,
! [F2: a > option_a,B2: set_option_a,A2: set_a] :
( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( ( ord_less_eq_set_a @ ( vimage_a_option_a @ F2 @ B2 ) @ A2 )
=> ( ord_le1955136853071979460tion_a @ B2 @ ( image_a_option_a @ F2 @ A2 ) ) ) ) ).
% vimage_subsetD
thf(fact_680_vimage__subsetD,axiom,
! [F2: option_a > a,B2: set_a,A2: set_option_a] :
( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( ( ord_le1955136853071979460tion_a @ ( vimage_option_a_a @ F2 @ B2 ) @ A2 )
=> ( ord_less_eq_set_a @ B2 @ ( image_option_a_a @ F2 @ A2 ) ) ) ) ).
% vimage_subsetD
thf(fact_681_vimage__subsetD,axiom,
! [F2: option_a > option_a,B2: set_option_a,A2: set_option_a] :
( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( ( ord_le1955136853071979460tion_a @ ( vimage1562710927270423099tion_a @ F2 @ B2 ) @ A2 )
=> ( ord_le1955136853071979460tion_a @ B2 @ ( image_7439109396645324421tion_a @ F2 @ A2 ) ) ) ) ).
% vimage_subsetD
thf(fact_682_inj__vimage__image__eq,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( vimage_a_option_a @ F2 @ ( image_a_option_a @ F2 @ A2 ) )
= A2 ) ) ).
% inj_vimage_image_eq
thf(fact_683_inj__vimage__image__eq,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( vimage_option_a_a @ F2 @ ( image_option_a_a @ F2 @ A2 ) )
= A2 ) ) ).
% inj_vimage_image_eq
thf(fact_684_the__inv__into__comp,axiom,
! [F2: a > a,G: option_a > a,A2: set_option_a,X: a] :
( ( inj_on_a_a @ F2 @ ( image_option_a_a @ G @ A2 ) )
=> ( ( inj_on_option_a_a @ G @ A2 )
=> ( ( member_a @ X @ ( image_a_a @ F2 @ ( image_option_a_a @ G @ A2 ) ) )
=> ( ( the_in1757154643552616557on_a_a @ A2 @ ( comp_a_a_option_a @ F2 @ G ) @ X )
= ( comp_a_option_a_a @ ( the_in1757154643552616557on_a_a @ A2 @ G ) @ ( the_inv_into_a_a @ ( image_option_a_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_685_the__inv__into__comp,axiom,
! [F2: option_a > a,G: a > option_a,A2: set_a,X: a] :
( ( inj_on_option_a_a @ F2 @ ( image_a_option_a @ G @ A2 ) )
=> ( ( inj_on_a_option_a @ G @ A2 )
=> ( ( member_a @ X @ ( image_option_a_a @ F2 @ ( image_a_option_a @ G @ A2 ) ) )
=> ( ( the_inv_into_a_a @ A2 @ ( comp_option_a_a_a @ F2 @ G ) @ X )
= ( comp_option_a_a_a @ ( the_in8758012798868597241tion_a @ A2 @ G ) @ ( the_in1757154643552616557on_a_a @ ( image_a_option_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_686_the__inv__into__comp,axiom,
! [F2: option_a > option_a,G: a > option_a,A2: set_a,X: option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ ( image_a_option_a @ G @ A2 ) )
=> ( ( inj_on_a_option_a @ G @ A2 )
=> ( ( member_option_a @ X @ ( image_7439109396645324421tion_a @ F2 @ ( image_a_option_a @ G @ A2 ) ) )
=> ( ( the_in8758012798868597241tion_a @ A2 @ ( comp_o6087033147929006299on_a_a @ F2 @ G ) @ X )
= ( comp_o3864519266390211175tion_a @ ( the_in8758012798868597241tion_a @ A2 @ G ) @ ( the_in2538339130118444083tion_a @ ( image_a_option_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_687_the__inv__into__comp,axiom,
! [F2: a > option_a,G: option_a > a,A2: set_option_a,X: option_a] :
( ( inj_on_a_option_a @ F2 @ ( image_option_a_a @ G @ A2 ) )
=> ( ( inj_on_option_a_a @ G @ A2 )
=> ( ( member_option_a @ X @ ( image_a_option_a @ F2 @ ( image_option_a_a @ G @ A2 ) ) )
=> ( ( the_in2538339130118444083tion_a @ A2 @ ( comp_a6249931511552232923tion_a @ F2 @ G ) @ X )
= ( comp_a6249931511552232923tion_a @ ( the_in1757154643552616557on_a_a @ A2 @ G ) @ ( the_in8758012798868597241tion_a @ ( image_option_a_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_688_the__inv__into__comp,axiom,
! [F2: a > b,G: option_a > a,A2: set_option_a,X: b] :
( ( inj_on_a_b @ F2 @ ( image_option_a_a @ G @ A2 ) )
=> ( ( inj_on_option_a_a @ G @ A2 )
=> ( ( member_b @ X @ ( image_a_b @ F2 @ ( image_option_a_a @ G @ A2 ) ) )
=> ( ( the_in1757154643552616558on_a_b @ A2 @ ( comp_a_b_option_a @ F2 @ G ) @ X )
= ( comp_a_option_a_b @ ( the_in1757154643552616557on_a_a @ A2 @ G ) @ ( the_inv_into_a_b @ ( image_option_a_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_689_the__inv__into__comp,axiom,
! [F2: option_a > b,G: a > option_a,A2: set_a,X: b] :
( ( inj_on_option_a_b @ F2 @ ( image_a_option_a @ G @ A2 ) )
=> ( ( inj_on_a_option_a @ G @ A2 )
=> ( ( member_b @ X @ ( image_option_a_b @ F2 @ ( image_a_option_a @ G @ A2 ) ) )
=> ( ( the_inv_into_a_b @ A2 @ ( comp_option_a_b_a @ F2 @ G ) @ X )
= ( comp_option_a_a_b @ ( the_in8758012798868597241tion_a @ A2 @ G ) @ ( the_in1757154643552616558on_a_b @ ( image_a_option_a @ G @ A2 ) @ F2 ) @ X ) ) ) ) ) ).
% the_inv_into_comp
thf(fact_690_map__conv__bind__option,axiom,
( map_option_a_a
= ( ^ [F: a > a,X5: option_a] : ( bind_a_a @ X5 @ ( comp_a_option_a_a @ some_a @ F ) ) ) ) ).
% map_conv_bind_option
thf(fact_691_inj__on__vimage__singleton,axiom,
! [F2: b > a,A2: set_b,A: a] :
( ( inj_on_b_a @ F2 @ A2 )
=> ( ord_less_eq_set_b @ ( inf_inf_set_b @ ( vimage_b_a @ F2 @ ( insert_a @ A @ bot_bot_set_a ) ) @ A2 )
@ ( insert_b
@ ( the_b
@ ^ [X5: b] :
( ( member_b @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_b ) ) ) ).
% inj_on_vimage_singleton
thf(fact_692_inj__on__vimage__singleton,axiom,
! [F2: a > a,A2: set_a,A: a] :
( ( inj_on_a_a @ F2 @ A2 )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ ( vimage_a_a @ F2 @ ( insert_a @ A @ bot_bot_set_a ) ) @ A2 )
@ ( insert_a
@ ( the_a
@ ^ [X5: a] :
( ( member_a @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_a ) ) ) ).
% inj_on_vimage_singleton
thf(fact_693_inj__on__vimage__singleton,axiom,
! [F2: option_a > a,A2: set_option_a,A: a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ord_le1955136853071979460tion_a @ ( inf_inf_set_option_a @ ( vimage_option_a_a @ F2 @ ( insert_a @ A @ bot_bot_set_a ) ) @ A2 )
@ ( insert_option_a
@ ( the_option_a
@ ^ [X5: option_a] :
( ( member_option_a @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_option_a ) ) ) ).
% inj_on_vimage_singleton
thf(fact_694_inj__on__vimage__singleton,axiom,
! [F2: b > option_a,A2: set_b,A: option_a] :
( ( inj_on_b_option_a @ F2 @ A2 )
=> ( ord_less_eq_set_b @ ( inf_inf_set_b @ ( vimage_b_option_a @ F2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) @ A2 )
@ ( insert_b
@ ( the_b
@ ^ [X5: b] :
( ( member_b @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_b ) ) ) ).
% inj_on_vimage_singleton
thf(fact_695_inj__on__vimage__singleton,axiom,
! [F2: a > option_a,A2: set_a,A: option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ ( vimage_a_option_a @ F2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) @ A2 )
@ ( insert_a
@ ( the_a
@ ^ [X5: a] :
( ( member_a @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_a ) ) ) ).
% inj_on_vimage_singleton
thf(fact_696_inj__on__vimage__singleton,axiom,
! [F2: option_a > option_a,A2: set_option_a,A: option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ A2 )
=> ( ord_le1955136853071979460tion_a @ ( inf_inf_set_option_a @ ( vimage1562710927270423099tion_a @ F2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) @ A2 )
@ ( insert_option_a
@ ( the_option_a
@ ^ [X5: option_a] :
( ( member_option_a @ X5 @ A2 )
& ( ( F2 @ X5 )
= A ) ) )
@ bot_bot_set_option_a ) ) ) ).
% inj_on_vimage_singleton
thf(fact_697_inj__vimage__singleton,axiom,
! [F2: a > a,A: a] :
( ( inj_on_a_a @ F2 @ top_top_set_a )
=> ( ord_less_eq_set_a @ ( vimage_a_a @ F2 @ ( insert_a @ A @ bot_bot_set_a ) )
@ ( insert_a
@ ( the_a
@ ^ [X5: a] :
( ( F2 @ X5 )
= A ) )
@ bot_bot_set_a ) ) ) ).
% inj_vimage_singleton
thf(fact_698_inj__vimage__singleton,axiom,
! [F2: a > option_a,A: option_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ord_less_eq_set_a @ ( vimage_a_option_a @ F2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
@ ( insert_a
@ ( the_a
@ ^ [X5: a] :
( ( F2 @ X5 )
= A ) )
@ bot_bot_set_a ) ) ) ).
% inj_vimage_singleton
thf(fact_699_inj__vimage__singleton,axiom,
! [F2: option_a > a,A: a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ord_le1955136853071979460tion_a @ ( vimage_option_a_a @ F2 @ ( insert_a @ A @ bot_bot_set_a ) )
@ ( insert_option_a
@ ( the_option_a
@ ^ [X5: option_a] :
( ( F2 @ X5 )
= A ) )
@ bot_bot_set_option_a ) ) ) ).
% inj_vimage_singleton
thf(fact_700_inj__vimage__singleton,axiom,
! [F2: option_a > option_a,A: option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
=> ( ord_le1955136853071979460tion_a @ ( vimage1562710927270423099tion_a @ F2 @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
@ ( insert_option_a
@ ( the_option_a
@ ^ [X5: option_a] :
( ( F2 @ X5 )
= A ) )
@ bot_bot_set_option_a ) ) ) ).
% inj_vimage_singleton
thf(fact_701_comp__the__Some,axiom,
( ( comp_option_a_a_a @ the_a2 @ some_a )
= id_a ) ).
% comp_the_Some
thf(fact_702_vimage__subset__eq,axiom,
! [F2: a > a,B2: set_a,A2: set_a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( ( ord_less_eq_set_a @ ( vimage_a_a @ F2 @ B2 ) @ A2 )
= ( ord_less_eq_set_a @ B2 @ ( image_a_a @ F2 @ A2 ) ) ) ) ).
% vimage_subset_eq
thf(fact_703_vimage__subset__eq,axiom,
! [F2: a > option_a,B2: set_option_a,A2: set_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( ( ord_less_eq_set_a @ ( vimage_a_option_a @ F2 @ B2 ) @ A2 )
= ( ord_le1955136853071979460tion_a @ B2 @ ( image_a_option_a @ F2 @ A2 ) ) ) ) ).
% vimage_subset_eq
thf(fact_704_vimage__subset__eq,axiom,
! [F2: option_a > a,B2: set_a,A2: set_option_a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( ( ord_le1955136853071979460tion_a @ ( vimage_option_a_a @ F2 @ B2 ) @ A2 )
= ( ord_less_eq_set_a @ B2 @ ( image_option_a_a @ F2 @ A2 ) ) ) ) ).
% vimage_subset_eq
thf(fact_705_vimage__subset__eq,axiom,
! [F2: option_a > option_a,B2: set_option_a,A2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( ( ord_le1955136853071979460tion_a @ ( vimage1562710927270423099tion_a @ F2 @ B2 ) @ A2 )
= ( ord_le1955136853071979460tion_a @ B2 @ ( image_7439109396645324421tion_a @ F2 @ A2 ) ) ) ) ).
% vimage_subset_eq
thf(fact_706_id__apply,axiom,
( id_a
= ( ^ [X5: a] : X5 ) ) ).
% id_apply
thf(fact_707_image__id,axiom,
( ( image_a_a @ id_a )
= id_set_a ) ).
% image_id
thf(fact_708_bij__betw__id,axiom,
! [A2: set_a] : ( bij_betw_a_a @ id_a @ A2 @ A2 ) ).
% bij_betw_id
thf(fact_709_vimage__id,axiom,
( ( vimage_a_a @ id_a )
= id_set_a ) ).
% vimage_id
thf(fact_710_bij__betw__imp__inj__on,axiom,
! [F2: a > option_a,A2: set_a,B2: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ B2 )
=> ( inj_on_a_option_a @ F2 @ A2 ) ) ).
% bij_betw_imp_inj_on
thf(fact_711_inj__on__id,axiom,
! [A2: set_a] : ( inj_on_a_a @ id_a @ A2 ) ).
% inj_on_id
thf(fact_712_bij__betw__comp__iff,axiom,
! [F2: a > option_a,A2: set_a,A9: set_option_a,F4: option_a > a,A10: set_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ A9 )
=> ( ( bij_betw_option_a_a @ F4 @ A9 @ A10 )
= ( bij_betw_a_a @ ( comp_option_a_a_a @ F4 @ F2 ) @ A2 @ A10 ) ) ) ).
% bij_betw_comp_iff
thf(fact_713_comp__eq__id__dest,axiom,
! [A: option_a > a,B: a > option_a,C: a > a,V4: a] :
( ( ( comp_option_a_a_a @ A @ B )
= ( comp_a_a_a @ id_a @ C ) )
=> ( ( A @ ( B @ V4 ) )
= ( C @ V4 ) ) ) ).
% comp_eq_id_dest
thf(fact_714_bij__betw__trans,axiom,
! [F2: a > option_a,A2: set_a,B2: set_option_a,G: option_a > a,C3: set_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ B2 )
=> ( ( bij_betw_option_a_a @ G @ B2 @ C3 )
=> ( bij_betw_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ A2 @ C3 ) ) ) ).
% bij_betw_trans
thf(fact_715_bij__betw__imp__surj__on,axiom,
! [F2: a > option_a,A2: set_a,B2: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ B2 )
=> ( ( image_a_option_a @ F2 @ A2 )
= B2 ) ) ).
% bij_betw_imp_surj_on
thf(fact_716_bij__betw__imp__surj__on,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ B2 )
=> ( ( image_option_a_a @ F2 @ A2 )
= B2 ) ) ).
% bij_betw_imp_surj_on
thf(fact_717_bij__betw__empty1,axiom,
! [F2: a > a,A2: set_a] :
( ( bij_betw_a_a @ F2 @ bot_bot_set_a @ A2 )
=> ( A2 = bot_bot_set_a ) ) ).
% bij_betw_empty1
thf(fact_718_bij__betw__empty1,axiom,
! [F2: a > option_a,A2: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ bot_bot_set_a @ A2 )
=> ( A2 = bot_bot_set_option_a ) ) ).
% bij_betw_empty1
thf(fact_719_bij__betw__empty1,axiom,
! [F2: option_a > a,A2: set_a] :
( ( bij_betw_option_a_a @ F2 @ bot_bot_set_option_a @ A2 )
=> ( A2 = bot_bot_set_a ) ) ).
% bij_betw_empty1
thf(fact_720_bij__betw__empty1,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ bot_bot_set_option_a @ A2 )
=> ( A2 = bot_bot_set_option_a ) ) ).
% bij_betw_empty1
thf(fact_721_bij__betw__empty2,axiom,
! [F2: a > a,A2: set_a] :
( ( bij_betw_a_a @ F2 @ A2 @ bot_bot_set_a )
=> ( A2 = bot_bot_set_a ) ) ).
% bij_betw_empty2
thf(fact_722_bij__betw__empty2,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ bot_bot_set_a )
=> ( A2 = bot_bot_set_option_a ) ) ).
% bij_betw_empty2
thf(fact_723_bij__betw__empty2,axiom,
! [F2: a > option_a,A2: set_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ bot_bot_set_option_a )
=> ( A2 = bot_bot_set_a ) ) ).
% bij_betw_empty2
thf(fact_724_bij__betw__empty2,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ bot_bot_set_option_a )
=> ( A2 = bot_bot_set_option_a ) ) ).
% bij_betw_empty2
thf(fact_725_id__def,axiom,
( id_a
= ( ^ [X5: a] : X5 ) ) ).
% id_def
thf(fact_726_eq__id__iff,axiom,
! [F2: a > a] :
( ( ! [X5: a] :
( ( F2 @ X5 )
= X5 ) )
= ( F2 = id_a ) ) ).
% eq_id_iff
thf(fact_727_bij__betw__apply,axiom,
! [F2: a > a,A2: set_a,B2: set_a,A: a] :
( ( bij_betw_a_a @ F2 @ A2 @ B2 )
=> ( ( member_a @ A @ A2 )
=> ( member_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_728_bij__betw__apply,axiom,
! [F2: a > option_a,A2: set_a,B2: set_option_a,A: a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ B2 )
=> ( ( member_a @ A @ A2 )
=> ( member_option_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_729_bij__betw__apply,axiom,
! [F2: a > b,A2: set_a,B2: set_b,A: a] :
( ( bij_betw_a_b @ F2 @ A2 @ B2 )
=> ( ( member_a @ A @ A2 )
=> ( member_b @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_730_bij__betw__apply,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_a,A: option_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ B2 )
=> ( ( member_option_a @ A @ A2 )
=> ( member_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_731_bij__betw__apply,axiom,
! [F2: option_a > option_a,A2: set_option_a,B2: set_option_a,A: option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ B2 )
=> ( ( member_option_a @ A @ A2 )
=> ( member_option_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_732_bij__betw__apply,axiom,
! [F2: option_a > b,A2: set_option_a,B2: set_b,A: option_a] :
( ( bij_betw_option_a_b @ F2 @ A2 @ B2 )
=> ( ( member_option_a @ A @ A2 )
=> ( member_b @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_733_bij__betw__apply,axiom,
! [F2: b > a,A2: set_b,B2: set_a,A: b] :
( ( bij_betw_b_a @ F2 @ A2 @ B2 )
=> ( ( member_b @ A @ A2 )
=> ( member_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_734_bij__betw__apply,axiom,
! [F2: b > option_a,A2: set_b,B2: set_option_a,A: b] :
( ( bij_betw_b_option_a @ F2 @ A2 @ B2 )
=> ( ( member_b @ A @ A2 )
=> ( member_option_a @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_735_bij__betw__apply,axiom,
! [F2: b > b,A2: set_b,B2: set_b,A: b] :
( ( bij_betw_b_b @ F2 @ A2 @ B2 )
=> ( ( member_b @ A @ A2 )
=> ( member_b @ ( F2 @ A ) @ B2 ) ) ) ).
% bij_betw_apply
thf(fact_736_bij__betw__id__iff,axiom,
! [A2: set_a,B2: set_a] :
( ( bij_betw_a_a @ id_a @ A2 @ B2 )
= ( A2 = B2 ) ) ).
% bij_betw_id_iff
thf(fact_737_bij__betw__iff__bijections,axiom,
( bij_betw_a_a
= ( ^ [F: a > a,A7: set_a,B6: set_a] :
? [G2: a > a] :
( ! [X5: a] :
( ( member_a @ X5 @ A7 )
=> ( ( member_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: a] :
( ( member_a @ X5 @ B6 )
=> ( ( member_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_738_bij__betw__iff__bijections,axiom,
( bij_betw_option_a_a
= ( ^ [F: option_a > a,A7: set_option_a,B6: set_a] :
? [G2: a > option_a] :
( ! [X5: option_a] :
( ( member_option_a @ X5 @ A7 )
=> ( ( member_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: a] :
( ( member_a @ X5 @ B6 )
=> ( ( member_option_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_739_bij__betw__iff__bijections,axiom,
( bij_betw_b_a
= ( ^ [F: b > a,A7: set_b,B6: set_a] :
? [G2: a > b] :
( ! [X5: b] :
( ( member_b @ X5 @ A7 )
=> ( ( member_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: a] :
( ( member_a @ X5 @ B6 )
=> ( ( member_b @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_740_bij__betw__iff__bijections,axiom,
( bij_betw_a_option_a
= ( ^ [F: a > option_a,A7: set_a,B6: set_option_a] :
? [G2: option_a > a] :
( ! [X5: a] :
( ( member_a @ X5 @ A7 )
=> ( ( member_option_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: option_a] :
( ( member_option_a @ X5 @ B6 )
=> ( ( member_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_741_bij__betw__iff__bijections,axiom,
( bij_be5431266891817924854tion_a
= ( ^ [F: option_a > option_a,A7: set_option_a,B6: set_option_a] :
? [G2: option_a > option_a] :
( ! [X5: option_a] :
( ( member_option_a @ X5 @ A7 )
=> ( ( member_option_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: option_a] :
( ( member_option_a @ X5 @ B6 )
=> ( ( member_option_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_742_bij__betw__iff__bijections,axiom,
( bij_betw_b_option_a
= ( ^ [F: b > option_a,A7: set_b,B6: set_option_a] :
? [G2: option_a > b] :
( ! [X5: b] :
( ( member_b @ X5 @ A7 )
=> ( ( member_option_a @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: option_a] :
( ( member_option_a @ X5 @ B6 )
=> ( ( member_b @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_743_bij__betw__iff__bijections,axiom,
( bij_betw_a_b
= ( ^ [F: a > b,A7: set_a,B6: set_b] :
? [G2: b > a] :
( ! [X5: a] :
( ( member_a @ X5 @ A7 )
=> ( ( member_b @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: b] :
( ( member_b @ X5 @ B6 )
=> ( ( member_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_744_bij__betw__iff__bijections,axiom,
( bij_betw_option_a_b
= ( ^ [F: option_a > b,A7: set_option_a,B6: set_b] :
? [G2: b > option_a] :
( ! [X5: option_a] :
( ( member_option_a @ X5 @ A7 )
=> ( ( member_b @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: b] :
( ( member_b @ X5 @ B6 )
=> ( ( member_option_a @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_745_bij__betw__iff__bijections,axiom,
( bij_betw_b_b
= ( ^ [F: b > b,A7: set_b,B6: set_b] :
? [G2: b > b] :
( ! [X5: b] :
( ( member_b @ X5 @ A7 )
=> ( ( member_b @ ( F @ X5 ) @ B6 )
& ( ( G2 @ ( F @ X5 ) )
= X5 ) ) )
& ! [X5: b] :
( ( member_b @ X5 @ B6 )
=> ( ( member_b @ ( G2 @ X5 ) @ A7 )
& ( ( F @ ( G2 @ X5 ) )
= X5 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_746_option_Omap__id0,axiom,
( ( map_option_a_a @ id_a )
= id_option_a ) ).
% option.map_id0
thf(fact_747_option_Omap__id,axiom,
! [T: option_a] :
( ( map_option_a_a @ id_a @ T )
= T ) ).
% option.map_id
thf(fact_748_bij__id,axiom,
bij_betw_a_a @ id_a @ top_top_set_a @ top_top_set_a ).
% bij_id
thf(fact_749_bij__id,axiom,
bij_be5431266891817924854tion_a @ id_option_a @ top_top_set_option_a @ top_top_set_option_a ).
% bij_id
thf(fact_750_bij__iff,axiom,
! [F2: a > a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
= ( ! [X5: a] :
? [Y2: a] :
( ( ( F2 @ Y2 )
= X5 )
& ! [Z: a] :
( ( ( F2 @ Z )
= X5 )
=> ( Z = Y2 ) ) ) ) ) ).
% bij_iff
thf(fact_751_bij__iff,axiom,
! [F2: a > option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
= ( ! [X5: option_a] :
? [Y2: a] :
( ( ( F2 @ Y2 )
= X5 )
& ! [Z: a] :
( ( ( F2 @ Z )
= X5 )
=> ( Z = Y2 ) ) ) ) ) ).
% bij_iff
thf(fact_752_bij__iff,axiom,
! [F2: option_a > a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
= ( ! [X5: a] :
? [Y2: option_a] :
( ( ( F2 @ Y2 )
= X5 )
& ! [Z: option_a] :
( ( ( F2 @ Z )
= X5 )
=> ( Z = Y2 ) ) ) ) ) ).
% bij_iff
thf(fact_753_bij__iff,axiom,
! [F2: option_a > option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
= ( ! [X5: option_a] :
? [Y2: option_a] :
( ( ( F2 @ Y2 )
= X5 )
& ! [Z: option_a] :
( ( ( F2 @ Z )
= X5 )
=> ( Z = Y2 ) ) ) ) ) ).
% bij_iff
thf(fact_754_bij__pointE,axiom,
! [F2: a > a,Y: a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ~ ! [X4: a] :
( ( Y
= ( F2 @ X4 ) )
=> ~ ! [X9: a] :
( ( Y
= ( F2 @ X9 ) )
=> ( X9 = X4 ) ) ) ) ).
% bij_pointE
thf(fact_755_bij__pointE,axiom,
! [F2: a > option_a,Y: option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ~ ! [X4: a] :
( ( Y
= ( F2 @ X4 ) )
=> ~ ! [X9: a] :
( ( Y
= ( F2 @ X9 ) )
=> ( X9 = X4 ) ) ) ) ).
% bij_pointE
thf(fact_756_bij__pointE,axiom,
! [F2: option_a > a,Y: a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ~ ! [X4: option_a] :
( ( Y
= ( F2 @ X4 ) )
=> ~ ! [X9: option_a] :
( ( Y
= ( F2 @ X9 ) )
=> ( X9 = X4 ) ) ) ) ).
% bij_pointE
thf(fact_757_bij__pointE,axiom,
! [F2: option_a > option_a,Y: option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ~ ! [X4: option_a] :
( ( Y
= ( F2 @ X4 ) )
=> ~ ! [X9: option_a] :
( ( Y
= ( F2 @ X9 ) )
=> ( X9 = X4 ) ) ) ) ).
% bij_pointE
thf(fact_758_involuntory__imp__bij,axiom,
! [F2: a > a] :
( ! [X4: a] :
( ( F2 @ ( F2 @ X4 ) )
= X4 )
=> ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a ) ) ).
% involuntory_imp_bij
thf(fact_759_involuntory__imp__bij,axiom,
! [F2: option_a > option_a] :
( ! [X4: option_a] :
( ( F2 @ ( F2 @ X4 ) )
= X4 )
=> ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a ) ) ).
% involuntory_imp_bij
thf(fact_760_map__option_Oidentity,axiom,
( ( map_option_a_a
@ ^ [X5: a] : X5 )
= id_option_a ) ).
% map_option.identity
thf(fact_761_bij__betw__imp__surj,axiom,
! [F2: a > a,A2: set_a] :
( ( bij_betw_a_a @ F2 @ A2 @ top_top_set_a )
=> ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a ) ) ).
% bij_betw_imp_surj
thf(fact_762_bij__betw__imp__surj,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ top_top_set_a )
=> ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a ) ) ).
% bij_betw_imp_surj
thf(fact_763_bij__betw__imp__surj,axiom,
! [F2: a > option_a,A2: set_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ top_top_set_option_a )
=> ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a ) ) ).
% bij_betw_imp_surj
thf(fact_764_bij__betw__imp__surj,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a ) ) ).
% bij_betw_imp_surj
thf(fact_765_bij__is__surj,axiom,
! [F2: a > a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a ) ) ).
% bij_is_surj
thf(fact_766_bij__is__surj,axiom,
! [F2: a > option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a ) ) ).
% bij_is_surj
thf(fact_767_bij__is__surj,axiom,
! [F2: option_a > a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a ) ) ).
% bij_is_surj
thf(fact_768_bij__is__surj,axiom,
! [F2: option_a > option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a ) ) ).
% bij_is_surj
thf(fact_769_bij__betw__subset,axiom,
! [F2: a > option_a,A2: set_a,A9: set_option_a,B2: set_a,B7: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ A9 )
=> ( ( ord_less_eq_set_a @ B2 @ A2 )
=> ( ( ( image_a_option_a @ F2 @ B2 )
= B7 )
=> ( bij_betw_a_option_a @ F2 @ B2 @ B7 ) ) ) ) ).
% bij_betw_subset
thf(fact_770_bij__betw__subset,axiom,
! [F2: option_a > a,A2: set_option_a,A9: set_a,B2: set_option_a,B7: set_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ A9 )
=> ( ( ord_le1955136853071979460tion_a @ B2 @ A2 )
=> ( ( ( image_option_a_a @ F2 @ B2 )
= B7 )
=> ( bij_betw_option_a_a @ F2 @ B2 @ B7 ) ) ) ) ).
% bij_betw_subset
thf(fact_771_bij__betw__byWitness,axiom,
! [A2: set_a,F4: option_a > a,F2: a > option_a,A9: set_option_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A2 )
=> ( ( F4 @ ( F2 @ X4 ) )
= X4 ) )
=> ( ! [X4: option_a] :
( ( member_option_a @ X4 @ A9 )
=> ( ( F2 @ ( F4 @ X4 ) )
= X4 ) )
=> ( ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ F2 @ A2 ) @ A9 )
=> ( ( ord_less_eq_set_a @ ( image_option_a_a @ F4 @ A9 ) @ A2 )
=> ( bij_betw_a_option_a @ F2 @ A2 @ A9 ) ) ) ) ) ).
% bij_betw_byWitness
thf(fact_772_bij__betw__byWitness,axiom,
! [A2: set_option_a,F4: a > option_a,F2: option_a > a,A9: set_a] :
( ! [X4: option_a] :
( ( member_option_a @ X4 @ A2 )
=> ( ( F4 @ ( F2 @ X4 ) )
= X4 ) )
=> ( ! [X4: a] :
( ( member_a @ X4 @ A9 )
=> ( ( F2 @ ( F4 @ X4 ) )
= X4 ) )
=> ( ( ord_less_eq_set_a @ ( image_option_a_a @ F2 @ A2 ) @ A9 )
=> ( ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ F4 @ A9 ) @ A2 )
=> ( bij_betw_option_a_a @ F2 @ A2 @ A9 ) ) ) ) ) ).
% bij_betw_byWitness
thf(fact_773_bij__comp,axiom,
! [F2: a > a,G: a > a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( ( bij_betw_a_a @ G @ top_top_set_a @ top_top_set_a )
=> ( bij_betw_a_a @ ( comp_a_a_a @ G @ F2 ) @ top_top_set_a @ top_top_set_a ) ) ) ).
% bij_comp
thf(fact_774_bij__comp,axiom,
! [F2: a > a,G: a > option_a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( ( bij_betw_a_option_a @ G @ top_top_set_a @ top_top_set_option_a )
=> ( bij_betw_a_option_a @ ( comp_a_option_a_a @ G @ F2 ) @ top_top_set_a @ top_top_set_option_a ) ) ) ).
% bij_comp
thf(fact_775_bij__comp,axiom,
! [F2: a > option_a,G: option_a > a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( ( bij_betw_option_a_a @ G @ top_top_set_option_a @ top_top_set_a )
=> ( bij_betw_a_a @ ( comp_option_a_a_a @ G @ F2 ) @ top_top_set_a @ top_top_set_a ) ) ) ).
% bij_comp
thf(fact_776_bij__comp,axiom,
! [F2: a > option_a,G: option_a > option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( ( bij_be5431266891817924854tion_a @ G @ top_top_set_option_a @ top_top_set_option_a )
=> ( bij_betw_a_option_a @ ( comp_o6087033147929006299on_a_a @ G @ F2 ) @ top_top_set_a @ top_top_set_option_a ) ) ) ).
% bij_comp
thf(fact_777_bij__comp,axiom,
! [F2: option_a > a,G: a > a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( ( bij_betw_a_a @ G @ top_top_set_a @ top_top_set_a )
=> ( bij_betw_option_a_a @ ( comp_a_a_option_a @ G @ F2 ) @ top_top_set_option_a @ top_top_set_a ) ) ) ).
% bij_comp
thf(fact_778_bij__comp,axiom,
! [F2: option_a > a,G: a > option_a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( ( bij_betw_a_option_a @ G @ top_top_set_a @ top_top_set_option_a )
=> ( bij_be5431266891817924854tion_a @ ( comp_a6249931511552232923tion_a @ G @ F2 ) @ top_top_set_option_a @ top_top_set_option_a ) ) ) ).
% bij_comp
thf(fact_779_bij__comp,axiom,
! [F2: option_a > option_a,G: option_a > a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( ( bij_betw_option_a_a @ G @ top_top_set_option_a @ top_top_set_a )
=> ( bij_betw_option_a_a @ ( comp_o3864519266390211175tion_a @ G @ F2 ) @ top_top_set_option_a @ top_top_set_a ) ) ) ).
% bij_comp
thf(fact_780_bij__comp,axiom,
! [F2: option_a > option_a,G: option_a > option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( ( bij_be5431266891817924854tion_a @ G @ top_top_set_option_a @ top_top_set_option_a )
=> ( bij_be5431266891817924854tion_a @ ( comp_o3154387707078715297tion_a @ G @ F2 ) @ top_top_set_option_a @ top_top_set_option_a ) ) ) ).
% bij_comp
thf(fact_781_bij__betw__def,axiom,
( bij_betw_option_a_a
= ( ^ [F: option_a > a,A7: set_option_a,B6: set_a] :
( ( inj_on_option_a_a @ F @ A7 )
& ( ( image_option_a_a @ F @ A7 )
= B6 ) ) ) ) ).
% bij_betw_def
thf(fact_782_bij__betw__def,axiom,
( bij_betw_a_option_a
= ( ^ [F: a > option_a,A7: set_a,B6: set_option_a] :
( ( inj_on_a_option_a @ F @ A7 )
& ( ( image_a_option_a @ F @ A7 )
= B6 ) ) ) ) ).
% bij_betw_def
thf(fact_783_bij__betw__imageI,axiom,
! [F2: option_a > a,A2: set_option_a,B2: set_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( ( ( image_option_a_a @ F2 @ A2 )
= B2 )
=> ( bij_betw_option_a_a @ F2 @ A2 @ B2 ) ) ) ).
% bij_betw_imageI
thf(fact_784_bij__betw__imageI,axiom,
! [F2: a > option_a,A2: set_a,B2: set_option_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( ( ( image_a_option_a @ F2 @ A2 )
= B2 )
=> ( bij_betw_a_option_a @ F2 @ A2 @ B2 ) ) ) ).
% bij_betw_imageI
thf(fact_785_inj__on__imp__bij__betw,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( bij_betw_option_a_a @ F2 @ A2 @ ( image_option_a_a @ F2 @ A2 ) ) ) ).
% inj_on_imp_bij_betw
thf(fact_786_inj__on__imp__bij__betw,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( bij_betw_a_option_a @ F2 @ A2 @ ( image_a_option_a @ F2 @ A2 ) ) ) ).
% inj_on_imp_bij_betw
thf(fact_787_bij__is__inj,axiom,
! [F2: a > a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( inj_on_a_a @ F2 @ top_top_set_a ) ) ).
% bij_is_inj
thf(fact_788_bij__is__inj,axiom,
! [F2: a > option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( inj_on_a_option_a @ F2 @ top_top_set_a ) ) ).
% bij_is_inj
thf(fact_789_bij__is__inj,axiom,
! [F2: option_a > a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( inj_on_option_a_a @ F2 @ top_top_set_option_a ) ) ).
% bij_is_inj
thf(fact_790_bij__is__inj,axiom,
! [F2: option_a > option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a ) ) ).
% bij_is_inj
thf(fact_791_surj__id,axiom,
( ( image_a_a @ id_a @ top_top_set_a )
= top_top_set_a ) ).
% surj_id
thf(fact_792_surj__id,axiom,
( ( image_7439109396645324421tion_a @ id_option_a @ top_top_set_option_a )
= top_top_set_option_a ) ).
% surj_id
thf(fact_793_bij__betw__comp__iff2,axiom,
! [F4: option_a > a,A9: set_option_a,A10: set_a,F2: a > option_a,A2: set_a] :
( ( bij_betw_option_a_a @ F4 @ A9 @ A10 )
=> ( ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ F2 @ A2 ) @ A9 )
=> ( ( bij_betw_a_option_a @ F2 @ A2 @ A9 )
= ( bij_betw_a_a @ ( comp_option_a_a_a @ F4 @ F2 ) @ A2 @ A10 ) ) ) ) ).
% bij_betw_comp_iff2
thf(fact_794_bij__def,axiom,
! [F2: a > a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
= ( ( inj_on_a_a @ F2 @ top_top_set_a )
& ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a ) ) ) ).
% bij_def
thf(fact_795_bij__def,axiom,
! [F2: a > option_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
= ( ( inj_on_a_option_a @ F2 @ top_top_set_a )
& ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a ) ) ) ).
% bij_def
thf(fact_796_bij__def,axiom,
! [F2: option_a > a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
= ( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
& ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a ) ) ) ).
% bij_def
thf(fact_797_bij__def,axiom,
! [F2: option_a > option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
= ( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
& ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a ) ) ) ).
% bij_def
thf(fact_798_bijI,axiom,
! [F2: a > a] :
( ( inj_on_a_a @ F2 @ top_top_set_a )
=> ( ( ( image_a_a @ F2 @ top_top_set_a )
= top_top_set_a )
=> ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a ) ) ) ).
% bijI
thf(fact_799_bijI,axiom,
! [F2: a > option_a] :
( ( inj_on_a_option_a @ F2 @ top_top_set_a )
=> ( ( ( image_a_option_a @ F2 @ top_top_set_a )
= top_top_set_option_a )
=> ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a ) ) ) ).
% bijI
thf(fact_800_bijI,axiom,
! [F2: option_a > a] :
( ( inj_on_option_a_a @ F2 @ top_top_set_option_a )
=> ( ( ( image_option_a_a @ F2 @ top_top_set_option_a )
= top_top_set_a )
=> ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a ) ) ) ).
% bijI
thf(fact_801_bijI,axiom,
! [F2: option_a > option_a] :
( ( inj_on8559383841115902449tion_a @ F2 @ top_top_set_option_a )
=> ( ( ( image_7439109396645324421tion_a @ F2 @ top_top_set_option_a )
= top_top_set_option_a )
=> ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a ) ) ) ).
% bijI
thf(fact_802_notIn__Un__bij__betw3,axiom,
! [B: b,A2: set_b,F2: b > b,A9: set_b] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_b @ F2 @ A2 @ A9 )
= ( bij_betw_b_b @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_803_notIn__Un__bij__betw3,axiom,
! [B: b,A2: set_b,F2: b > a,A9: set_a] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_a @ F2 @ A2 @ A9 )
= ( bij_betw_b_a @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_804_notIn__Un__bij__betw3,axiom,
! [B: b,A2: set_b,F2: b > option_a,A9: set_option_a] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_option_a @ F2 @ A2 @ A9 )
= ( bij_betw_b_option_a @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_805_notIn__Un__bij__betw3,axiom,
! [B: a,A2: set_a,F2: a > b,A9: set_b] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_b @ F2 @ A2 @ A9 )
= ( bij_betw_a_b @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_806_notIn__Un__bij__betw3,axiom,
! [B: a,A2: set_a,F2: a > a,A9: set_a] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_a @ F2 @ A2 @ A9 )
= ( bij_betw_a_a @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_807_notIn__Un__bij__betw3,axiom,
! [B: a,A2: set_a,F2: a > option_a,A9: set_option_a] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_option_a @ F2 @ A2 @ A9 )
= ( bij_betw_a_option_a @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_808_notIn__Un__bij__betw3,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > b,A9: set_b] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_option_a_b @ F2 @ A2 @ A9 )
= ( bij_betw_option_a_b @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_809_notIn__Un__bij__betw3,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > a,A9: set_a] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_option_a_a @ F2 @ A2 @ A9 )
= ( bij_betw_option_a_a @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_810_notIn__Un__bij__betw3,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > option_a,A9: set_option_a] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ A9 )
= ( bij_be5431266891817924854tion_a @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw3
thf(fact_811_notIn__Un__bij__betw,axiom,
! [B: b,A2: set_b,F2: b > b,A9: set_b] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_b @ F2 @ A2 @ A9 )
=> ( bij_betw_b_b @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_812_notIn__Un__bij__betw,axiom,
! [B: b,A2: set_b,F2: b > a,A9: set_a] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_a @ F2 @ A2 @ A9 )
=> ( bij_betw_b_a @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_813_notIn__Un__bij__betw,axiom,
! [B: b,A2: set_b,F2: b > option_a,A9: set_option_a] :
( ~ ( member_b @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_b_option_a @ F2 @ A2 @ A9 )
=> ( bij_betw_b_option_a @ F2 @ ( sup_sup_set_b @ A2 @ ( insert_b @ B @ bot_bot_set_b ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_814_notIn__Un__bij__betw,axiom,
! [B: a,A2: set_a,F2: a > b,A9: set_b] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_b @ F2 @ A2 @ A9 )
=> ( bij_betw_a_b @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_815_notIn__Un__bij__betw,axiom,
! [B: a,A2: set_a,F2: a > a,A9: set_a] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_a @ F2 @ A2 @ A9 )
=> ( bij_betw_a_a @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_816_notIn__Un__bij__betw,axiom,
! [B: a,A2: set_a,F2: a > option_a,A9: set_option_a] :
( ~ ( member_a @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_a_option_a @ F2 @ A2 @ A9 )
=> ( bij_betw_a_option_a @ F2 @ ( sup_sup_set_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_817_notIn__Un__bij__betw,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > b,A9: set_b] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_b @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_option_a_b @ F2 @ A2 @ A9 )
=> ( bij_betw_option_a_b @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_b @ A9 @ ( insert_b @ ( F2 @ B ) @ bot_bot_set_b ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_818_notIn__Un__bij__betw,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > a,A9: set_a] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_betw_option_a_a @ F2 @ A2 @ A9 )
=> ( bij_betw_option_a_a @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_a @ A9 @ ( insert_a @ ( F2 @ B ) @ bot_bot_set_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_819_notIn__Un__bij__betw,axiom,
! [B: option_a,A2: set_option_a,F2: option_a > option_a,A9: set_option_a] :
( ~ ( member_option_a @ B @ A2 )
=> ( ~ ( member_option_a @ ( F2 @ B ) @ A9 )
=> ( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ A9 )
=> ( bij_be5431266891817924854tion_a @ F2 @ ( sup_sup_set_option_a @ A2 @ ( insert_option_a @ B @ bot_bot_set_option_a ) ) @ ( sup_sup_set_option_a @ A9 @ ( insert_option_a @ ( F2 @ B ) @ bot_bot_set_option_a ) ) ) ) ) ) ).
% notIn_Un_bij_betw
thf(fact_820_bij__betw__partition,axiom,
! [F2: b > b,A2: set_b,C3: set_b,B2: set_b,D2: set_b] :
( ( bij_betw_b_b @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_b @ B2 @ D2 ) )
=> ( ( bij_betw_b_b @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ C3 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_b @ B2 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_b_b @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_821_bij__betw__partition,axiom,
! [F2: b > a,A2: set_b,C3: set_b,B2: set_a,D2: set_a] :
( ( bij_betw_b_a @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_a @ B2 @ D2 ) )
=> ( ( bij_betw_b_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ C3 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_a @ B2 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_b_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_822_bij__betw__partition,axiom,
! [F2: b > option_a,A2: set_b,C3: set_b,B2: set_option_a,D2: set_option_a] :
( ( bij_betw_b_option_a @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_option_a @ B2 @ D2 ) )
=> ( ( bij_betw_b_option_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ C3 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_option_a @ B2 @ D2 )
= bot_bot_set_option_a )
=> ( bij_betw_b_option_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_823_bij__betw__partition,axiom,
! [F2: a > b,A2: set_a,C3: set_a,B2: set_b,D2: set_b] :
( ( bij_betw_a_b @ F2 @ ( sup_sup_set_a @ A2 @ C3 ) @ ( sup_sup_set_b @ B2 @ D2 ) )
=> ( ( bij_betw_a_b @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ C3 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_b @ B2 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_a_b @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_824_bij__betw__partition,axiom,
! [F2: a > a,A2: set_a,C3: set_a,B2: set_a,D2: set_a] :
( ( bij_betw_a_a @ F2 @ ( sup_sup_set_a @ A2 @ C3 ) @ ( sup_sup_set_a @ B2 @ D2 ) )
=> ( ( bij_betw_a_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ C3 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_a @ B2 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_a_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_825_bij__betw__partition,axiom,
! [F2: a > option_a,A2: set_a,C3: set_a,B2: set_option_a,D2: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ ( sup_sup_set_a @ A2 @ C3 ) @ ( sup_sup_set_option_a @ B2 @ D2 ) )
=> ( ( bij_betw_a_option_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ C3 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_option_a @ B2 @ D2 )
= bot_bot_set_option_a )
=> ( bij_betw_a_option_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_826_bij__betw__partition,axiom,
! [F2: option_a > b,A2: set_option_a,C3: set_option_a,B2: set_b,D2: set_b] :
( ( bij_betw_option_a_b @ F2 @ ( sup_sup_set_option_a @ A2 @ C3 ) @ ( sup_sup_set_b @ B2 @ D2 ) )
=> ( ( bij_betw_option_a_b @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ C3 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_b @ B2 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_option_a_b @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_827_bij__betw__partition,axiom,
! [F2: option_a > a,A2: set_option_a,C3: set_option_a,B2: set_a,D2: set_a] :
( ( bij_betw_option_a_a @ F2 @ ( sup_sup_set_option_a @ A2 @ C3 ) @ ( sup_sup_set_a @ B2 @ D2 ) )
=> ( ( bij_betw_option_a_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ C3 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_a @ B2 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_option_a_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_828_bij__betw__partition,axiom,
! [F2: option_a > option_a,A2: set_option_a,C3: set_option_a,B2: set_option_a,D2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ ( sup_sup_set_option_a @ A2 @ C3 ) @ ( sup_sup_set_option_a @ B2 @ D2 ) )
=> ( ( bij_be5431266891817924854tion_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ C3 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_option_a @ B2 @ D2 )
= bot_bot_set_option_a )
=> ( bij_be5431266891817924854tion_a @ F2 @ A2 @ B2 ) ) ) ) ) ).
% bij_betw_partition
thf(fact_829_bij__betw__combine,axiom,
! [F2: b > b,A2: set_b,B2: set_b,C3: set_b,D2: set_b] :
( ( bij_betw_b_b @ F2 @ A2 @ B2 )
=> ( ( bij_betw_b_b @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_b @ B2 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_b_b @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_b @ B2 @ D2 ) ) ) ) ) ).
% bij_betw_combine
thf(fact_830_bij__betw__combine,axiom,
! [F2: b > a,A2: set_b,B2: set_a,C3: set_b,D2: set_a] :
( ( bij_betw_b_a @ F2 @ A2 @ B2 )
=> ( ( bij_betw_b_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_a @ B2 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_b_a @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_a @ B2 @ D2 ) ) ) ) ) ).
% bij_betw_combine
thf(fact_831_bij__betw__combine,axiom,
! [F2: b > option_a,A2: set_b,B2: set_option_a,C3: set_b,D2: set_option_a] :
( ( bij_betw_b_option_a @ F2 @ A2 @ B2 )
=> ( ( bij_betw_b_option_a @ F2 @ C3 @ D2 )
=> ( ( ( inf_inf_set_option_a @ B2 @ D2 )
= bot_bot_set_option_a )
=> ( bij_betw_b_option_a @ F2 @ ( sup_sup_set_b @ A2 @ C3 ) @ ( sup_sup_set_option_a @ B2 @ D2 ) ) ) ) ) ).
% bij_betw_combine
thf(fact_832_bij__image__Compl__eq,axiom,
! [F2: a > a,A2: set_a] :
( ( bij_betw_a_a @ F2 @ top_top_set_a @ top_top_set_a )
=> ( ( image_a_a @ F2 @ ( uminus_uminus_set_a @ A2 ) )
= ( uminus_uminus_set_a @ ( image_a_a @ F2 @ A2 ) ) ) ) ).
% bij_image_Compl_eq
thf(fact_833_bij__image__Compl__eq,axiom,
! [F2: a > option_a,A2: set_a] :
( ( bij_betw_a_option_a @ F2 @ top_top_set_a @ top_top_set_option_a )
=> ( ( image_a_option_a @ F2 @ ( uminus_uminus_set_a @ A2 ) )
= ( uminus6205308855922866075tion_a @ ( image_a_option_a @ F2 @ A2 ) ) ) ) ).
% bij_image_Compl_eq
thf(fact_834_bij__image__Compl__eq,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( bij_betw_option_a_a @ F2 @ top_top_set_option_a @ top_top_set_a )
=> ( ( image_option_a_a @ F2 @ ( uminus6205308855922866075tion_a @ A2 ) )
= ( uminus_uminus_set_a @ ( image_option_a_a @ F2 @ A2 ) ) ) ) ).
% bij_image_Compl_eq
thf(fact_835_bij__image__Compl__eq,axiom,
! [F2: option_a > option_a,A2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ top_top_set_option_a @ top_top_set_option_a )
=> ( ( image_7439109396645324421tion_a @ F2 @ ( uminus6205308855922866075tion_a @ A2 ) )
= ( uminus6205308855922866075tion_a @ ( image_7439109396645324421tion_a @ F2 @ A2 ) ) ) ) ).
% bij_image_Compl_eq
thf(fact_836_bij__betw__disjoint__Un,axiom,
! [F2: b > b,A2: set_b,C3: set_b,G: b > b,B2: set_b,D2: set_b] :
( ( bij_betw_b_b @ F2 @ A2 @ C3 )
=> ( ( bij_betw_b_b @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ B2 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_b @ C3 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_b_b
@ ^ [X5: b] : ( if_b @ ( member_b @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_b @ A2 @ B2 )
@ ( sup_sup_set_b @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_837_bij__betw__disjoint__Un,axiom,
! [F2: b > a,A2: set_b,C3: set_a,G: b > a,B2: set_b,D2: set_a] :
( ( bij_betw_b_a @ F2 @ A2 @ C3 )
=> ( ( bij_betw_b_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ B2 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_a @ C3 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_b_a
@ ^ [X5: b] : ( if_a @ ( member_b @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_b @ A2 @ B2 )
@ ( sup_sup_set_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_838_bij__betw__disjoint__Un,axiom,
! [F2: b > option_a,A2: set_b,C3: set_option_a,G: b > option_a,B2: set_b,D2: set_option_a] :
( ( bij_betw_b_option_a @ F2 @ A2 @ C3 )
=> ( ( bij_betw_b_option_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_b @ A2 @ B2 )
= bot_bot_set_b )
=> ( ( ( inf_inf_set_option_a @ C3 @ D2 )
= bot_bot_set_option_a )
=> ( bij_betw_b_option_a
@ ^ [X5: b] : ( if_option_a @ ( member_b @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_b @ A2 @ B2 )
@ ( sup_sup_set_option_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_839_bij__betw__disjoint__Un,axiom,
! [F2: a > b,A2: set_a,C3: set_b,G: a > b,B2: set_a,D2: set_b] :
( ( bij_betw_a_b @ F2 @ A2 @ C3 )
=> ( ( bij_betw_a_b @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ B2 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_b @ C3 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_a_b
@ ^ [X5: a] : ( if_b @ ( member_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_a @ A2 @ B2 )
@ ( sup_sup_set_b @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_840_bij__betw__disjoint__Un,axiom,
! [F2: a > a,A2: set_a,C3: set_a,G: a > a,B2: set_a,D2: set_a] :
( ( bij_betw_a_a @ F2 @ A2 @ C3 )
=> ( ( bij_betw_a_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ B2 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_a @ C3 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_a_a
@ ^ [X5: a] : ( if_a @ ( member_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_a @ A2 @ B2 )
@ ( sup_sup_set_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_841_bij__betw__disjoint__Un,axiom,
! [F2: a > option_a,A2: set_a,C3: set_option_a,G: a > option_a,B2: set_a,D2: set_option_a] :
( ( bij_betw_a_option_a @ F2 @ A2 @ C3 )
=> ( ( bij_betw_a_option_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_a @ A2 @ B2 )
= bot_bot_set_a )
=> ( ( ( inf_inf_set_option_a @ C3 @ D2 )
= bot_bot_set_option_a )
=> ( bij_betw_a_option_a
@ ^ [X5: a] : ( if_option_a @ ( member_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_a @ A2 @ B2 )
@ ( sup_sup_set_option_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_842_bij__betw__disjoint__Un,axiom,
! [F2: option_a > b,A2: set_option_a,C3: set_b,G: option_a > b,B2: set_option_a,D2: set_b] :
( ( bij_betw_option_a_b @ F2 @ A2 @ C3 )
=> ( ( bij_betw_option_a_b @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ B2 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_b @ C3 @ D2 )
= bot_bot_set_b )
=> ( bij_betw_option_a_b
@ ^ [X5: option_a] : ( if_b @ ( member_option_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_option_a @ A2 @ B2 )
@ ( sup_sup_set_b @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_843_bij__betw__disjoint__Un,axiom,
! [F2: option_a > a,A2: set_option_a,C3: set_a,G: option_a > a,B2: set_option_a,D2: set_a] :
( ( bij_betw_option_a_a @ F2 @ A2 @ C3 )
=> ( ( bij_betw_option_a_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ B2 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_a @ C3 @ D2 )
= bot_bot_set_a )
=> ( bij_betw_option_a_a
@ ^ [X5: option_a] : ( if_a @ ( member_option_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_option_a @ A2 @ B2 )
@ ( sup_sup_set_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_844_bij__betw__disjoint__Un,axiom,
! [F2: option_a > option_a,A2: set_option_a,C3: set_option_a,G: option_a > option_a,B2: set_option_a,D2: set_option_a] :
( ( bij_be5431266891817924854tion_a @ F2 @ A2 @ C3 )
=> ( ( bij_be5431266891817924854tion_a @ G @ B2 @ D2 )
=> ( ( ( inf_inf_set_option_a @ A2 @ B2 )
= bot_bot_set_option_a )
=> ( ( ( inf_inf_set_option_a @ C3 @ D2 )
= bot_bot_set_option_a )
=> ( bij_be5431266891817924854tion_a
@ ^ [X5: option_a] : ( if_option_a @ ( member_option_a @ X5 @ A2 ) @ ( F2 @ X5 ) @ ( G @ X5 ) )
@ ( sup_sup_set_option_a @ A2 @ B2 )
@ ( sup_sup_set_option_a @ C3 @ D2 ) ) ) ) ) ) ).
% bij_betw_disjoint_Un
thf(fact_845_option_Osize__gen__o__map,axiom,
! [F2: a > nat,G: a > a] :
( ( comp_o8583038678572498833tion_a @ ( size_option_a @ F2 ) @ ( map_option_a_a @ G ) )
= ( size_option_a @ ( comp_a_nat_a @ F2 @ G ) ) ) ).
% option.size_gen_o_map
thf(fact_846_set__bind__option,axiom,
! [X: option_a,F2: a > option_a] :
( ( set_option_a2 @ ( bind_a_a @ X @ F2 ) )
= ( comple2307003609928055243_set_a @ ( image_a_set_a @ ( comp_o6143895765626710849et_a_a @ set_option_a2 @ F2 ) @ ( set_option_a2 @ X ) ) ) ) ).
% set_bind_option
thf(fact_847_fcomp__comp,axiom,
( fcomp_a_option_a_a
= ( ^ [F: a > option_a,G2: option_a > a] : ( comp_option_a_a_a @ G2 @ F ) ) ) ).
% fcomp_comp
thf(fact_848_monotone__on__o,axiom,
! [A2: set_option_a,Orda: option_a > option_a > $o,Ordb: a > a > $o,F2: option_a > a,B2: set_a,Ordc: a > a > $o,G: a > option_a] :
( ( monoto4483592047695070497on_a_a @ A2 @ Orda @ Ordb @ F2 )
=> ( ( monoto2261078166156275373tion_a @ B2 @ Ordc @ Orda @ G )
=> ( ( ord_le1955136853071979460tion_a @ ( image_a_option_a @ G @ B2 ) @ A2 )
=> ( monotone_on_a_a @ B2 @ Ordc @ Ordb @ ( comp_option_a_a_a @ F2 @ G ) ) ) ) ) ).
% monotone_on_o
thf(fact_849_mono__sup,axiom,
! [F2: set_b > set_b,A2: set_b,B2: set_b] :
( ( monoto8660672184891397159_set_b @ top_top_set_set_b @ ord_less_eq_set_b @ ord_less_eq_set_b @ F2 )
=> ( ord_less_eq_set_b @ ( sup_sup_set_b @ ( F2 @ A2 ) @ ( F2 @ B2 ) ) @ ( F2 @ ( sup_sup_set_b @ A2 @ B2 ) ) ) ) ).
% mono_sup
thf(fact_850_mono__Un,axiom,
! [F2: set_b > set_b,A2: set_b,B2: set_b] :
( ( monoto8660672184891397159_set_b @ top_top_set_set_b @ ord_less_eq_set_b @ ord_less_eq_set_b @ F2 )
=> ( ord_less_eq_set_b @ ( sup_sup_set_b @ ( F2 @ A2 ) @ ( F2 @ B2 ) ) @ ( F2 @ ( sup_sup_set_b @ A2 @ B2 ) ) ) ) ).
% mono_Un
thf(fact_851_image__strict__mono,axiom,
! [F2: option_a > a,B2: set_option_a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ B2 )
=> ( ( ord_le5631237216984945872tion_a @ A2 @ B2 )
=> ( ord_less_set_a @ ( image_option_a_a @ F2 @ A2 ) @ ( image_option_a_a @ F2 @ B2 ) ) ) ) ).
% image_strict_mono
thf(fact_852_image__strict__mono,axiom,
! [F2: a > option_a,B2: set_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ B2 )
=> ( ( ord_less_set_a @ A2 @ B2 )
=> ( ord_le5631237216984945872tion_a @ ( image_a_option_a @ F2 @ A2 ) @ ( image_a_option_a @ F2 @ B2 ) ) ) ) ).
% image_strict_mono
thf(fact_853_Sup__fin_Oeq__fold_H,axiom,
( lattic2918178361130032022_set_b
= ( ^ [A7: set_set_b] :
( the_set_b
@ ( finite4684332809091328718_set_b
@ ^ [X5: set_b,Y2: option_set_b] : ( some_set_b @ ( case_o6570817238820213323_set_b @ X5 @ ( sup_sup_set_b @ X5 ) @ Y2 ) )
@ none_set_b
@ A7 ) ) ) ) ).
% Sup_fin.eq_fold'
thf(fact_854_semilattice__set_Oeq__fold_H,axiom,
! [F2: a > a > a,A2: set_a] :
( ( lattic5961991414251573132_set_a @ F2 )
=> ( ( lattic5116578512385870296ce_F_a @ F2 @ A2 )
= ( the_a2
@ ( finite6501707464432451470tion_a
@ ^ [X5: a,Y2: option_a] : ( some_a @ ( case_option_a_a @ X5 @ ( F2 @ X5 ) @ Y2 ) )
@ none_a
@ A2 ) ) ) ) ).
% semilattice_set.eq_fold'
thf(fact_855_semilattice__set_Oinfinite,axiom,
! [F2: option_a > option_a > option_a,A2: set_option_a] :
( ( lattic4111267149900974290tion_a @ F2 )
=> ( ~ ( finite1674126218327898605tion_a @ A2 )
=> ( ( lattic5543840709497872670tion_a @ F2 @ A2 )
= ( the_option_a2 @ none_option_a ) ) ) ) ).
% semilattice_set.infinite
thf(fact_856_semilattice__set_Oinfinite,axiom,
! [F2: a > a > a,A2: set_a] :
( ( lattic5961991414251573132_set_a @ F2 )
=> ( ~ ( finite_finite_a @ A2 )
=> ( ( lattic5116578512385870296ce_F_a @ F2 @ A2 )
= ( the_a2 @ none_a ) ) ) ) ).
% semilattice_set.infinite
thf(fact_857_inj__on__iff__Uniq,axiom,
( inj_on_a_option_a
= ( ^ [F: a > option_a,A7: set_a] :
! [X5: a] :
( ( member_a @ X5 @ A7 )
=> ( uniq_a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ A7 )
& ( ( F @ X5 )
= ( F @ Y2 ) ) ) ) ) ) ) ).
% inj_on_iff_Uniq
thf(fact_858_rel__optionI,axiom,
! [X: option_a,Y: option_a,P4: a > a > $o] :
( ( ( is_none_a @ X )
= ( is_none_a @ Y ) )
=> ( ( ~ ( is_none_a @ X )
=> ( ~ ( is_none_a @ Y )
=> ( P4 @ ( the_a2 @ X ) @ ( the_a2 @ Y ) ) ) )
=> ( rel_option_a_a @ P4 @ X @ Y ) ) ) ).
% rel_optionI
thf(fact_859_rel__option__unfold,axiom,
( rel_option_a_a
= ( ^ [R4: a > a > $o,X5: option_a,Y2: option_a] :
( ( ( is_none_a @ X5 )
= ( is_none_a @ Y2 ) )
& ( ~ ( is_none_a @ X5 )
=> ( ~ ( is_none_a @ Y2 )
=> ( R4 @ ( the_a2 @ X5 ) @ ( the_a2 @ Y2 ) ) ) ) ) ) ) ).
% rel_option_unfold
thf(fact_860_rel__option__None1,axiom,
! [P4: a > a > $o,X: option_a] :
( ( rel_option_a_a @ P4 @ none_a @ X )
= ( X = none_a ) ) ).
% rel_option_None1
thf(fact_861_rel__option__None2,axiom,
! [P4: a > a > $o,X: option_a] :
( ( rel_option_a_a @ P4 @ X @ none_a )
= ( X = none_a ) ) ).
% rel_option_None2
thf(fact_862_option_Orel__distinct_I2_J,axiom,
! [R3: a > a > $o,Y23: a] :
~ ( rel_option_a_a @ R3 @ ( some_a @ Y23 ) @ none_a ) ).
% option.rel_distinct(2)
thf(fact_863_option_Orel__distinct_I1_J,axiom,
! [R3: a > a > $o,Y23: a] :
~ ( rel_option_a_a @ R3 @ none_a @ ( some_a @ Y23 ) ) ).
% option.rel_distinct(1)
thf(fact_864_option_Orel__cases,axiom,
! [R3: a > a > $o,A: option_a,B: option_a] :
( ( rel_option_a_a @ R3 @ A @ B )
=> ( ( ( A = none_a )
=> ( B != none_a ) )
=> ~ ! [X4: a] :
( ( A
= ( some_a @ X4 ) )
=> ! [Y3: a] :
( ( B
= ( some_a @ Y3 ) )
=> ~ ( R3 @ X4 @ Y3 ) ) ) ) ) ).
% option.rel_cases
thf(fact_865_option_Orel__induct,axiom,
! [R3: a > a > $o,X: option_a,Y: option_a,Q4: option_a > option_a > $o] :
( ( rel_option_a_a @ R3 @ X @ Y )
=> ( ( Q4 @ none_a @ none_a )
=> ( ! [A23: a,B23: a] :
( ( R3 @ A23 @ B23 )
=> ( Q4 @ ( some_a @ A23 ) @ ( some_a @ B23 ) ) )
=> ( Q4 @ X @ Y ) ) ) ) ).
% option.rel_induct
thf(fact_866_rel__option__inf,axiom,
! [A2: a > a > $o,B2: a > a > $o] :
( ( inf_in5160421943901843420on_a_o @ ( rel_option_a_a @ A2 ) @ ( rel_option_a_a @ B2 ) )
= ( rel_option_a_a @ ( inf_inf_a_a_o @ A2 @ B2 ) ) ) ).
% rel_option_inf
thf(fact_867_option_Orel__inject_I2_J,axiom,
! [R3: a > a > $o,X2: a,Y23: a] :
( ( rel_option_a_a @ R3 @ ( some_a @ X2 ) @ ( some_a @ Y23 ) )
= ( R3 @ X2 @ Y23 ) ) ).
% option.rel_inject(2)
thf(fact_868_option_Orel__intros_I2_J,axiom,
! [R3: a > a > $o,X2: a,Y23: a] :
( ( R3 @ X2 @ Y23 )
=> ( rel_option_a_a @ R3 @ ( some_a @ X2 ) @ ( some_a @ Y23 ) ) ) ).
% option.rel_intros(2)
thf(fact_869_option__rel__Some1,axiom,
! [A2: a > a > $o,X: a,Y: option_a] :
( ( rel_option_a_a @ A2 @ ( some_a @ X ) @ Y )
= ( ? [Y4: a] :
( ( Y
= ( some_a @ Y4 ) )
& ( A2 @ X @ Y4 ) ) ) ) ).
% option_rel_Some1
thf(fact_870_option__rel__Some2,axiom,
! [A2: a > a > $o,X: option_a,Y: a] :
( ( rel_option_a_a @ A2 @ X @ ( some_a @ Y ) )
= ( ? [X10: a] :
( ( X
= ( some_a @ X10 ) )
& ( A2 @ X10 @ Y ) ) ) ) ).
% option_rel_Some2
thf(fact_871_option_Octr__transfer_I1_J,axiom,
! [R3: a > a > $o] : ( rel_option_a_a @ R3 @ none_a @ none_a ) ).
% option.ctr_transfer(1)
thf(fact_872_rel__option__reflI,axiom,
! [Y: option_option_a,P4: option_a > option_a > $o] :
( ! [X4: option_a] :
( ( member_option_a @ X4 @ ( set_option_option_a2 @ Y ) )
=> ( P4 @ X4 @ X4 ) )
=> ( rel_op4798662380513671176tion_a @ P4 @ Y @ Y ) ) ).
% rel_option_reflI
thf(fact_873_rel__option__reflI,axiom,
! [Y: option_b,P4: b > b > $o] :
( ! [X4: b] :
( ( member_b @ X4 @ ( set_option_b2 @ Y ) )
=> ( P4 @ X4 @ X4 ) )
=> ( rel_option_b_b @ P4 @ Y @ Y ) ) ).
% rel_option_reflI
thf(fact_874_rel__option__reflI,axiom,
! [Y: option_a,P4: a > a > $o] :
( ! [X4: a] :
( ( member_a @ X4 @ ( set_option_a2 @ Y ) )
=> ( P4 @ X4 @ X4 ) )
=> ( rel_option_a_a @ P4 @ Y @ Y ) ) ).
% rel_option_reflI
thf(fact_875_option_Orel__refl__strong,axiom,
! [X: option_option_a,Ra: option_a > option_a > $o] :
( ! [Z3: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( rel_op4798662380513671176tion_a @ Ra @ X @ X ) ) ).
% option.rel_refl_strong
thf(fact_876_option_Orel__refl__strong,axiom,
! [X: option_b,Ra: b > b > $o] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( rel_option_b_b @ Ra @ X @ X ) ) ).
% option.rel_refl_strong
thf(fact_877_option_Orel__refl__strong,axiom,
! [X: option_a,Ra: a > a > $o] :
( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( rel_option_a_a @ Ra @ X @ X ) ) ).
% option.rel_refl_strong
thf(fact_878_option_Orel__mono__strong,axiom,
! [R3: option_a > option_a > $o,X: option_option_a,Y: option_option_a,Ra: option_a > option_a > $o] :
( ( rel_op4798662380513671176tion_a @ R3 @ X @ Y )
=> ( ! [Z3: option_a,Yb2: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ X ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_op4798662380513671176tion_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_879_option_Orel__mono__strong,axiom,
! [R3: option_a > b > $o,X: option_option_a,Y: option_b,Ra: option_a > b > $o] :
( ( rel_op3736390606718109635on_a_b @ R3 @ X @ Y )
=> ( ! [Z3: option_a,Yb2: b] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ X ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_op3736390606718109635on_a_b @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_880_option_Orel__mono__strong,axiom,
! [R3: b > option_a > $o,X: option_b,Y: option_option_a,Ra: b > option_a > $o] :
( ( rel_op7651492520044095757tion_a @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: option_a] :
( ( member_b @ Z3 @ ( set_option_b2 @ X ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_op7651492520044095757tion_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_881_option_Orel__mono__strong,axiom,
! [R3: b > b > $o,X: option_b,Y: option_b,Ra: b > b > $o] :
( ( rel_option_b_b @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ X ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_option_b_b @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_882_option_Orel__mono__strong,axiom,
! [R3: option_a > a > $o,X: option_option_a,Y: option_a,Ra: option_a > a > $o] :
( ( rel_op3736390606718109634on_a_a @ R3 @ X @ Y )
=> ( ! [Z3: option_a,Yb2: a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ X ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_op3736390606718109634on_a_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_883_option_Orel__mono__strong,axiom,
! [R3: b > a > $o,X: option_b,Y: option_a,Ra: b > a > $o] :
( ( rel_option_b_a @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: a] :
( ( member_b @ Z3 @ ( set_option_b2 @ X ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_option_b_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_884_option_Orel__mono__strong,axiom,
! [R3: a > option_a > $o,X: option_a,Y: option_option_a,Ra: a > option_a > $o] :
( ( rel_op1513876725179314510tion_a @ R3 @ X @ Y )
=> ( ! [Z3: a,Yb2: option_a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_op1513876725179314510tion_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_885_option_Orel__mono__strong,axiom,
! [R3: a > b > $o,X: option_a,Y: option_b,Ra: a > b > $o] :
( ( rel_option_a_b @ R3 @ X @ Y )
=> ( ! [Z3: a,Yb2: b] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_option_a_b @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_886_option_Orel__mono__strong,axiom,
! [R3: a > a > $o,X: option_a,Y: option_a,Ra: a > a > $o] :
( ( rel_option_a_a @ R3 @ X @ Y )
=> ( ! [Z3: a,Yb2: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_option_a_a @ Ra @ X @ Y ) ) ) ).
% option.rel_mono_strong
thf(fact_887_option_Orel__cong,axiom,
! [X: option_option_a,Ya: option_option_a,Y: option_option_a,Xa2: option_option_a,R3: option_a > option_a > $o,Ra: option_a > option_a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: option_a,Yb2: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ Ya ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_op4798662380513671176tion_a @ R3 @ X @ Y )
= ( rel_op4798662380513671176tion_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_888_option_Orel__cong,axiom,
! [X: option_option_a,Ya: option_option_a,Y: option_b,Xa2: option_b,R3: option_a > b > $o,Ra: option_a > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: option_a,Yb2: b] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_op3736390606718109635on_a_b @ R3 @ X @ Y )
= ( rel_op3736390606718109635on_a_b @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_889_option_Orel__cong,axiom,
! [X: option_b,Ya: option_b,Y: option_option_a,Xa2: option_option_a,R3: b > option_a > $o,Ra: b > option_a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: option_a] :
( ( member_b @ Z3 @ ( set_option_b2 @ Ya ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_op7651492520044095757tion_a @ R3 @ X @ Y )
= ( rel_op7651492520044095757tion_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_890_option_Orel__cong,axiom,
! [X: option_b,Ya: option_b,Y: option_b,Xa2: option_b,R3: b > b > $o,Ra: b > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_option_b_b @ R3 @ X @ Y )
= ( rel_option_b_b @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_891_option_Orel__cong,axiom,
! [X: option_option_a,Ya: option_option_a,Y: option_a,Xa2: option_a,R3: option_a > a > $o,Ra: option_a > a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: option_a,Yb2: a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ Ya ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_op3736390606718109634on_a_a @ R3 @ X @ Y )
= ( rel_op3736390606718109634on_a_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_892_option_Orel__cong,axiom,
! [X: option_b,Ya: option_b,Y: option_a,Xa2: option_a,R3: b > a > $o,Ra: b > a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: a] :
( ( member_b @ Z3 @ ( set_option_b2 @ Ya ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_option_b_a @ R3 @ X @ Y )
= ( rel_option_b_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_893_option_Orel__cong,axiom,
! [X: option_a,Ya: option_a,Y: option_option_a,Xa2: option_option_a,R3: a > option_a > $o,Ra: a > option_a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: a,Yb2: option_a] :
( ( member_a @ Z3 @ ( set_option_a2 @ Ya ) )
=> ( ( member_option_a @ Yb2 @ ( set_option_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_op1513876725179314510tion_a @ R3 @ X @ Y )
= ( rel_op1513876725179314510tion_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_894_option_Orel__cong,axiom,
! [X: option_a,Ya: option_a,Y: option_b,Xa2: option_b,R3: a > b > $o,Ra: a > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: a,Yb2: b] :
( ( member_a @ Z3 @ ( set_option_a2 @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_option_b2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_option_a_b @ R3 @ X @ Y )
= ( rel_option_a_b @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_895_option_Orel__cong,axiom,
! [X: option_a,Ya: option_a,Y: option_a,Xa2: option_a,R3: a > a > $o,Ra: a > a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: a,Yb2: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ Ya ) )
=> ( ( member_a @ Yb2 @ ( set_option_a2 @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_option_a_a @ R3 @ X @ Y )
= ( rel_option_a_a @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% option.rel_cong
thf(fact_896_option_Orel__eq,axiom,
( ( rel_option_a_a
@ ^ [Y5: a,Z4: a] : ( Y5 = Z4 ) )
= ( ^ [Y5: option_a,Z4: option_a] : ( Y5 = Z4 ) ) ) ).
% option.rel_eq
thf(fact_897_option_Orel__refl,axiom,
! [Ra: a > a > $o,X: option_a] :
( ! [X4: a] : ( Ra @ X4 @ X4 )
=> ( rel_option_a_a @ Ra @ X @ X ) ) ).
% option.rel_refl
thf(fact_898_option_Orel__map_I2_J,axiom,
! [Sa: a > a > $o,X: option_a,G: a > a,Y: option_a] :
( ( rel_option_a_a @ Sa @ X @ ( map_option_a_a @ G @ Y ) )
= ( rel_option_a_a
@ ^ [X5: a,Y2: a] : ( Sa @ X5 @ ( G @ Y2 ) )
@ X
@ Y ) ) ).
% option.rel_map(2)
thf(fact_899_option_Orel__map_I1_J,axiom,
! [Sb: a > a > $o,I: a > a,X: option_a,Y: option_a] :
( ( rel_option_a_a @ Sb @ ( map_option_a_a @ I @ X ) @ Y )
= ( rel_option_a_a
@ ^ [X5: a] : ( Sb @ ( I @ X5 ) )
@ X
@ Y ) ) ).
% option.rel_map(1)
thf(fact_900_option_Orel__mono,axiom,
! [R3: a > a > $o,Ra: a > a > $o] :
( ( ord_less_eq_a_a_o @ R3 @ Ra )
=> ( ord_le3058241657886854542on_a_o @ ( rel_option_a_a @ R3 ) @ ( rel_option_a_a @ Ra ) ) ) ).
% option.rel_mono
thf(fact_901_option_Orel__sel,axiom,
( rel_option_a_a
= ( ^ [R4: a > a > $o,A6: option_a,B5: option_a] :
( ( ( A6 = none_a )
= ( B5 = none_a ) )
& ( ( A6 != none_a )
=> ( ( B5 != none_a )
=> ( R4 @ ( the_a2 @ A6 ) @ ( the_a2 @ B5 ) ) ) ) ) ) ) ).
% option.rel_sel
thf(fact_902_rel__option__iff,axiom,
( rel_option_a_a
= ( ^ [R4: a > a > $o,X5: option_a,Y2: option_a] :
( produc7248784972643495020on_a_o
@ ^ [A6: option_a,B5: option_a] :
( case_option_o_a
@ ( case_option_o_a @ $true
@ ^ [C2: a] : $false
@ B5 )
@ ^ [Z: a] : ( case_option_o_a @ $false @ ( R4 @ Z ) @ B5 )
@ A6 )
@ ( produc9011544418120257559tion_a @ X5 @ Y2 ) ) ) ) ).
% rel_option_iff
thf(fact_903_option_Orel__Grp,axiom,
! [A2: set_a,F2: a > a] :
( ( rel_option_a_a @ ( bNF_Grp_a_a @ A2 @ F2 ) )
= ( bNF_Gr5654676046521400910tion_a
@ ( collect_option_a
@ ^ [X5: option_a] : ( ord_less_eq_set_a @ ( set_option_a2 @ X5 ) @ A2 ) )
@ ( map_option_a_a @ F2 ) ) ) ).
% option.rel_Grp
thf(fact_904_option_Odisc__transfer_I2_J,axiom,
! [R3: a > a > $o] :
( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ R3 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
@ ^ [Option3: option_a] : ( Option3 != none_a )
@ ^ [Option3: option_a] : ( Option3 != none_a ) ) ).
% option.disc_transfer(2)
thf(fact_905_option_Ocase__transfer,axiom,
! [S4: $o > $o > $o,R3: a > a > $o] : ( bNF_re1464701735350397069on_a_o @ S4 @ ( bNF_re4859868158825367505on_a_o @ ( bNF_rel_fun_a_a_o_o @ R3 @ S4 ) @ ( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_o_a @ case_option_o_a ) ).
% option.case_transfer
thf(fact_906_option_Ocase__transfer,axiom,
! [S4: $o > a > $o,R3: a > a > $o] : ( bNF_re4337018088969878591on_a_a @ S4 @ ( bNF_re102678143051736477on_a_a @ ( bNF_rel_fun_a_a_o_a @ R3 @ S4 ) @ ( bNF_re8815814597387604803_a_o_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_o_a @ case_option_a_a ) ).
% option.case_transfer
thf(fact_907_option_Ocase__transfer,axiom,
! [S4: a > $o > $o,R3: a > a > $o] : ( bNF_re8717284581917077363on_a_o @ S4 @ ( bNF_re4058884933032857501on_a_o @ ( bNF_rel_fun_a_a_a_o @ R3 @ S4 ) @ ( bNF_re8895294753853352567_a_a_o @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_a_a @ case_option_o_a ) ).
% option.case_transfer
thf(fact_908_option_Ocase__transfer,axiom,
! [S4: a > a > $o,R3: a > a > $o] : ( bNF_re6523360481052543525on_a_a @ S4 @ ( bNF_re1079736789768479081on_a_a @ ( bNF_rel_fun_a_a_a_a @ R3 @ S4 ) @ ( bNF_re6951206947496014429_a_a_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_a_a @ case_option_a_a ) ).
% option.case_transfer
thf(fact_909_option_Ocase__transfer,axiom,
! [S4: $o > option_a > $o,R3: a > a > $o] : ( bNF_re7078363273947182481tion_a @ S4 @ ( bNF_re2369685550566307625tion_a @ ( bNF_re905553932590079753tion_a @ R3 @ S4 ) @ ( bNF_re1129020316103814665tion_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_o_a @ case_o3148979394504432965on_a_a ) ).
% option.case_transfer
thf(fact_910_option_Ocase__transfer,axiom,
! [S4: option_a > $o > $o,R3: a > a > $o] : ( bNF_re4311958519388381497on_a_o @ S4 @ ( bNF_re6058157240589548841on_a_o @ ( bNF_re1847112384428219057on_a_o @ R3 @ S4 ) @ ( bNF_re2070578767941953969on_a_o @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_o3148979394504432965on_a_a @ case_option_o_a ) ).
% option.case_transfer
thf(fact_911_option_Ocase__transfer,axiom,
! [S4: option_a > a > $o,R3: a > a > $o] : ( bNF_re5218620495166150379on_a_a @ S4 @ ( bNF_re5072729714030605557on_a_a @ ( bNF_re5794519239126689175on_a_a @ R3 @ S4 ) @ ( bNF_re4157831115608716439on_a_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_o3148979394504432965on_a_a @ case_option_a_a ) ).
% option.case_transfer
thf(fact_912_option_Ocase__transfer,axiom,
! [S4: a > option_a > $o,R3: a > a > $o] : ( bNF_re1882382041600142455tion_a @ S4 @ ( bNF_re7263069294043397365tion_a @ ( bNF_re3572005357587894051tion_a @ R3 @ S4 ) @ ( bNF_re1935317234069921315tion_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_option_a_a @ case_o3148979394504432965on_a_a ) ).
% option.case_transfer
thf(fact_913_option_Ocase__transfer,axiom,
! [S4: $o > $o > $o,R3: option_a > option_a > $o] : ( bNF_re7775980886671535221on_a_o @ S4 @ ( bNF_re8007680959799151545on_a_o @ ( bNF_re905040088260304477_a_o_o @ R3 @ S4 ) @ ( bNF_re669219658517073757_a_o_o @ ( rel_op4798662380513671176tion_a @ R3 ) @ S4 ) ) @ case_o3426643154261757367tion_a @ case_o3426643154261757367tion_a ) ).
% option.case_transfer
thf(fact_914_option_Ocase__transfer,axiom,
! [S4: option_a > option_a > $o,R3: a > a > $o] : ( bNF_re1266155380144051773tion_a @ S4 @ ( bNF_re2722752998287985793tion_a @ ( bNF_re1187871780581372509tion_a @ R3 @ S4 ) @ ( bNF_re8713957294334624093tion_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ case_o3148979394504432965on_a_a @ case_o3148979394504432965on_a_a ) ).
% option.case_transfer
thf(fact_915_option_Orec__transfer,axiom,
! [S4: $o > $o > $o,R3: option_a > option_a > $o] : ( bNF_re7775980886671535221on_a_o @ S4 @ ( bNF_re8007680959799151545on_a_o @ ( bNF_re905040088260304477_a_o_o @ R3 @ S4 ) @ ( bNF_re669219658517073757_a_o_o @ ( rel_op4798662380513671176tion_a @ R3 ) @ S4 ) ) @ rec_op1346285999958695467tion_a @ rec_op1346285999958695467tion_a ) ).
% option.rec_transfer
thf(fact_916_option_Orec__transfer,axiom,
! [S4: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o,R3: d > d > $o] : ( bNF_re188506143030329217_b_c_d @ S4 @ ( bNF_re2842133318421313373_b_c_d @ ( bNF_re7418416730241609193_b_c_d @ R3 @ S4 ) @ ( bNF_re4152538054372293993_b_c_d @ ( rel_option_d_d @ R3 ) @ S4 ) ) @ rec_op905682932589663963_c_d_d @ rec_op905682932589663963_c_d_d ) ).
% option.rec_transfer
thf(fact_917_option_Orec__transfer,axiom,
! [S4: assertion_a_b_c_d > assertion_a_b_c_d > $o,R3: assertion_a_b_c_d > assertion_a_b_c_d > $o] : ( bNF_re8287430210025019109_b_c_d @ S4 @ ( bNF_re7065123807510049385_b_c_d @ ( bNF_re2060205161886013149_b_c_d @ R3 @ S4 ) @ ( bNF_re6421063287152323421_b_c_d @ ( rel_op1902716345276195528_b_c_d @ R3 ) @ S4 ) ) @ rec_op3341093412072267839_b_c_d @ rec_op3341093412072267839_b_c_d ) ).
% option.rec_transfer
thf(fact_918_option_Orec__transfer,axiom,
! [S4: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o,R3: assertion_a_b_c_d > assertion_a_b_c_d > $o] : ( bNF_re706445162651761793_b_c_d @ S4 @ ( bNF_re1042997550465084509_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ R3 @ S4 ) @ ( bNF_re3325060626551612777_b_c_d @ ( rel_op1902716345276195528_b_c_d @ R3 ) @ S4 ) ) @ rec_op6099162144272762835_b_c_d @ rec_op6099162144272762835_b_c_d ) ).
% option.rec_transfer
thf(fact_919_option_Orec__transfer,axiom,
! [S4: $o > $o > $o,R3: a > a > $o] : ( bNF_re1464701735350397069on_a_o @ S4 @ ( bNF_re4859868158825367505on_a_o @ ( bNF_rel_fun_a_a_o_o @ R3 @ S4 ) @ ( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ rec_option_o_a @ rec_option_o_a ) ).
% option.rec_transfer
thf(fact_920_option_Orec__transfer,axiom,
! [S4: option_a > option_a > $o,R3: a > a > $o] : ( bNF_re1266155380144051773tion_a @ S4 @ ( bNF_re2722752998287985793tion_a @ ( bNF_re1187871780581372509tion_a @ R3 @ S4 ) @ ( bNF_re8713957294334624093tion_a @ ( rel_option_a_a @ R3 ) @ S4 ) ) @ rec_op3997991240598549433on_a_a @ rec_op3997991240598549433on_a_a ) ).
% option.rec_transfer
thf(fact_921_option_Omap__transfer,axiom,
! [Rb: option_a > option_a > $o,Sd: $o > $o > $o] : ( bNF_re5724521104517466949tion_o @ ( bNF_re905040088260304477_a_o_o @ Rb @ Sd ) @ ( bNF_re7165334401771760221tion_o @ ( rel_op4798662380513671176tion_a @ Rb ) @ ( rel_option_o_o @ Sd ) ) @ map_op2529087131052605791on_a_o @ map_op2529087131052605791on_a_o ) ).
% option.map_transfer
thf(fact_922_option_Omap__transfer,axiom,
! [Rb: d > d > $o,Sd: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o] : ( bNF_re7892989858577796701_b_c_d @ ( bNF_re7418416730241609193_b_c_d @ Rb @ Sd ) @ ( bNF_re7977768539823379977_b_c_d @ ( rel_option_d_d @ Rb ) @ ( rel_op2232639710186594644_b_c_d @ Sd ) ) @ map_op1826348495503636827_b_c_d @ map_op1826348495503636827_b_c_d ) ).
% option.map_transfer
thf(fact_923_option_Omap__transfer,axiom,
! [Rb: assertion_a_b_c_d > assertion_a_b_c_d > $o,Sd: assertion_a_b_c_d > assertion_a_b_c_d > $o] : ( bNF_re3402983428571792885_b_c_d @ ( bNF_re2060205161886013149_b_c_d @ Rb @ Sd ) @ ( bNF_re1760841454573502429_b_c_d @ ( rel_op1902716345276195528_b_c_d @ Rb ) @ ( rel_op1902716345276195528_b_c_d @ Sd ) ) @ map_op4138611287120429003_b_c_d @ map_op4138611287120429003_b_c_d ) ).
% option.map_transfer
thf(fact_924_option_Omap__transfer,axiom,
! [Rb: assertion_a_b_c_d > assertion_a_b_c_d > $o,Sd: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o] : ( bNF_re5092460513005817693_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ Rb @ Sd ) @ ( bNF_re1839893911826710025_b_c_d @ ( rel_op1902716345276195528_b_c_d @ Rb ) @ ( rel_op2232639710186594644_b_c_d @ Sd ) ) @ map_op7273698777129206611_b_c_d @ map_op7273698777129206611_b_c_d ) ).
% option.map_transfer
thf(fact_925_option_Omap__transfer,axiom,
! [Rb: a > a > $o,Sd: option_a > option_a > $o] : ( bNF_re2496629990708770829tion_a @ ( bNF_re1187871780581372509tion_a @ Rb @ Sd ) @ ( bNF_re1595600300046643805tion_a @ ( rel_option_a_a @ Rb ) @ ( rel_op4798662380513671176tion_a @ Sd ) ) @ map_op2340691886215429841tion_a @ map_op2340691886215429841tion_a ) ).
% option.map_transfer
thf(fact_926_option_Omap__transfer,axiom,
! [Rb: a > a > $o,Sd: a > a > $o] : ( bNF_re8471833820502647285tion_a @ ( bNF_rel_fun_a_a_a_a @ Rb @ Sd ) @ ( bNF_re8713957294334624093tion_a @ ( rel_option_a_a @ Rb ) @ ( rel_option_a_a @ Sd ) ) @ map_option_a_a @ map_option_a_a ) ).
% option.map_transfer
thf(fact_927_option_Odisc__transfer_I1_J,axiom,
! [R3: a > a > $o] :
( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ R3 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
@ ^ [Option3: option_a] : ( Option3 = none_a )
@ ^ [Option3: option_a] : ( Option3 = none_a ) ) ).
% option.disc_transfer(1)
thf(fact_928_option_Oin__rel,axiom,
( rel_option_a_a
= ( ^ [R4: a > a > $o,A6: option_a,B5: option_a] :
? [Z: option5210160422955383789od_a_a] :
( ( member8183384484874023062od_a_a @ Z
@ ( collec431113534271933400od_a_a
@ ^ [X5: option5210160422955383789od_a_a] : ( ord_le746702958409616551od_a_a @ ( set_op3367984300228426933od_a_a @ X5 ) @ ( collec3336397797384452498od_a_a @ ( produc6436628058953941356_a_a_o @ R4 ) ) ) ) )
& ( ( map_op713297920823408162_a_a_a @ product_fst_a_a @ Z )
= A6 )
& ( ( map_op713297920823408162_a_a_a @ product_snd_a_a @ Z )
= B5 ) ) ) ) ).
% option.in_rel
thf(fact_929_inj__on__image__Pow,axiom,
! [F2: option_a > a,A2: set_option_a] :
( ( inj_on_option_a_a @ F2 @ A2 )
=> ( inj_on8475384959944041899_set_a @ ( image_option_a_a @ F2 ) @ ( pow_option_a @ A2 ) ) ) ).
% inj_on_image_Pow
thf(fact_930_inj__on__image__Pow,axiom,
! [F2: a > option_a,A2: set_a] :
( ( inj_on_a_option_a @ F2 @ A2 )
=> ( inj_on478642083548346935tion_a @ ( image_a_option_a @ F2 ) @ ( pow_a @ A2 ) ) ) ).
% inj_on_image_Pow
thf(fact_931_option_Omap__cong__pred,axiom,
! [X: option_a,Ya: option_a,F2: a > a,G: a > a] :
( ( X = Ya )
=> ( ( pred_option_a
@ ^ [Z: a] :
( ( F2 @ Z )
= ( G @ Z ) )
@ Ya )
=> ( ( map_option_a_a @ F2 @ X )
= ( map_option_a_a @ G @ Ya ) ) ) ) ).
% option.map_cong_pred
thf(fact_932_option_Opred__inject_I2_J,axiom,
! [P4: a > $o,A: a] :
( ( pred_option_a @ P4 @ ( some_a @ A ) )
= ( P4 @ A ) ) ).
% option.pred_inject(2)
thf(fact_933_option_Octr__transfer_I2_J,axiom,
! [R3: a > a > $o] : ( bNF_re1187871780581372509tion_a @ R3 @ ( rel_option_a_a @ R3 ) @ some_a @ some_a ) ).
% option.ctr_transfer(2)
thf(fact_934_option_Orel__transfer,axiom,
! [Sa: a > a > $o,Sc: option_a > option_a > $o] :
( bNF_re3412046433515172957on_a_o
@ ( bNF_re6100770640034910033on_a_o @ Sa
@ ( bNF_re905040088260304477_a_o_o @ Sc
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ ( bNF_re3043890739735069381on_a_o @ ( rel_option_a_a @ Sa )
@ ( bNF_re669219658517073757_a_o_o @ ( rel_op4798662380513671176tion_a @ Sc )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ rel_op1513876725179314510tion_a
@ rel_op1513876725179314510tion_a ) ).
% option.rel_transfer
thf(fact_935_option_Orel__transfer,axiom,
! [Sa: a > a > $o,Sc: a > a > $o] :
( bNF_re4921454823102592605on_a_o
@ ( bNF_re6468246989568818141_o_a_o @ Sa
@ ( bNF_rel_fun_a_a_o_o @ Sc
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ ( bNF_re1541143192665202257on_a_o @ ( rel_option_a_a @ Sa )
@ ( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ Sc )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ rel_option_a_a
@ rel_option_a_a ) ).
% option.rel_transfer
thf(fact_936_option_Opred__transfer,axiom,
! [R3: option_a > option_a > $o] :
( bNF_re8007680959799151545on_a_o
@ ( bNF_re905040088260304477_a_o_o @ R3
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ ( bNF_re669219658517073757_a_o_o @ ( rel_op4798662380513671176tion_a @ R3 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ pred_option_option_a
@ pred_option_option_a ) ).
% option.pred_transfer
thf(fact_937_option_Opred__transfer,axiom,
! [R3: a > a > $o] :
( bNF_re4859868158825367505on_a_o
@ ( bNF_rel_fun_a_a_o_o @ R3
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ ( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ R3 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ pred_option_a
@ pred_option_a ) ).
% option.pred_transfer
thf(fact_938_pred__option__parametric,axiom,
! [A2: option_a > option_a > $o] :
( bNF_re8007680959799151545on_a_o
@ ( bNF_re905040088260304477_a_o_o @ A2
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ ( bNF_re669219658517073757_a_o_o @ ( rel_op4798662380513671176tion_a @ A2 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ pred_option_option_a
@ pred_option_option_a ) ).
% pred_option_parametric
thf(fact_939_pred__option__parametric,axiom,
! [A2: a > a > $o] :
( bNF_re4859868158825367505on_a_o
@ ( bNF_rel_fun_a_a_o_o @ A2
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ ( bNF_re905040088260304477_a_o_o @ ( rel_option_a_a @ A2 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ pred_option_a
@ pred_option_a ) ).
% pred_option_parametric
thf(fact_940_option__bind__transfer,axiom,
! [A2: a > a > $o,B2: a > a > $o] : ( bNF_re5708320262762544989tion_a @ ( rel_option_a_a @ A2 ) @ ( bNF_re5527783635739595829tion_a @ ( bNF_re1187871780581372509tion_a @ A2 @ ( rel_option_a_a @ B2 ) ) @ ( rel_option_a_a @ B2 ) ) @ bind_a_a @ bind_a_a ) ).
% option_bind_transfer
thf(fact_941_option_Opred__mono,axiom,
! [P4: a > $o,Pa: a > $o] :
( ( ord_less_eq_a_o @ P4 @ Pa )
=> ( ord_le8889544289526388249on_a_o @ ( pred_option_a @ P4 ) @ ( pred_option_a @ Pa ) ) ) ).
% option.pred_mono
thf(fact_942_option_Opred__mono__strong,axiom,
! [P4: option_a > $o,X: option_option_a,Pa: option_a > $o] :
( ( pred_option_option_a @ P4 @ X )
=> ( ! [Z3: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ X ) )
=> ( ( P4 @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( pred_option_option_a @ Pa @ X ) ) ) ).
% option.pred_mono_strong
thf(fact_943_option_Opred__mono__strong,axiom,
! [P4: b > $o,X: option_b,Pa: b > $o] :
( ( pred_option_b @ P4 @ X )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ X ) )
=> ( ( P4 @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( pred_option_b @ Pa @ X ) ) ) ).
% option.pred_mono_strong
thf(fact_944_option_Opred__mono__strong,axiom,
! [P4: a > $o,X: option_a,Pa: a > $o] :
( ( pred_option_a @ P4 @ X )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ X ) )
=> ( ( P4 @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( pred_option_a @ Pa @ X ) ) ) ).
% option.pred_mono_strong
thf(fact_945_option_Opred__cong,axiom,
! [X: option_option_a,Ya: option_option_a,P4: option_a > $o,Pa: option_a > $o] :
( ( X = Ya )
=> ( ! [Z3: option_a] :
( ( member_option_a @ Z3 @ ( set_option_option_a2 @ Ya ) )
=> ( ( P4 @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( pred_option_option_a @ P4 @ X )
= ( pred_option_option_a @ Pa @ Ya ) ) ) ) ).
% option.pred_cong
thf(fact_946_option_Opred__cong,axiom,
! [X: option_b,Ya: option_b,P4: b > $o,Pa: b > $o] :
( ( X = Ya )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_option_b2 @ Ya ) )
=> ( ( P4 @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( pred_option_b @ P4 @ X )
= ( pred_option_b @ Pa @ Ya ) ) ) ) ).
% option.pred_cong
thf(fact_947_option_Opred__cong,axiom,
! [X: option_a,Ya: option_a,P4: a > $o,Pa: a > $o] :
( ( X = Ya )
=> ( ! [Z3: a] :
( ( member_a @ Z3 @ ( set_option_a2 @ Ya ) )
=> ( ( P4 @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( pred_option_a @ P4 @ X )
= ( pred_option_a @ Pa @ Ya ) ) ) ) ).
% option.pred_cong
thf(fact_948_option_Opred__inject_I1_J,axiom,
! [P4: a > $o] : ( pred_option_a @ P4 @ none_a ) ).
% option.pred_inject(1)
thf(fact_949_option_Opred__True,axiom,
( ( pred_option_a
@ ^ [Uu: a] : $true )
= ( ^ [Uu: option_a] : $true ) ) ).
% option.pred_True
thf(fact_950_option_Opred__map,axiom,
! [Q4: a > $o,F2: a > a,X: option_a] :
( ( pred_option_a @ Q4 @ ( map_option_a_a @ F2 @ X ) )
= ( pred_option_a @ ( comp_a_o_a @ Q4 @ F2 ) @ X ) ) ).
% option.pred_map
thf(fact_951_option_Orel__compp__Grp,axiom,
( rel_option_a_a
= ( ^ [R4: a > a > $o] :
( relcom7597457113570619114tion_a
@ ( conver6736784915673013132tion_a
@ ( bNF_Gr1758829368316449381tion_a
@ ( collec431113534271933400od_a_a
@ ^ [X5: option5210160422955383789od_a_a] : ( ord_le746702958409616551od_a_a @ ( set_op3367984300228426933od_a_a @ X5 ) @ ( collec3336397797384452498od_a_a @ ( produc6436628058953941356_a_a_o @ R4 ) ) ) )
@ ( map_op713297920823408162_a_a_a @ product_fst_a_a ) ) )
@ ( bNF_Gr1758829368316449381tion_a
@ ( collec431113534271933400od_a_a
@ ^ [X5: option5210160422955383789od_a_a] : ( ord_le746702958409616551od_a_a @ ( set_op3367984300228426933od_a_a @ X5 ) @ ( collec3336397797384452498od_a_a @ ( produc6436628058953941356_a_a_o @ R4 ) ) ) )
@ ( map_op713297920823408162_a_a_a @ product_snd_a_a ) ) ) ) ) ).
% option.rel_compp_Grp
thf(fact_952_fun__upd__transfer,axiom,
! [A2: d > d > $o,B2: c > c > $o] :
( ( bi_unique_d_d @ A2 )
=> ( bNF_re6057820304915472923_c_d_c @ ( bNF_rel_fun_d_d_c_c @ A2 @ B2 ) @ ( bNF_re1711706644904726749_c_d_c @ A2 @ ( bNF_re8281275612740045991_c_d_c @ B2 @ ( bNF_rel_fun_d_d_c_c @ A2 @ B2 ) ) ) @ fun_upd_d_c @ fun_upd_d_c ) ) ).
% fun_upd_transfer
thf(fact_953_fun__upd__transfer,axiom,
! [A2: option_a > option_a > $o,B2: $o > $o > $o] :
( ( bi_uni6217441781253053455tion_a @ A2 )
=> ( bNF_re294699121693105817on_a_o @ ( bNF_re905040088260304477_a_o_o @ A2 @ B2 ) @ ( bNF_re8312531103195455325on_a_o @ A2 @ ( bNF_re5310993362035161937on_a_o @ B2 @ ( bNF_re905040088260304477_a_o_o @ A2 @ B2 ) ) ) @ fun_upd_option_a_o @ fun_upd_option_a_o ) ) ).
% fun_upd_transfer
thf(fact_954_fun__upd__transfer,axiom,
! [A2: a > a > $o,B2: option_a > option_a > $o] :
( ( bi_unique_a_a @ A2 )
=> ( bNF_re4933961146405920325tion_a @ ( bNF_re1187871780581372509tion_a @ A2 @ B2 ) @ ( bNF_re845666378725559389tion_a @ A2 @ ( bNF_re8162217253061806133tion_a @ B2 @ ( bNF_re1187871780581372509tion_a @ A2 @ B2 ) ) ) @ fun_upd_a_option_a @ fun_upd_a_option_a ) ) ).
% fun_upd_transfer
thf(fact_955_fun__upd__transfer,axiom,
! [A2: d > d > $o,B2: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o] :
( ( bi_unique_d_d @ A2 )
=> ( bNF_re2236548867734660665_b_c_d @ ( bNF_re7418416730241609193_b_c_d @ A2 @ B2 ) @ ( bNF_re8856927315010765021_b_c_d @ A2 @ ( bNF_re3141103876165256041_b_c_d @ B2 @ ( bNF_re7418416730241609193_b_c_d @ A2 @ B2 ) ) ) @ fun_up3232119017247106793_b_c_d @ fun_up3232119017247106793_b_c_d ) ) ).
% fun_upd_transfer
thf(fact_956_fun__upd__transfer,axiom,
! [A2: assertion_a_b_c_d > assertion_a_b_c_d > $o,B2: assertion_a_b_c_d > assertion_a_b_c_d > $o] :
( ( bi_uni3681814365736818383_b_c_d @ A2 )
=> ( bNF_re2162194351488232737_b_c_d @ ( bNF_re2060205161886013149_b_c_d @ A2 @ B2 ) @ ( bNF_re6925915701013295965_b_c_d @ A2 @ ( bNF_re8352491382599487721_b_c_d @ B2 @ ( bNF_re2060205161886013149_b_c_d @ A2 @ B2 ) ) ) @ fun_up1040808460924108221_b_c_d @ fun_up1040808460924108221_b_c_d ) ) ).
% fun_upd_transfer
thf(fact_957_fun__upd__transfer,axiom,
! [A2: assertion_a_b_c_d > assertion_a_b_c_d > $o,B2: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o] :
( ( bi_uni3681814365736818383_b_c_d @ A2 )
=> ( bNF_re7200934695671800889_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ A2 @ B2 ) @ ( bNF_re2297306203449973469_b_c_d @ A2 @ ( bNF_re2130736366441412457_b_c_d @ B2 @ ( bNF_re8352491382599487721_b_c_d @ A2 @ B2 ) ) ) @ fun_up5063514507276981217_b_c_d @ fun_up5063514507276981217_b_c_d ) ) ).
% fun_upd_transfer
thf(fact_958_option_Opred__rel,axiom,
( pred_option_a
= ( ^ [P6: a > $o,X5: option_a] : ( rel_option_a_a @ ( bNF_eq_onp_a @ P6 ) @ X5 @ X5 ) ) ) ).
% option.pred_rel
thf(fact_959_option_Orel__eq__onp,axiom,
! [P4: a > $o] :
( ( rel_option_a_a @ ( bNF_eq_onp_a @ P4 ) )
= ( bNF_eq_onp_option_a @ ( pred_option_a @ P4 ) ) ) ).
% option.rel_eq_onp
thf(fact_960_option_Obi__unique__rel,axiom,
! [R3: a > a > $o] :
( ( bi_unique_a_a @ R3 )
=> ( bi_uni6217441781253053455tion_a @ ( rel_option_a_a @ R3 ) ) ) ).
% option.bi_unique_rel
thf(fact_961_option_Orel__flip,axiom,
! [R3: a > a > $o,A: option_a,B: option_a] :
( ( rel_option_a_a @ ( conversep_a_a @ R3 ) @ A @ B )
= ( rel_option_a_a @ R3 @ B @ A ) ) ).
% option.rel_flip
thf(fact_962_option_Orel__compp,axiom,
! [R3: a > a > $o,S4: a > a > $o] :
( ( rel_option_a_a @ ( relcompp_a_a_a @ R3 @ S4 ) )
= ( relcom1089236864311994323tion_a @ ( rel_option_a_a @ R3 ) @ ( rel_option_a_a @ S4 ) ) ) ).
% option.rel_compp
thf(fact_963_option_Orel__conversep,axiom,
! [R3: a > a > $o] :
( ( rel_option_a_a @ ( conversep_a_a @ R3 ) )
= ( conver2091984906772465269tion_a @ ( rel_option_a_a @ R3 ) ) ) ).
% option.rel_conversep
thf(fact_964_option_Opred__set,axiom,
( pred_option_a
= ( ^ [P6: a > $o,X5: option_a] :
! [Y2: a] :
( ( member_a @ Y2 @ ( set_option_a2 @ X5 ) )
=> ( P6 @ Y2 ) ) ) ) ).
% option.pred_set
thf(fact_965_assertion_Opred__set,axiom,
( pred_a8195579292382433461_a_c_d
= ( ^ [P6: b > $o,X5: assertion_a_b_c_d] :
! [Y2: b] :
( ( member_b @ Y2 @ ( set_as796765862704242958_b_c_d @ X5 ) )
=> ( P6 @ Y2 ) ) ) ) ).
% assertion.pred_set
thf(fact_966_assertion_Opred__inject_I2_J,axiom,
! [P4: b > $o,A: b,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( mult_b_a_c_d @ A @ Aa2 ) )
= ( ( P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(2)
thf(fact_967_assertion_Opred__inject_I3_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( star_a_b_c_d @ A @ Aa2 ) )
= ( ( pred_a8195579292382433461_a_c_d @ P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(3)
thf(fact_968_assertion_Opred__inject_I4_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( wand_a_b_c_d @ A @ Aa2 ) )
= ( ( pred_a8195579292382433461_a_c_d @ P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(4)
thf(fact_969_assertion_Opred__inject_I9_J,axiom,
! [P4: b > $o,A: d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( forall_d_a_b_c @ A @ Aa2 ) )
= ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ).
% assertion.pred_inject(9)
thf(fact_970_assertion_Opred__inject_I11_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( bounded_a_b_c_d @ A ) )
= ( pred_a8195579292382433461_a_c_d @ P4 @ A ) ) ).
% assertion.pred_inject(11)
thf(fact_971_assertion_Opred__inject_I6_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( and_a_b_c_d @ A @ Aa2 ) )
= ( ( pred_a8195579292382433461_a_c_d @ P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(6)
thf(fact_972_assertion_Opred__inject_I7_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( imp_a_b_c_d @ A @ Aa2 ) )
= ( ( pred_a8195579292382433461_a_c_d @ P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(7)
thf(fact_973_assertion_Opred__inject_I8_J,axiom,
! [P4: b > $o,A: d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( exists_d_a_b_c @ A @ Aa2 ) )
= ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ).
% assertion.pred_inject(8)
thf(fact_974_assertion_Opred__inject_I5_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d,Aa2: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( or_a_b_c_d @ A @ Aa2 ) )
= ( ( pred_a8195579292382433461_a_c_d @ P4 @ A )
& ( pred_a8195579292382433461_a_c_d @ P4 @ Aa2 ) ) ) ).
% assertion.pred_inject(5)
thf(fact_975_assertion_Opred__inject_I12_J,axiom,
! [P4: b > $o,A: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( wildcard_a_b_c_d @ A ) )
= ( pred_a8195579292382433461_a_c_d @ P4 @ A ) ) ).
% assertion.pred_inject(12)
thf(fact_976_assertion_Opred__True,axiom,
( ( pred_a8195579292382433461_a_c_d
@ ^ [Uu: b] : $true )
= ( ^ [Uu: assertion_a_b_c_d] : $true ) ) ).
% assertion.pred_True
thf(fact_977_assertion_Opred__cong,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,P4: b > $o,Pa: b > $o] :
( ( X = Ya )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ Ya ) )
=> ( ( P4 @ Z3 )
= ( Pa @ Z3 ) ) )
=> ( ( pred_a8195579292382433461_a_c_d @ P4 @ X )
= ( pred_a8195579292382433461_a_c_d @ Pa @ Ya ) ) ) ) ).
% assertion.pred_cong
thf(fact_978_assertion_Opred__mono__strong,axiom,
! [P4: b > $o,X: assertion_a_b_c_d,Pa: b > $o] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ X )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( P4 @ Z3 )
=> ( Pa @ Z3 ) ) )
=> ( pred_a8195579292382433461_a_c_d @ Pa @ X ) ) ) ).
% assertion.pred_mono_strong
thf(fact_979_assertion_Opred__inject_I10_J,axiom,
! [P4: b > $o] : ( pred_a8195579292382433461_a_c_d @ P4 @ pred_a_b_c_d ) ).
% assertion.pred_inject(10)
thf(fact_980_assertion_Opred__mono,axiom,
! [P4: b > $o,Pa: b > $o] :
( ( ord_less_eq_b_o @ P4 @ Pa )
=> ( ord_le6795694934652756260_c_d_o @ ( pred_a8195579292382433461_a_c_d @ P4 ) @ ( pred_a8195579292382433461_a_c_d @ Pa ) ) ) ).
% assertion.pred_mono
thf(fact_981_assertion_Opred__map,axiom,
! [Q4: b > $o,F2: b > b,X: assertion_a_b_c_d] :
( ( pred_a8195579292382433461_a_c_d @ Q4 @ ( map_as4919457480576020172_a_c_d @ F2 @ X ) )
= ( pred_a8195579292382433461_a_c_d @ ( comp_b_o_b @ Q4 @ F2 ) @ X ) ) ).
% assertion.pred_map
thf(fact_982_assertion_Opred__inject_I1_J,axiom,
! [P4: b > $o,A: ( d > c ) > a > $o] :
( ( pred_a8195579292382433461_a_c_d @ P4 @ ( sem_d_c_a_b @ A ) )
= ( top_top_d_c_a_o_o @ A ) ) ).
% assertion.pred_inject(1)
thf(fact_983_assertion_Omap__cong__pred,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,F2: b > b,G: b > b] :
( ( X = Ya )
=> ( ( pred_a8195579292382433461_a_c_d
@ ^ [Z: b] :
( ( F2 @ Z )
= ( G @ Z ) )
@ Ya )
=> ( ( map_as4919457480576020172_a_c_d @ F2 @ X )
= ( map_as4919457480576020172_a_c_d @ G @ Ya ) ) ) ) ).
% assertion.map_cong_pred
thf(fact_984_assertion_Omap__comp,axiom,
! [G: b > b,F2: b > b,V4: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ G @ ( map_as4919457480576020172_a_c_d @ F2 @ V4 ) )
= ( map_as4919457480576020172_a_c_d @ ( comp_b_b_b @ G @ F2 ) @ V4 ) ) ).
% assertion.map_comp
thf(fact_985_assertion_Oset__map,axiom,
! [F2: b > b,V4: assertion_a_b_c_d] :
( ( set_as796765862704242958_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ V4 ) )
= ( image_b_b @ F2 @ ( set_as796765862704242958_b_c_d @ V4 ) ) ) ).
% assertion.set_map
thf(fact_986_assertion_Omap__id,axiom,
! [T: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ id_b @ T )
= T ) ).
% assertion.map_id
thf(fact_987_assertion_Omap__id0,axiom,
( ( map_as4919457480576020172_a_c_d @ id_b )
= id_assertion_a_b_c_d ) ).
% assertion.map_id0
thf(fact_988_assertion_Omap__ident__strong,axiom,
! [T: assertion_a_b_c_d,F2: b > b] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ T ) )
=> ( ( F2 @ Z3 )
= Z3 ) )
=> ( ( map_as4919457480576020172_a_c_d @ F2 @ T )
= T ) ) ).
% assertion.map_ident_strong
thf(fact_989_assertion_Oinj__map__strong,axiom,
! [X: assertion_a_b_c_d,Xa2: assertion_a_b_c_d,F2: b > b,Fa: b > b] :
( ! [Z3: b,Za: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( member_b @ Za @ ( set_as796765862704242958_b_c_d @ Xa2 ) )
=> ( ( ( F2 @ Z3 )
= ( Fa @ Za ) )
=> ( Z3 = Za ) ) ) )
=> ( ( ( map_as4919457480576020172_a_c_d @ F2 @ X )
= ( map_as4919457480576020172_a_c_d @ Fa @ Xa2 ) )
=> ( X = Xa2 ) ) ) ).
% assertion.inj_map_strong
thf(fact_990_assertion_Omap__cong0,axiom,
! [X: assertion_a_b_c_d,F2: b > b,G: b > b] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( F2 @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( map_as4919457480576020172_a_c_d @ F2 @ X )
= ( map_as4919457480576020172_a_c_d @ G @ X ) ) ) ).
% assertion.map_cong0
thf(fact_991_assertion_Omap__cong,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,F2: b > b,G: b > b] :
( ( X = Ya )
=> ( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ Ya ) )
=> ( ( F2 @ Z3 )
= ( G @ Z3 ) ) )
=> ( ( map_as4919457480576020172_a_c_d @ F2 @ X )
= ( map_as4919457480576020172_a_c_d @ G @ Ya ) ) ) ) ).
% assertion.map_cong
thf(fact_992_assertion_Osimps_I169_J,axiom,
! [F2: b > b,X21: b,X22: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( mult_b_a_c_d @ X21 @ X22 ) )
= ( mult_b_a_c_d @ ( F2 @ X21 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X22 ) ) ) ).
% assertion.simps(169)
thf(fact_993_assertion_Osimps_I170_J,axiom,
! [F2: b > b,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( star_a_b_c_d @ X31 @ X32 ) )
= ( star_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X31 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X32 ) ) ) ).
% assertion.simps(170)
thf(fact_994_assertion_Osimps_I171_J,axiom,
! [F2: b > b,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( wand_a_b_c_d @ X41 @ X42 ) )
= ( wand_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X41 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X42 ) ) ) ).
% assertion.simps(171)
thf(fact_995_assertion_Osimps_I178_J,axiom,
! [F2: b > b,X11: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( bounded_a_b_c_d @ X11 ) )
= ( bounded_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X11 ) ) ) ).
% assertion.simps(178)
thf(fact_996_assertion_Osimps_I176_J,axiom,
! [F2: b > b,X91: d,X92: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( forall_d_a_b_c @ X91 @ X92 ) )
= ( forall_d_a_b_c @ X91 @ ( map_as4919457480576020172_a_c_d @ F2 @ X92 ) ) ) ).
% assertion.simps(176)
thf(fact_997_assertion_Osimps_I174_J,axiom,
! [F2: b > b,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( imp_a_b_c_d @ X71 @ X72 ) )
= ( imp_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X71 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X72 ) ) ) ).
% assertion.simps(174)
thf(fact_998_assertion_Osimps_I173_J,axiom,
! [F2: b > b,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( and_a_b_c_d @ X61 @ X62 ) )
= ( and_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X61 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X62 ) ) ) ).
% assertion.simps(173)
thf(fact_999_assertion_Osimps_I175_J,axiom,
! [F2: b > b,X81: d,X82: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( exists_d_a_b_c @ X81 @ X82 ) )
= ( exists_d_a_b_c @ X81 @ ( map_as4919457480576020172_a_c_d @ F2 @ X82 ) ) ) ).
% assertion.simps(175)
thf(fact_1000_assertion_Osimps_I172_J,axiom,
! [F2: b > b,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( or_a_b_c_d @ X51 @ X52 ) )
= ( or_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X51 ) @ ( map_as4919457480576020172_a_c_d @ F2 @ X52 ) ) ) ).
% assertion.simps(172)
thf(fact_1001_assertion_Osimps_I179_J,axiom,
! [F2: b > b,X12: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( wildcard_a_b_c_d @ X12 ) )
= ( wildcard_a_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 @ X12 ) ) ) ).
% assertion.simps(179)
thf(fact_1002_assertion_Osimps_I168_J,axiom,
! [F2: b > b,X1: ( d > c ) > a > $o] :
( ( map_as4919457480576020172_a_c_d @ F2 @ ( sem_d_c_a_b @ X1 ) )
= ( sem_d_c_a_b @ X1 ) ) ).
% assertion.simps(168)
thf(fact_1003_assertion_Osimps_I177_J,axiom,
! [F2: b > b] :
( ( map_as4919457480576020172_a_c_d @ F2 @ pred_a_b_c_d )
= pred_a_b_c_d ) ).
% assertion.simps(177)
thf(fact_1004_assertion_Omap__ident,axiom,
! [T: assertion_a_b_c_d] :
( ( map_as4919457480576020172_a_c_d
@ ^ [X5: b] : X5
@ T )
= T ) ).
% assertion.map_ident
thf(fact_1005_assertion_Oinj__map,axiom,
! [F2: b > b] :
( ( inj_on_b_b @ F2 @ top_top_set_b )
=> ( inj_on8546820862575520945_b_c_d @ ( map_as4919457480576020172_a_c_d @ F2 ) @ top_to5797442083933759657_b_c_d ) ) ).
% assertion.inj_map
thf(fact_1006_assertion_Orel__Grp,axiom,
! [A2: set_b,F2: b > b] :
( ( rel_as4648444602768287561_a_c_d @ ( bNF_Grp_b_b @ A2 @ F2 ) )
= ( bNF_Gr3951314207136893198_b_c_d
@ ( collec747544926041312740_b_c_d
@ ^ [X5: assertion_a_b_c_d] : ( ord_less_eq_set_b @ ( set_as796765862704242958_b_c_d @ X5 ) @ A2 ) )
@ ( map_as4919457480576020172_a_c_d @ F2 ) ) ) ).
% assertion.rel_Grp
thf(fact_1007_assertion_Oin__rel,axiom,
( rel_as4648444602768287561_a_c_d
= ( ^ [R4: b > b > $o,A6: assertion_a_b_c_d,B5: assertion_a_b_c_d] :
? [Z: assert5325495410138902753_b_c_d] :
( ( member2208103261226737034_b_c_d @ Z
@ ( collec1337203158693800140_b_c_d
@ ^ [X5: assert5325495410138902753_b_c_d] : ( ord_le182087997850975847od_b_b @ ( set_as9022474982623750902_b_c_d @ X5 ) @ ( collec548942219715005266od_b_b @ ( produc4772849988445941548_b_b_o @ R4 ) ) ) ) )
& ( ( map_as225457026910506420_a_c_d @ product_fst_b_b @ Z )
= A6 )
& ( ( map_as225457026910506420_a_c_d @ product_snd_b_b @ Z )
= B5 ) ) ) ) ).
% assertion.in_rel
thf(fact_1008_assertion_Orel__mono,axiom,
! [R3: b > b > $o,Ra: b > b > $o] :
( ( ord_less_eq_b_b_o @ R3 @ Ra )
=> ( ord_le3165238294362408398_c_d_o @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ Ra ) ) ) ).
% assertion.rel_mono
thf(fact_1009_assertion_Omap__transfer,axiom,
! [Rb: b > b > $o,Sd: b > b > $o] : ( bNF_re2761730750983628277_b_c_d @ ( bNF_rel_fun_b_b_b_b @ Rb @ Sd ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ Rb ) @ ( rel_as4648444602768287561_a_c_d @ Sd ) ) @ map_as4919457480576020172_a_c_d @ map_as4919457480576020172_a_c_d ) ).
% assertion.map_transfer
thf(fact_1010_assertion_Orel__map_I2_J,axiom,
! [Sa: b > b > $o,X: assertion_a_b_c_d,G: b > b,Y: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ Sa @ X @ ( map_as4919457480576020172_a_c_d @ G @ Y ) )
= ( rel_as4648444602768287561_a_c_d
@ ^ [X5: b,Y2: b] : ( Sa @ X5 @ ( G @ Y2 ) )
@ X
@ Y ) ) ).
% assertion.rel_map(2)
thf(fact_1011_assertion_Orel__map_I1_J,axiom,
! [Sb: b > b > $o,I: b > b,X: assertion_a_b_c_d,Y: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ Sb @ ( map_as4919457480576020172_a_c_d @ I @ X ) @ Y )
= ( rel_as4648444602768287561_a_c_d
@ ^ [X5: b] : ( Sb @ ( I @ X5 ) )
@ X
@ Y ) ) ).
% assertion.rel_map(1)
thf(fact_1012_assertion_Orel__conversep,axiom,
! [R3: b > b > $o] :
( ( rel_as4648444602768287561_a_c_d @ ( conversep_b_b @ R3 ) )
= ( conver81709274662576437_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) ) ).
% assertion.rel_conversep
thf(fact_1013_assertion_Orel__compp,axiom,
! [R3: b > b > $o,S4: b > b > $o] :
( ( rel_as4648444602768287561_a_c_d @ ( relcompp_b_b_b @ R3 @ S4 ) )
= ( relcom5312131986986172104_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ S4 ) ) ) ).
% assertion.rel_compp
thf(fact_1014_assertion_Orel__flip,axiom,
! [R3: b > b > $o,A: assertion_a_b_c_d,B: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ ( conversep_b_b @ R3 ) @ A @ B )
= ( rel_as4648444602768287561_a_c_d @ R3 @ B @ A ) ) ).
% assertion.rel_flip
thf(fact_1015_assertion_Orel__distinct_I25_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( wand_a_b_c_d @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(25)
thf(fact_1016_assertion_Orel__distinct_I26_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ Y41 @ Y42 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(26)
thf(fact_1017_assertion_Orel__distinct_I35_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(35)
thf(fact_1018_assertion_Orel__distinct_I36_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(36)
thf(fact_1019_assertion_Orel__distinct_I40_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(40)
thf(fact_1020_assertion_Orel__distinct_I39_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(39)
thf(fact_1021_assertion_Orel__distinct_I43_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( wand_a_b_c_d @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(43)
thf(fact_1022_assertion_Orel__distinct_I44_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ Y41 @ Y42 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(44)
thf(fact_1023_assertion_Orel__distinct_I29_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(29)
thf(fact_1024_assertion_Orel__distinct_I30_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ Y61 @ Y62 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(30)
thf(fact_1025_assertion_Orel__distinct_I32_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(32)
thf(fact_1026_assertion_Orel__distinct_I31_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(31)
thf(fact_1027_assertion_Orel__distinct_I53_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(53)
thf(fact_1028_assertion_Orel__distinct_I54_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(54)
thf(fact_1029_assertion_Orel__distinct_I58_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(58)
thf(fact_1030_assertion_Orel__distinct_I57_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(57)
thf(fact_1031_assertion_Orel__distinct_I34_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(34)
thf(fact_1032_assertion_Orel__distinct_I33_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(33)
thf(fact_1033_assertion_Orel__distinct_I47_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(47)
thf(fact_1034_assertion_Orel__distinct_I48_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ Y61 @ Y62 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(48)
thf(fact_1035_assertion_Orel__distinct_I50_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(50)
thf(fact_1036_assertion_Orel__distinct_I49_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(49)
thf(fact_1037_assertion_Orel__distinct_I28_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ Y51 @ Y52 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(28)
thf(fact_1038_assertion_Orel__distinct_I27_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(27)
thf(fact_1039_assertion_Orel__distinct_I52_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(52)
thf(fact_1040_assertion_Orel__distinct_I51_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(51)
thf(fact_1041_assertion_Orel__distinct_I42_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(42)
thf(fact_1042_assertion_Orel__distinct_I41_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(41)
thf(fact_1043_assertion_Orel__distinct_I46_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ Y51 @ Y52 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(46)
thf(fact_1044_assertion_Orel__distinct_I45_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(45)
thf(fact_1045_assertion_Orel__distinct_I2_J,axiom,
! [R3: b > b > $o,Y21: b,Y22: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ Y21 @ Y22 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(2)
thf(fact_1046_assertion_Orel__distinct_I1_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y21: b,Y22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( mult_b_a_c_d @ Y21 @ Y22 ) ) ).
% assertion.rel_distinct(1)
thf(fact_1047_assertion_Orel__distinct_I60_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(60)
thf(fact_1048_assertion_Orel__distinct_I59_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(59)
thf(fact_1049_assertion_Orel__distinct_I4_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ Y31 @ Y32 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(4)
thf(fact_1050_assertion_Orel__distinct_I3_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( star_a_b_c_d @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(3)
thf(fact_1051_assertion_Orel__distinct_I69_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(69)
thf(fact_1052_assertion_Orel__distinct_I70_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(70)
thf(fact_1053_assertion_Orel__distinct_I74_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(74)
thf(fact_1054_assertion_Orel__distinct_I73_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(73)
thf(fact_1055_assertion_Orel__distinct_I124_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.rel_distinct(124)
thf(fact_1056_assertion_Orel__distinct_I123_J,axiom,
! [R3: b > b > $o,X91: d,X92: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ X91 @ X92 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(123)
thf(fact_1057_assertion_Orel__distinct_I63_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(63)
thf(fact_1058_assertion_Orel__distinct_I64_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ Y61 @ Y62 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(64)
thf(fact_1059_assertion_Orel__distinct_I66_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(66)
thf(fact_1060_assertion_Orel__distinct_I65_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(65)
thf(fact_1061_assertion_Orel__distinct_I95_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(95)
thf(fact_1062_assertion_Orel__distinct_I96_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(96)
thf(fact_1063_assertion_Orel__distinct_I106_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.rel_distinct(106)
thf(fact_1064_assertion_Orel__distinct_I105_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(105)
thf(fact_1065_assertion_Orel__distinct_I100_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(100)
thf(fact_1066_assertion_Orel__distinct_I99_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(99)
thf(fact_1067_assertion_Orel__distinct_I109_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(109)
thf(fact_1068_assertion_Orel__distinct_I110_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.rel_distinct(110)
thf(fact_1069_assertion_Orel__distinct_I68_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(68)
thf(fact_1070_assertion_Orel__distinct_I67_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(67)
thf(fact_1071_assertion_Orel__distinct_I92_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(92)
thf(fact_1072_assertion_Orel__distinct_I91_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(91)
thf(fact_1073_assertion_Orel__distinct_I114_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.rel_distinct(114)
thf(fact_1074_assertion_Orel__distinct_I113_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(113)
thf(fact_1075_assertion_Orel__distinct_I117_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(117)
thf(fact_1076_assertion_Orel__distinct_I118_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.rel_distinct(118)
thf(fact_1077_assertion_Orel__distinct_I62_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ Y51 @ Y52 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(62)
thf(fact_1078_assertion_Orel__distinct_I61_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(61)
thf(fact_1079_assertion_Orel__distinct_I94_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(94)
thf(fact_1080_assertion_Orel__distinct_I93_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(93)
thf(fact_1081_assertion_Orel__distinct_I103_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(103)
thf(fact_1082_assertion_Orel__distinct_I104_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.rel_distinct(104)
thf(fact_1083_assertion_Orel__distinct_I84_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(84)
thf(fact_1084_assertion_Orel__distinct_I83_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(83)
thf(fact_1085_assertion_Orel__distinct_I87_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(87)
thf(fact_1086_assertion_Orel__distinct_I88_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(88)
thf(fact_1087_assertion_Orel__distinct_I76_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(76)
thf(fact_1088_assertion_Orel__distinct_I75_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(75)
thf(fact_1089_assertion_Orel__distinct_I78_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ Y61 @ Y62 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(78)
thf(fact_1090_assertion_Orel__distinct_I77_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(77)
thf(fact_1091_assertion_Orel__distinct_I79_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(79)
thf(fact_1092_assertion_Orel__distinct_I80_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(80)
thf(fact_1093_assertion_Orel__distinct_I126_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X91: d,X92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.rel_distinct(126)
thf(fact_1094_assertion_Orel__distinct_I125_J,axiom,
! [R3: b > b > $o,X91: d,X92: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ X91 @ X92 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(125)
thf(fact_1095_assertion_Orel__distinct_I131_J,axiom,
! [R3: b > b > $o,X11: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ X11 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(131)
thf(fact_1096_assertion_Orel__distinct_I132_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( bounded_a_b_c_d @ X11 ) ) ).
% assertion.rel_distinct(132)
thf(fact_1097_assertion_Orel__distinct_I6_J,axiom,
! [R3: b > b > $o,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ Y41 @ Y42 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(6)
thf(fact_1098_assertion_Orel__distinct_I5_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( wand_a_b_c_d @ Y41 @ Y42 ) ) ).
% assertion.rel_distinct(5)
thf(fact_1099_assertion_Orel__distinct_I38_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(38)
thf(fact_1100_assertion_Orel__distinct_I37_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(37)
thf(fact_1101_assertion_Orel__refl,axiom,
! [Ra: b > b > $o,X: assertion_a_b_c_d] :
( ! [X4: b] : ( Ra @ X4 @ X4 )
=> ( rel_as4648444602768287561_a_c_d @ Ra @ X @ X ) ) ).
% assertion.rel_refl
thf(fact_1102_assertion_Orel__eq,axiom,
( ( rel_as4648444602768287561_a_c_d
@ ^ [Y5: b,Z4: b] : ( Y5 = Z4 ) )
= ( ^ [Y5: assertion_a_b_c_d,Z4: assertion_a_b_c_d] : ( Y5 = Z4 ) ) ) ).
% assertion.rel_eq
thf(fact_1103_assertion_Octr__transfer_I10_J,axiom,
! [R3: b > b > $o] : ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ pred_a_b_c_d ) ).
% assertion.ctr_transfer(10)
thf(fact_1104_assertion_Orel__inject_I1_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y1: ( d > c ) > a > $o] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( sem_d_c_a_b @ Y1 ) )
= ( X1 = Y1 ) ) ).
% assertion.rel_inject(1)
thf(fact_1105_assertion_Orel__intros_I1_J,axiom,
! [X1: ( d > c ) > a > $o,Y1: ( d > c ) > a > $o,R3: b > b > $o] :
( ( X1 = Y1 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( sem_d_c_a_b @ Y1 ) ) ) ).
% assertion.rel_intros(1)
thf(fact_1106_assertion_Orel__intros_I12_J,axiom,
! [R3: b > b > $o,X12: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X12 @ Y12 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ X12 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ) ).
% assertion.rel_intros(12)
thf(fact_1107_assertion_Orel__inject_I12_J,axiom,
! [R3: b > b > $o,X12: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ X12 ) @ ( wildcard_a_b_c_d @ Y12 ) )
= ( rel_as4648444602768287561_a_c_d @ R3 @ X12 @ Y12 ) ) ).
% assertion.rel_inject(12)
thf(fact_1108_assertion_Orel__intros_I5_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,Y51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X51 @ Y51 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X52 @ Y52 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) ) ) ) ).
% assertion.rel_intros(5)
thf(fact_1109_assertion_Orel__inject_I5_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) )
= ( ( rel_as4648444602768287561_a_c_d @ R3 @ X51 @ Y51 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X52 @ Y52 ) ) ) ).
% assertion.rel_inject(5)
thf(fact_1110_assertion_Orel__intros_I8_J,axiom,
! [X81: d,Y81: d,R3: b > b > $o,X82: assertion_a_b_c_d,Y82: assertion_a_b_c_d] :
( ( X81 = Y81 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X82 @ Y82 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ) ) ).
% assertion.rel_intros(8)
thf(fact_1111_assertion_Orel__inject_I8_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) )
= ( ( X81 = Y81 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X82 @ Y82 ) ) ) ).
% assertion.rel_inject(8)
thf(fact_1112_assertion_Orel__intros_I6_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,Y61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X61 @ Y61 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X62 @ Y62 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ) ) ).
% assertion.rel_intros(6)
thf(fact_1113_assertion_Orel__inject_I6_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) )
= ( ( rel_as4648444602768287561_a_c_d @ R3 @ X61 @ Y61 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X62 @ Y62 ) ) ) ).
% assertion.rel_inject(6)
thf(fact_1114_assertion_Orel__intros_I7_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,Y71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X71 @ Y71 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X72 @ Y72 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ) ) ).
% assertion.rel_intros(7)
thf(fact_1115_assertion_Orel__inject_I7_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) )
= ( ( rel_as4648444602768287561_a_c_d @ R3 @ X71 @ Y71 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X72 @ Y72 ) ) ) ).
% assertion.rel_inject(7)
thf(fact_1116_assertion_Orel__intros_I9_J,axiom,
! [X91: d,Y91: d,R3: b > b > $o,X92: assertion_a_b_c_d,Y92: assertion_a_b_c_d] :
( ( X91 = Y91 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X92 @ Y92 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ X91 @ X92 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ) ) ).
% assertion.rel_intros(9)
thf(fact_1117_assertion_Orel__inject_I9_J,axiom,
! [R3: b > b > $o,X91: d,X92: assertion_a_b_c_d,Y91: d,Y92: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ X91 @ X92 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) )
= ( ( X91 = Y91 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X92 @ Y92 ) ) ) ).
% assertion.rel_inject(9)
thf(fact_1118_assertion_Orel__intros_I11_J,axiom,
! [R3: b > b > $o,X11: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X11 @ Y11 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ X11 ) @ ( bounded_a_b_c_d @ Y11 ) ) ) ).
% assertion.rel_intros(11)
thf(fact_1119_assertion_Orel__inject_I11_J,axiom,
! [R3: b > b > $o,X11: assertion_a_b_c_d,Y11: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ X11 ) @ ( bounded_a_b_c_d @ Y11 ) )
= ( rel_as4648444602768287561_a_c_d @ R3 @ X11 @ Y11 ) ) ).
% assertion.rel_inject(11)
thf(fact_1120_assertion_Orel__intros_I4_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,Y41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X41 @ Y41 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X42 @ Y42 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( wand_a_b_c_d @ Y41 @ Y42 ) ) ) ) ).
% assertion.rel_intros(4)
thf(fact_1121_assertion_Orel__inject_I4_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d,Y41: assertion_a_b_c_d,Y42: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ ( wand_a_b_c_d @ Y41 @ Y42 ) )
= ( ( rel_as4648444602768287561_a_c_d @ R3 @ X41 @ Y41 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X42 @ Y42 ) ) ) ).
% assertion.rel_inject(4)
thf(fact_1122_assertion_Orel__intros_I3_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,Y31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y32: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X31 @ Y31 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X32 @ Y32 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( star_a_b_c_d @ Y31 @ Y32 ) ) ) ) ).
% assertion.rel_intros(3)
thf(fact_1123_assertion_Orel__inject_I3_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ ( star_a_b_c_d @ Y31 @ Y32 ) )
= ( ( rel_as4648444602768287561_a_c_d @ R3 @ X31 @ Y31 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X32 @ Y32 ) ) ) ).
% assertion.rel_inject(3)
thf(fact_1124_assertion_Orel__intros_I2_J,axiom,
! [R3: b > b > $o,X21: b,Y21: b,X22: assertion_a_b_c_d,Y22: assertion_a_b_c_d] :
( ( R3 @ X21 @ Y21 )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X22 @ Y22 )
=> ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( mult_b_a_c_d @ Y21 @ Y22 ) ) ) ) ).
% assertion.rel_intros(2)
thf(fact_1125_assertion_Orel__inject_I2_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y21: b,Y22: assertion_a_b_c_d] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( mult_b_a_c_d @ Y21 @ Y22 ) )
= ( ( R3 @ X21 @ Y21 )
& ( rel_as4648444602768287561_a_c_d @ R3 @ X22 @ Y22 ) ) ) ).
% assertion.rel_inject(2)
thf(fact_1126_assertion_Orel__cong,axiom,
! [X: assertion_a_a_c_d,Ya: assertion_a_a_c_d,Y: assertion_a_b_c_d,Xa2: assertion_a_b_c_d,R3: a > b > $o,Ra: a > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: a,Yb2: b] :
( ( member_a @ Z3 @ ( set_as4423919284370888077_a_c_d @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_as3981545127228379208_a_c_d @ R3 @ X @ Y )
= ( rel_as3981545127228379208_a_c_d @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_1127_assertion_Orel__cong,axiom,
! [X: assert5894900919346993214_a_c_d,Ya: assert5894900919346993214_a_c_d,Y: assertion_a_b_c_d,Xa2: assertion_a_b_c_d,R3: option_a > b > $o,Ra: option_a > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: option_a,Yb2: b] :
( ( member_option_a @ Z3 @ ( set_as3758641881469047763_a_c_d @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_as8093967732909205902_a_c_d @ R3 @ X @ Y )
= ( rel_as8093967732909205902_a_c_d @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_1128_assertion_Orel__cong,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,Y: assertion_a_a_c_d,Xa2: assertion_a_a_c_d,R3: b > a > $o,Ra: b > a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: a] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ Ya ) )
=> ( ( member_a @ Yb2 @ ( set_as4423919284370888077_a_c_d @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_as3160482565473489034_a_c_d @ R3 @ X @ Y )
= ( rel_as3160482565473489034_a_c_d @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_1129_assertion_Orel__cong,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,Y: assert5894900919346993214_a_c_d,Xa2: assert5894900919346993214_a_c_d,R3: b > option_a > $o,Ra: b > option_a > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: option_a] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ Ya ) )
=> ( ( member_option_a @ Yb2 @ ( set_as3758641881469047763_a_c_d @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_as6688652118001638340_a_c_d @ R3 @ X @ Y )
= ( rel_as6688652118001638340_a_c_d @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_1130_assertion_Orel__cong,axiom,
! [X: assertion_a_b_c_d,Ya: assertion_a_b_c_d,Y: assertion_a_b_c_d,Xa2: assertion_a_b_c_d,R3: b > b > $o,Ra: b > b > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: b,Yb2: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ Ya ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Xa2 ) )
=> ( ( R3 @ Z3 @ Yb2 )
= ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( ( rel_as4648444602768287561_a_c_d @ R3 @ X @ Y )
= ( rel_as4648444602768287561_a_c_d @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% assertion.rel_cong
thf(fact_1131_assertion_Orel__mono__strong,axiom,
! [R3: a > b > $o,X: assertion_a_a_c_d,Y: assertion_a_b_c_d,Ra: a > b > $o] :
( ( rel_as3981545127228379208_a_c_d @ R3 @ X @ Y )
=> ( ! [Z3: a,Yb2: b] :
( ( member_a @ Z3 @ ( set_as4423919284370888077_a_c_d @ X ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_as3981545127228379208_a_c_d @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_1132_assertion_Orel__mono__strong,axiom,
! [R3: option_a > b > $o,X: assert5894900919346993214_a_c_d,Y: assertion_a_b_c_d,Ra: option_a > b > $o] :
( ( rel_as8093967732909205902_a_c_d @ R3 @ X @ Y )
=> ( ! [Z3: option_a,Yb2: b] :
( ( member_option_a @ Z3 @ ( set_as3758641881469047763_a_c_d @ X ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_as8093967732909205902_a_c_d @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_1133_assertion_Orel__mono__strong,axiom,
! [R3: b > a > $o,X: assertion_a_b_c_d,Y: assertion_a_a_c_d,Ra: b > a > $o] :
( ( rel_as3160482565473489034_a_c_d @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: a] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( member_a @ Yb2 @ ( set_as4423919284370888077_a_c_d @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_as3160482565473489034_a_c_d @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_1134_assertion_Orel__mono__strong,axiom,
! [R3: b > option_a > $o,X: assertion_a_b_c_d,Y: assert5894900919346993214_a_c_d,Ra: b > option_a > $o] :
( ( rel_as6688652118001638340_a_c_d @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: option_a] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( member_option_a @ Yb2 @ ( set_as3758641881469047763_a_c_d @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_as6688652118001638340_a_c_d @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_1135_assertion_Orel__mono__strong,axiom,
! [R3: b > b > $o,X: assertion_a_b_c_d,Y: assertion_a_b_c_d,Ra: b > b > $o] :
( ( rel_as4648444602768287561_a_c_d @ R3 @ X @ Y )
=> ( ! [Z3: b,Yb2: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( ( member_b @ Yb2 @ ( set_as796765862704242958_b_c_d @ Y ) )
=> ( ( R3 @ Z3 @ Yb2 )
=> ( Ra @ Z3 @ Yb2 ) ) ) )
=> ( rel_as4648444602768287561_a_c_d @ Ra @ X @ Y ) ) ) ).
% assertion.rel_mono_strong
thf(fact_1136_assertion_Orel__refl__strong,axiom,
! [X: assertion_a_b_c_d,Ra: b > b > $o] :
( ! [Z3: b] :
( ( member_b @ Z3 @ ( set_as796765862704242958_b_c_d @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( rel_as4648444602768287561_a_c_d @ Ra @ X @ X ) ) ).
% assertion.rel_refl_strong
thf(fact_1137_assertion_Orel__distinct_I23_J,axiom,
! [R3: b > b > $o,X21: b,X22: assertion_a_b_c_d,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( mult_b_a_c_d @ X21 @ X22 ) @ ( star_a_b_c_d @ Y31 @ Y32 ) ) ).
% assertion.rel_distinct(23)
thf(fact_1138_assertion_Orel__distinct_I24_J,axiom,
! [R3: b > b > $o,Y31: assertion_a_b_c_d,Y32: assertion_a_b_c_d,X21: b,X22: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ Y31 @ Y32 ) @ ( mult_b_a_c_d @ X21 @ X22 ) ) ).
% assertion.rel_distinct(24)
thf(fact_1139_assertion_Orel__distinct_I17_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(17)
thf(fact_1140_assertion_Orel__distinct_I18_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(18)
thf(fact_1141_assertion_Orel__distinct_I129_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(129)
thf(fact_1142_assertion_Orel__distinct_I130_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(130)
thf(fact_1143_assertion_Orel__distinct_I85_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(85)
thf(fact_1144_assertion_Orel__distinct_I86_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(86)
thf(fact_1145_assertion_Orel__distinct_I115_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(115)
thf(fact_1146_assertion_Orel__distinct_I116_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.rel_distinct(116)
thf(fact_1147_assertion_Orel__distinct_I98_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(98)
thf(fact_1148_assertion_Orel__distinct_I97_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(97)
thf(fact_1149_assertion_Orel__distinct_I107_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(107)
thf(fact_1150_assertion_Orel__distinct_I108_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.rel_distinct(108)
thf(fact_1151_assertion_Orel__distinct_I122_J,axiom,
! [R3: b > b > $o,X91: d,X92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( forall_d_a_b_c @ X91 @ X92 ) ) ).
% assertion.rel_distinct(122)
thf(fact_1152_assertion_Orel__distinct_I121_J,axiom,
! [R3: b > b > $o,X91: d,X92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ X91 @ X92 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(121)
thf(fact_1153_assertion_Orel__distinct_I127_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(127)
thf(fact_1154_assertion_Orel__distinct_I128_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(128)
thf(fact_1155_assertion_Orel__distinct_I72_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( wand_a_b_c_d @ X41 @ X42 ) ) ).
% assertion.rel_distinct(72)
thf(fact_1156_assertion_Orel__distinct_I71_J,axiom,
! [R3: b > b > $o,X41: assertion_a_b_c_d,X42: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wand_a_b_c_d @ X41 @ X42 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(71)
thf(fact_1157_assertion_Orel__distinct_I21_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(21)
thf(fact_1158_assertion_Orel__distinct_I22_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(22)
thf(fact_1159_assertion_Orel__distinct_I7_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( or_a_b_c_d @ Y51 @ Y52 ) ) ).
% assertion.rel_distinct(7)
thf(fact_1160_assertion_Orel__distinct_I8_J,axiom,
! [R3: b > b > $o,Y51: assertion_a_b_c_d,Y52: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ Y51 @ Y52 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(8)
thf(fact_1161_assertion_Orel__distinct_I13_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(13)
thf(fact_1162_assertion_Orel__distinct_I14_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(14)
thf(fact_1163_assertion_Orel__distinct_I89_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(89)
thf(fact_1164_assertion_Orel__distinct_I90_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(90)
thf(fact_1165_assertion_Orel__distinct_I56_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ pred_a_b_c_d @ ( star_a_b_c_d @ X31 @ X32 ) ) ).
% assertion.rel_distinct(56)
thf(fact_1166_assertion_Orel__distinct_I55_J,axiom,
! [R3: b > b > $o,X31: assertion_a_b_c_d,X32: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( star_a_b_c_d @ X31 @ X32 ) @ pred_a_b_c_d ) ).
% assertion.rel_distinct(55)
thf(fact_1167_assertion_Orel__distinct_I10_J,axiom,
! [R3: b > b > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ Y61 @ Y62 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(10)
thf(fact_1168_assertion_Orel__distinct_I9_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y61: assertion_a_b_c_d,Y62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( and_a_b_c_d @ Y61 @ Y62 ) ) ).
% assertion.rel_distinct(9)
thf(fact_1169_assertion_Orel__distinct_I11_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( imp_a_b_c_d @ Y71 @ Y72 ) ) ).
% assertion.rel_distinct(11)
thf(fact_1170_assertion_Orel__distinct_I12_J,axiom,
! [R3: b > b > $o,Y71: assertion_a_b_c_d,Y72: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ Y71 @ Y72 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(12)
thf(fact_1171_assertion_Orel__distinct_I119_J,axiom,
! [R3: b > b > $o,X81: d,X82: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ X81 @ X82 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(119)
thf(fact_1172_assertion_Orel__distinct_I120_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X81: d,X82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( exists_d_a_b_c @ X81 @ X82 ) ) ).
% assertion.rel_distinct(120)
thf(fact_1173_assertion_Orel__distinct_I16_J,axiom,
! [R3: b > b > $o,Y91: d,Y92: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( forall_d_a_b_c @ Y91 @ Y92 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(16)
thf(fact_1174_assertion_Orel__distinct_I15_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y91: d,Y92: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( forall_d_a_b_c @ Y91 @ Y92 ) ) ).
% assertion.rel_distinct(15)
thf(fact_1175_assertion_Orel__distinct_I19_J,axiom,
! [R3: b > b > $o,X1: ( d > c ) > a > $o,Y11: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( sem_d_c_a_b @ X1 ) @ ( bounded_a_b_c_d @ Y11 ) ) ).
% assertion.rel_distinct(19)
thf(fact_1176_assertion_Orel__distinct_I20_J,axiom,
! [R3: b > b > $o,Y11: assertion_a_b_c_d,X1: ( d > c ) > a > $o] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( bounded_a_b_c_d @ Y11 ) @ ( sem_d_c_a_b @ X1 ) ) ).
% assertion.rel_distinct(20)
thf(fact_1177_assertion_Orel__distinct_I102_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( and_a_b_c_d @ X61 @ X62 ) ) ).
% assertion.rel_distinct(102)
thf(fact_1178_assertion_Orel__distinct_I101_J,axiom,
! [R3: b > b > $o,X61: assertion_a_b_c_d,X62: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( and_a_b_c_d @ X61 @ X62 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(101)
thf(fact_1179_assertion_Orel__distinct_I111_J,axiom,
! [R3: b > b > $o,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d,Y12: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( imp_a_b_c_d @ X71 @ X72 ) @ ( wildcard_a_b_c_d @ Y12 ) ) ).
% assertion.rel_distinct(111)
thf(fact_1180_assertion_Orel__distinct_I112_J,axiom,
! [R3: b > b > $o,Y12: assertion_a_b_c_d,X71: assertion_a_b_c_d,X72: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( wildcard_a_b_c_d @ Y12 ) @ ( imp_a_b_c_d @ X71 @ X72 ) ) ).
% assertion.rel_distinct(112)
thf(fact_1181_assertion_Orel__distinct_I81_J,axiom,
! [R3: b > b > $o,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d,Y81: d,Y82: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( or_a_b_c_d @ X51 @ X52 ) @ ( exists_d_a_b_c @ Y81 @ Y82 ) ) ).
% assertion.rel_distinct(81)
thf(fact_1182_assertion_Orel__distinct_I82_J,axiom,
! [R3: b > b > $o,Y81: d,Y82: assertion_a_b_c_d,X51: assertion_a_b_c_d,X52: assertion_a_b_c_d] :
~ ( rel_as4648444602768287561_a_c_d @ R3 @ ( exists_d_a_b_c @ Y81 @ Y82 ) @ ( or_a_b_c_d @ X51 @ X52 ) ) ).
% assertion.rel_distinct(82)
thf(fact_1183_assertion_Octr__transfer_I12_J,axiom,
! [R3: b > b > $o] : ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ wildcard_a_b_c_d @ wildcard_a_b_c_d ) ).
% assertion.ctr_transfer(12)
thf(fact_1184_assertion_Octr__transfer_I11_J,axiom,
! [R3: b > b > $o] : ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ bounded_a_b_c_d @ bounded_a_b_c_d ) ).
% assertion.ctr_transfer(11)
thf(fact_1185_assertion_Octr__transfer_I7_J,axiom,
! [R3: b > b > $o] : ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ imp_a_b_c_d @ imp_a_b_c_d ) ).
% assertion.ctr_transfer(7)
thf(fact_1186_assertion_Octr__transfer_I5_J,axiom,
! [R3: b > b > $o] : ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ or_a_b_c_d @ or_a_b_c_d ) ).
% assertion.ctr_transfer(5)
thf(fact_1187_assertion_Octr__transfer_I1_J,axiom,
! [R3: b > b > $o] :
( bNF_re507190721467377699_b_c_d
@ ^ [Y5: ( d > c ) > a > $o,Z4: ( d > c ) > a > $o] : ( Y5 = Z4 )
@ ( rel_as4648444602768287561_a_c_d @ R3 )
@ sem_d_c_a_b
@ sem_d_c_a_b ) ).
% assertion.ctr_transfer(1)
thf(fact_1188_assertion_Orel__transfer,axiom,
! [Sa: b > b > $o,Sc: option_a > option_a > $o] :
( bNF_re7611673848298757341_c_d_o
@ ( bNF_re6771475999719625105on_a_o @ Sa
@ ( bNF_re905040088260304477_a_o_o @ Sc
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ ( bNF_re7785604200236268829_c_d_o @ ( rel_as4648444602768287561_a_c_d @ Sa )
@ ( bNF_re7564118739466000477_d_o_o @ ( rel_as660020871172297353_a_c_d @ Sc )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ rel_as6688652118001638340_a_c_d
@ rel_as6688652118001638340_a_c_d ) ).
% assertion.rel_transfer
thf(fact_1189_assertion_Orel__transfer,axiom,
! [Sa: b > b > $o,Sc: b > b > $o] :
( bNF_re263456917604132445_c_d_o
@ ( bNF_re4413358128099268379_o_b_o @ Sa
@ ( bNF_rel_fun_b_b_o_o @ Sc
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ ( bNF_re6323699832948026919_c_d_o @ ( rel_as4648444602768287561_a_c_d @ Sa )
@ ( bNF_re1650022584898132253_d_o_o @ ( rel_as4648444602768287561_a_c_d @ Sc )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) ) )
@ rel_as4648444602768287561_a_c_d
@ rel_as4648444602768287561_a_c_d ) ).
% assertion.rel_transfer
thf(fact_1190_assertion_Octr__transfer_I9_J,axiom,
! [R3: b > b > $o] :
( bNF_re7418416730241609193_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) )
@ forall_d_a_b_c
@ forall_d_a_b_c ) ).
% assertion.ctr_transfer(9)
thf(fact_1191_assertion_Octr__transfer_I6_J,axiom,
! [R3: b > b > $o] : ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ and_a_b_c_d @ and_a_b_c_d ) ).
% assertion.ctr_transfer(6)
thf(fact_1192_assertion_Octr__transfer_I4_J,axiom,
! [R3: b > b > $o] : ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ wand_a_b_c_d @ wand_a_b_c_d ) ).
% assertion.ctr_transfer(4)
thf(fact_1193_assertion_Octr__transfer_I3_J,axiom,
! [R3: b > b > $o] : ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ star_a_b_c_d @ star_a_b_c_d ) ).
% assertion.ctr_transfer(3)
thf(fact_1194_assertion_Octr__transfer_I2_J,axiom,
! [R3: b > b > $o] : ( bNF_re7904742758403352937_b_c_d @ R3 @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) ) @ mult_b_a_c_d @ mult_b_a_c_d ) ).
% assertion.ctr_transfer(2)
thf(fact_1195_assertion_Octr__transfer_I8_J,axiom,
! [R3: b > b > $o] :
( bNF_re7418416730241609193_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( rel_as4648444602768287561_a_c_d @ R3 ) )
@ exists_d_a_b_c
@ exists_d_a_b_c ) ).
% assertion.ctr_transfer(8)
thf(fact_1196_assertion_Opred__transfer,axiom,
! [R3: b > b > $o] :
( bNF_re4274080607382512101_c_d_o
@ ( bNF_rel_fun_b_b_o_o @ R3
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ ( bNF_re1650022584898132253_d_o_o @ ( rel_as4648444602768287561_a_c_d @ R3 )
@ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
@ pred_a8195579292382433461_a_c_d
@ pred_a8195579292382433461_a_c_d ) ).
% assertion.pred_transfer
thf(fact_1197_assertion_Opred__rel,axiom,
( pred_a8195579292382433461_a_c_d
= ( ^ [P6: b > $o,X5: assertion_a_b_c_d] : ( rel_as4648444602768287561_a_c_d @ ( bNF_eq_onp_b @ P6 ) @ X5 @ X5 ) ) ) ).
% assertion.pred_rel
thf(fact_1198_assertion_Orel__eq__onp,axiom,
! [P4: b > $o] :
( ( rel_as4648444602768287561_a_c_d @ ( bNF_eq_onp_b @ P4 ) )
= ( bNF_eq117459932171339370_b_c_d @ ( pred_a8195579292382433461_a_c_d @ P4 ) ) ) ).
% assertion.rel_eq_onp
thf(fact_1199_assertion_Orel__compp__Grp,axiom,
( rel_as4648444602768287561_a_c_d
= ( ^ [R4: b > b > $o] :
( relcom6640016704938620384_b_c_d
@ ( conver6185760717984097101_b_c_d
@ ( bNF_Gr5825982120753023526_b_c_d
@ ( collec1337203158693800140_b_c_d
@ ^ [X5: assert5325495410138902753_b_c_d] : ( ord_le182087997850975847od_b_b @ ( set_as9022474982623750902_b_c_d @ X5 ) @ ( collec548942219715005266od_b_b @ ( produc4772849988445941548_b_b_o @ R4 ) ) ) )
@ ( map_as225457026910506420_a_c_d @ product_fst_b_b ) ) )
@ ( bNF_Gr5825982120753023526_b_c_d
@ ( collec1337203158693800140_b_c_d
@ ^ [X5: assert5325495410138902753_b_c_d] : ( ord_le182087997850975847od_b_b @ ( set_as9022474982623750902_b_c_d @ X5 ) @ ( collec548942219715005266od_b_b @ ( produc4772849988445941548_b_b_o @ R4 ) ) ) )
@ ( map_as225457026910506420_a_c_d @ product_snd_b_b ) ) ) ) ) ).
% assertion.rel_compp_Grp
thf(fact_1200_assertion_Osize__gen__o__map,axiom,
! [F2: a > nat,Fa: b > nat,Fb: c > nat,Fc: d > nat,Ga: b > b] :
( ( comp_a8591870773727454801_b_c_d @ ( size_a5396279667297198487_b_c_d @ F2 @ Fa @ Fb @ Fc ) @ ( map_as4919457480576020172_a_c_d @ Ga ) )
= ( size_a5396279667297198487_b_c_d @ F2 @ ( comp_b_nat_b @ Fa @ Ga ) @ Fb @ Fc ) ) ).
% assertion.size_gen_o_map
thf(fact_1201_assertion_Ocase__transfer,axiom,
! [S4: assertion_a_b_c_d > assertion_a_b_c_d > $o,R3: b > b > $o] :
( bNF_re4165358468115902493_b_c_d
@ ( bNF_re507190721467377699_b_c_d
@ ^ [Y5: ( d > c ) > a > $o,Z4: ( d > c ) > a > $o] : ( Y5 = Z4 )
@ S4 )
@ ( bNF_re8177534222179943037_b_c_d @ ( bNF_re7904742758403352937_b_c_d @ R3 @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re6521478211583210845_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re1385902664069430737_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re1434271726693436637_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re2045653869035528613_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re857753254652161629_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re510987944908516713_b_c_d
@ ( bNF_re7418416730241609193_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re5229488851107796445_b_c_d
@ ( bNF_re7418416730241609193_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re7119773978271877369_b_c_d @ S4 @ ( bNF_re4346972822711717245_b_c_d @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) @ ( bNF_re5340157310235046645_b_c_d @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) @ ( bNF_re2060205161886013149_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a3488927611849131102_c_d_b
@ case_a3488927611849131102_c_d_b ) ).
% assertion.case_transfer
thf(fact_1202_assertion_Ocase__transfer,axiom,
! [S4: ( assertion_a_b_c_d > assertion_a_b_c_d ) > ( assertion_a_b_c_d > assertion_a_b_c_d ) > $o,R3: b > b > $o] :
( bNF_re409307387072406315_b_c_d
@ ( bNF_re7094559677772665647_b_c_d
@ ^ [Y5: ( d > c ) > a > $o,Z4: ( d > c ) > a > $o] : ( Y5 = Z4 )
@ S4 )
@ ( bNF_re4988404192636484745_b_c_d @ ( bNF_re2222577296431909853_b_c_d @ R3 @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re5728513783986320277_b_c_d @ ( bNF_re6925915701013295965_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re5409697069149878421_b_c_d @ ( bNF_re6925915701013295965_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re5882599885548590485_b_c_d @ ( bNF_re6925915701013295965_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re5572834386292656789_b_c_d @ ( bNF_re6925915701013295965_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re4584742235003721621_b_c_d @ ( bNF_re6925915701013295965_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re3466685140808306565_b_c_d
@ ( bNF_re8703476271064895581_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re1151994453571696261_b_c_d
@ ( bNF_re8703476271064895581_b_c_d
@ ^ [Y5: d,Z4: d] : ( Y5 = Z4 )
@ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) )
@ ( bNF_re2241830251785289705_b_c_d @ S4 @ ( bNF_re5347999660430809193_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) @ ( bNF_re2787993636544139229_b_c_d @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) @ ( bNF_re8352491382599487721_b_c_d @ ( rel_as4648444602768287561_a_c_d @ R3 ) @ S4 ) ) ) ) ) ) ) ) ) ) ) )
@ case_a3730527612158903040_c_d_b
@ case_a3730527612158903040_c_d_b ) ).
% assertion.case_transfer
% Helper facts (9)
thf(help_If_2_1_If_001tf__a_T,axiom,
! [X: a,Y: a] :
( ( if_a @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001tf__a_T,axiom,
! [X: a,Y: a] :
( ( if_a @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001tf__b_T,axiom,
! [X: b,Y: b] :
( ( if_b @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001tf__b_T,axiom,
! [X: b,Y: b] :
( ( if_b @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001tf__c_T,axiom,
! [X: c,Y: c] :
( ( if_c @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001tf__c_T,axiom,
! [X: c,Y: c] :
( ( if_c @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [P4: $o] :
( ( P4 = $true )
| ( P4 = $false ) ) ).
thf(help_If_2_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [X: option_a,Y: option_a] :
( ( if_option_a @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
! [X: option_a,Y: option_a] :
( ( if_option_a @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
combinable_a_b_d_c @ plus @ mult @ sadd @ valid @ delta @ a2 ).
%------------------------------------------------------------------------------