ITP001 Axioms: ITP042^5.ax
%------------------------------------------------------------------------------
% File : ITP042^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : patternMatches^2.ax [Gau20]
% : HL4042^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 159 ( 8 unt; 30 typ; 0 def)
% Number of atoms : 3784 ( 145 equ; 0 cnn)
% Maximal formula atoms : 93 ( 23 avg)
% Number of connectives : 7042 ( 19 ~; 4 |; 77 &;6373 @)
% ( 43 <=>; 526 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 18 avg;6373 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 89 usr; 64 con; 0-3 aty)
% Number of variables : 811 ( 56 ^ 741 !; 14 ?; 811 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO,type,
c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO: del > $i ).
thf(mem_c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO,axiom,
! [A_27a: del] : ( mem @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO,type,
c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO: del > del > $i ).
thf(mem_c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( arr @ bool @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ bool ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH,type,
c_2EpatternMatches_2EPMATCH: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ ( arr @ A_27b @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ A_27a ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__EQUIV__ROWS,type,
c_2EpatternMatches_2EPMATCH__EQUIV__ROWS: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__EQUIV__ROWS,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ bool ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__EXPAND__PRED,type,
c_2EpatternMatches_2EPMATCH__EXPAND__PRED: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__EXPAND__PRED,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ bool ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__FLATTEN__FUN,type,
c_2EpatternMatches_2EPMATCH__FLATTEN__FUN: del > del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__FLATTEN__FUN,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__INCOMPLETE,type,
c_2EpatternMatches_2EPMATCH__INCOMPLETE: del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__INCOMPLETE,axiom,
! [A_27a: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__INCOMPLETE @ A_27a ) @ A_27a ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE,type,
c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ bool ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW,type,
c_2EpatternMatches_2EPMATCH__ROW: del > del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__COND,type,
c_2EpatternMatches_2EPMATCH__ROW__COND: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__COND,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__COND__EX,type,
c_2EpatternMatches_2EPMATCH__ROW__COND__EX: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__COND__EX,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27b @ A_27a ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ,type,
c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ bool ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__LIFT,type,
c_2EpatternMatches_2EPMATCH__ROW__LIFT: del > del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__LIFT,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__LIFT @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27c @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT,type,
c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__magic__0,type,
c_2EpatternMatches_2EPMATCH__ROW__magic__0: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__magic__0,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__magic__0 @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ bool @ A_27b ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__magic__1,type,
c_2EpatternMatches_2EPMATCH__ROW__magic__1: del > del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__magic__1,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__magic__1 @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Epair_2Eprod @ bool @ A_27c ) ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__magic__2,type,
c_2EpatternMatches_2EPMATCH__ROW__magic__2: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__magic__2,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__magic__2 @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ bool @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ bool @ A_27b ) ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__magic__3,type,
c_2EpatternMatches_2EPMATCH__ROW__magic__3: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__magic__3,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__magic__3 @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ bool @ A_27b ) ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__ROW__magic__4,type,
c_2EpatternMatches_2EPMATCH__ROW__magic__4: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__ROW__magic__4,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__ROW__magic__4 @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ bool @ A_27b ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
thf(tp_c_2EpatternMatches_2EPMATCH__magic__1,type,
c_2EpatternMatches_2EPMATCH__magic__1: del > del > $i ).
thf(mem_c_2EpatternMatches_2EPMATCH__magic__1,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2EPMATCH__magic__1 @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ A_27b ) ) ) ).
thf(tp_c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ,type,
c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ: $i ).
thf(mem_c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ,axiom,
mem @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ,type,
c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ: $i ).
thf(mem_c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ,axiom,
mem @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO,type,
c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO: del > del > $i ).
thf(mem_c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: tp__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(tp_c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX,type,
c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX: del > del > $i ).
thf(mem_c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( arr @ bool @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Eoption_2Eoption_o,type,
tp__c_ty_2Eoption_2Eoption_o: $tType ).
thf(stp_inj_c_ty_2Eoption_2Eoption_o,type,
inj__c_ty_2Eoption_2Eoption_o: tp__c_ty_2Eoption_2Eoption_o > $i ).
thf(stp_surj_c_ty_2Eoption_2Eoption_o,type,
surj__c_ty_2Eoption_2Eoption_o: $i > tp__c_ty_2Eoption_2Eoption_o ).
thf(stp_inj_surj_c_ty_2Eoption_2Eoption_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_o] :
( ( surj__c_ty_2Eoption_2Eoption_o @ ( inj__c_ty_2Eoption_2Eoption_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eoption_2Eoption_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_o] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_o @ X ) @ ( ty_2Eoption_2Eoption @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eoption_2Eoption @ bool ) )
=> ( X
= ( inj__c_ty_2Eoption_2Eoption_o @ ( surj__c_ty_2Eoption_2Eoption_o @ X ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2Esome__var__bool__T,axiom,
( ( surj__c_ty_2Eoption_2Eoption_o
@ ( ap @ ( c_2Eoption_2Esome @ bool )
@ ( lam @ bool
@ ^ [V0x: $i] : V0x ) ) )
= ( surj__c_ty_2Eoption_2Eoption_o @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2ET ) ) ) ).
thf(conj_thm_2EpatternMatches_2Esome__var__bool__F,axiom,
( ( surj__c_ty_2Eoption_2Eoption_o
@ ( ap @ ( c_2Eoption_2Esome @ bool )
@ ( lam @ bool
@ ^ [V0x: $i] : ( ap @ c_2Ebool_2E_7E @ V0x ) ) ) )
= ( surj__c_ty_2Eoption_2Eoption_o @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__COND__def,axiom,
! [A_27a: del,A_27b: del,V0pat: $i] :
( ( mem @ V0pat @ ( arr @ A_27a @ A_27b ) )
=> ! [V1guard: $i] :
( ( mem @ V1guard @ ( arr @ A_27a @ bool ) )
=> ! [V2inp: $i] :
( ( mem @ V2inp @ A_27b )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b ) @ V0pat ) @ V1guard ) @ V2inp ) @ V3v ) )
<=> ( ( ( ap @ V0pat @ V3v )
= V2inp )
& ( p @ ( ap @ V1guard @ V3v ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0pat: $i] :
( ( mem @ V0pat @ ( arr @ A_27b @ A_27c ) )
=> ! [V1guard: $i] :
( ( mem @ V1guard @ ( arr @ A_27b @ bool ) )
=> ! [V2rhs: $i] :
( ( mem @ V2rhs @ ( arr @ A_27b @ A_27a ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ A_27c )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0pat ) @ V1guard ) @ V2rhs ) @ V3i )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a ) @ V2rhs )
@ ( ap @ ( c_2Eoption_2Esome @ A_27b )
@ ( lam @ A_27b
@ ^ [V4v: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c ) @ V0pat ) @ V1guard ) @ V3i ) @ V4v ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__INCOMPLETE__def,axiom,
! [A_27a: del] :
( ( c_2EpatternMatches_2EPMATCH__INCOMPLETE @ A_27a )
= ( c_2Ebool_2EARB @ A_27a ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ A_27b )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
= ( c_2EpatternMatches_2EPMATCH__INCOMPLETE @ A_27a ) ) )
& ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ! [V3rs: $i] :
( ( mem @ V3rs @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V2r ) @ V3rs ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27a ) @ ( ap @ V2r @ V1v ) ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ V3rs ) ) @ ( c_2Ecombin_2EI @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__CONG,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ! [V1p_27: $i] :
( ( mem @ V1p_27 @ ( arr @ A_27a @ A_27b ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27a @ bool ) )
=> ! [V3g_27: $i] :
( ( mem @ V3g_27 @ ( arr @ A_27a @ bool ) )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27a @ A_27c ) )
=> ! [V5r_27: $i] :
( ( mem @ V5r_27 @ ( arr @ A_27a @ A_27c ) )
=> ! [V6v: $i] :
( ( mem @ V6v @ A_27b )
=> ! [V7v_27: $i] :
( ( mem @ V7v_27 @ A_27b )
=> ( ( ( V0p = V1p_27 )
& ( V6v = V7v_27 )
& ! [V8x: $i] :
( ( mem @ V8x @ A_27a )
=> ( ( V6v
= ( ap @ V0p @ V8x ) )
=> ( ( p @ ( ap @ V2g @ V8x ) )
<=> ( p @ ( ap @ V3g_27 @ V8x ) ) ) ) )
& ! [V9x: $i] :
( ( mem @ V9x @ A_27a )
=> ( ( ( V6v
= ( ap @ V0p @ V9x ) )
& ( p @ ( ap @ V2g @ V9x ) ) )
=> ( ( ap @ V4r @ V9x )
= ( ap @ V5r_27 @ V9x ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V0p ) @ V2g ) @ V4r ) @ V6v )
= ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V1p_27 ) @ V3g_27 ) @ V5r_27 ) @ V7v_27 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__CONG,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1v_27: $i] :
( ( mem @ V1v_27 @ A_27a )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3rows_27: $i] :
( ( mem @ V3rows_27 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V5r_27: $i] :
( ( mem @ V5r_27 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ( ( ( V0v = V1v_27 )
& ( ( ap @ V4r @ V1v_27 )
= ( ap @ V5r_27 @ V1v_27 ) )
& ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V1v_27 ) @ V2rows )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V1v_27 ) @ V3rows_27 ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V4r ) @ V2rows ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V1v_27 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V5r_27 ) @ V3rows_27 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__EQ__AUX,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27a ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2p_27: $i] :
( ( mem @ V2p_27 @ ( arr @ A_27c @ A_27a ) )
=> ! [V3g_27: $i] :
( ( mem @ V3g_27 @ ( arr @ A_27c @ bool ) )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27b @ A_27d ) )
=> ! [V5r_27: $i] :
( ( mem @ V5r_27 @ ( arr @ A_27c @ A_27d ) )
=> ( ( ! [V6i: $i] :
( ( mem @ V6i @ A_27a )
=> ( ? [V7x: $i] :
( ( mem @ V7x @ A_27b )
& ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27a ) @ V0p ) @ V1g ) @ V6i ) @ V7x ) ) )
<=> ? [V8x_27: $i] :
( ( mem @ V8x_27 @ A_27c )
& ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27c @ A_27a ) @ V2p_27 ) @ V3g_27 ) @ V6i ) @ V8x_27 ) ) ) ) )
& ! [V9x: $i] :
( ( mem @ V9x @ A_27b )
=> ! [V10x_27: $i] :
( ( mem @ V10x_27 @ A_27c )
=> ( ( ( ( ap @ V0p @ V9x )
= ( ap @ V2p_27 @ V10x_27 ) )
& ( p @ ( ap @ V1g @ V9x ) )
& ( p @ ( ap @ V3g_27 @ V10x_27 ) ) )
=> ( ( ap @ V4r @ V9x )
= ( ap @ V5r_27 @ V10x_27 ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27b @ A_27a ) @ V0p ) @ V1g ) @ V4r )
= ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27a ) @ V2p_27 ) @ V3g_27 ) @ V5r_27 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__EQ__NONE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ A_27a ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2r ) @ V3i )
= ( c_2Eoption_2ENONE @ A_27a ) )
<=> ! [V4x: $i] :
( ( mem @ V4x @ A_27b )
=> ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V3i ) @ V4x ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__EQ__SOME,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ A_27a ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ A_27c )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2r ) @ V3i )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) )
=> ? [V5x: $i] :
( ( mem @ V5x @ A_27b )
& ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V3i ) @ V5x ) )
& ( V4y
= ( ap @ V2r @ V5x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__COND__SELECT__UNIQUE,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ bool ) )
=> ! [V2i: $i] :
( ( mem @ V2i @ A_27b )
=> ( ! [V3x1: $i] :
( ( mem @ V3x1 @ A_27a )
=> ! [V4x2: $i] :
( ( mem @ V4x2 @ A_27a )
=> ( ( ( p @ ( ap @ V1g @ V3x1 ) )
& ( p @ ( ap @ V1g @ V4x2 ) )
& ( ( ap @ V0p @ V3x1 )
= ( ap @ V0p @ V4x2 ) ) )
=> ( V3x1 = V4x2 ) ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2i ) @ V5x ) )
=> ( ( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V6y: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2i ) @ V6y ) ) )
= V5x ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__DEF__GSYM,axiom,
! [A_27a: del,A_27b: del,V0pat: $i] :
( ( mem @ V0pat @ ( arr @ A_27a @ A_27b ) )
=> ! [V1guard: $i] :
( ( mem @ V1guard @ ( arr @ A_27a @ bool ) )
=> ! [V2inp: $i] :
( ( mem @ V2inp @ A_27b )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b ) @ V0pat ) @ V1guard ) @ V2inp ) @ V3v ) )
<=> ( ( V2inp
= ( ap @ V0pat @ V3v ) )
& ( p @ ( ap @ V1guard @ V3v ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EVAL,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0v: $i] :
( ( mem @ V0v @ A_27b )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27d @ A_27b ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27d @ bool ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27d @ A_27c ) )
=> ! [V4rs: $i] :
( ( mem @ V4rs @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
= ( c_2EpatternMatches_2EPMATCH__INCOMPLETE @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27d @ A_27b ) @ V1p ) @ V2g ) @ V3r ) ) @ V4rs ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Ebool_2ECOND @ A_27c )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27d )
@ ( lam @ A_27d
@ ^ [V5x: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27d @ A_27b ) @ V1p ) @ V2g ) @ V0v ) @ V5x ) ) ) )
@ ( ap @ V3r
@ ( ap @ ( c_2Emin_2E_40 @ A_27d )
@ ( lam @ A_27d
@ ^ [V6x: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27d @ A_27b ) @ V1p ) @ V2g ) @ V0v ) @ V6x ) ) ) ) )
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V0v ) @ V4rs ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EVAL__MATCH,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ A_27a ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27c )
=> ! [V4rs: $i] :
( ( mem @ V4rs @ ( ty_2Elist_2Elist @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2r ) @ V3v )
!= ( c_2Eoption_2ENONE @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27c ) @ V3v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2r ) ) @ V4rs ) )
= ( ap @ V2r
@ ( ap @ ( c_2Emin_2E_40 @ A_27b )
@ ( lam @ A_27b
@ ^ [V5x: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V3v ) @ V5x ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXTEND__BASE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v__old: $i] :
( ( mem @ V0v__old @ A_27a )
=> ! [V1v__new: $i] :
( ( mem @ V1v__new @ A_27b )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v__old ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V1v__new ) @ ( c_2Elist_2ENIL @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXTEND__BOTH,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v__old: $i] :
( ( mem @ V0v__old @ A_27a )
=> ! [V1v__new: $i] :
( ( mem @ V1v__new @ A_27b )
=> ! [V2rows__old: $i] :
( ( mem @ V2rows__old @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V3rows__new: $i] :
( ( mem @ V3rows__new @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V4r__old: $i] :
( ( mem @ V4r__old @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
=> ! [V5r__new: $i] :
( ( mem @ V5r__new @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
=> ( ( ( ap @ V4r__old @ V0v__old )
= ( ap @ V5r__new @ V1v__new ) )
=> ( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v__old ) @ V2rows__old )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V1v__new ) @ V3rows__new ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v__old ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V4r__old ) @ V2rows__old ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V1v__new ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V5r__new ) @ V3rows__new ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXTEND__BOTH__ID,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows__old: $i] :
( ( mem @ V1rows__old @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows__new: $i] :
( ( mem @ V2rows__new @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V1rows__old )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V2rows__new ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V3r ) @ V1rows__old ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V3r ) @ V2rows__new ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXTEND__OLD,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v__old: $i] :
( ( mem @ V0v__old @ A_27a )
=> ! [V1v__new: $i] :
( ( mem @ V1v__new @ A_27b )
=> ! [V2rows__old: $i] :
( ( mem @ V2rows__old @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V3rows__new: $i] :
( ( mem @ V3rows__new @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V4r__old: $i] :
( ( mem @ V4r__old @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
=> ( ( ( ap @ V4r__old @ V0v__old )
= ( c_2Eoption_2ENONE @ A_27c ) )
=> ( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v__old ) @ V2rows__old )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V1v__new ) @ V3rows__new ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v__old ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V4r__old ) @ V2rows__old ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V1v__new ) @ V3rows__new ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__FUN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0ff: $i] :
( ( mem @ V0ff @ ( arr @ A_27a @ A_27b ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27a )
=> ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ A_27c @ A_27a ) )
=> ! [V3g: $i] :
( ( mem @ V3g @ ( arr @ A_27c @ bool ) )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27c @ A_27d ) )
=> ( ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27a )
=> ( ( ( ap @ V0ff @ V5x )
= ( ap @ V0ff @ V6y ) )
=> ( V5x = V6y ) ) ) )
=> ( ( ap
@ ( ap
@ ( ap
@ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27b )
@ ( lam @ A_27c
@ ^ [V7x: $i] : ( ap @ V0ff @ ( ap @ V2p @ V7x ) ) ) )
@ V3g )
@ V4r )
@ ( ap @ V0ff @ V1v ) )
= ( ap
@ ( ap
@ ( ap
@ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27a )
@ ( lam @ A_27c
@ ^ [V8x: $i] : ( ap @ V2p @ V8x ) ) )
@ V3g )
@ V4r )
@ V1v ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__EXTEND__INPUT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1v_27: $i] :
( ( mem @ V1v_27 @ A_27b )
=> ! [V2f_27: $i] :
( ( mem @ V2f_27 @ ( arr @ A_27b @ A_27c ) )
=> ! [V3f: $i] :
( ( mem @ V3f @ ( arr @ A_27d @ A_27e ) )
=> ! [V4p: $i] :
( ( mem @ V4p @ ( arr @ A_27e @ A_27a ) )
=> ! [V5g: $i] :
( ( mem @ V5g @ ( arr @ A_27c @ ( arr @ A_27e @ bool ) ) )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( arr @ A_27c @ ( arr @ A_27e @ A_27f ) ) )
=> ! [V7p_27: $i] :
( ( mem @ V7p_27 @ ( arr @ A_27d @ A_27b ) )
=> ( ( ! [V8x_27: $i] :
( ( mem @ V8x_27 @ A_27d )
=> ( ( V1v_27
= ( ap @ V7p_27 @ V8x_27 ) )
=> ( ( ap @ V4p @ ( ap @ V3f @ V8x_27 ) )
= V0v ) ) )
& ! [V9x: $i] :
( ( mem @ V9x @ A_27e )
=> ( ( V0v
= ( ap @ V4p @ V9x ) )
=> ? [V10x_27: $i] :
( ( mem @ V10x_27 @ A_27d )
& ( ( ap @ V7p_27 @ V10x_27 )
= V1v_27 ) ) ) )
& ! [V11x: $i] :
( ( mem @ V11x @ A_27e )
=> ! [V12y: $i] :
( ( mem @ V12y @ A_27e )
=> ( ( ( ap @ V4p @ V11x )
= ( ap @ V4p @ V12y ) )
=> ( V11x = V12y ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27f @ A_27e @ A_27a ) @ V4p ) @ ( ap @ V5g @ ( ap @ V2f_27 @ V1v_27 ) ) ) @ ( ap @ V6r @ ( ap @ V2f_27 @ V1v_27 ) ) ) @ V0v )
= ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27f @ A_27d @ A_27b ) @ V7p_27 )
@ ( lam @ A_27d
@ ^ [V13x: $i] : ( ap @ ( ap @ V5g @ ( ap @ V2f_27 @ ( ap @ V7p_27 @ V13x ) ) ) @ ( ap @ V3f @ V13x ) ) ) )
@ ( lam @ A_27d
@ ^ [V14x: $i] : ( ap @ ( ap @ V6r @ ( ap @ V2f_27 @ ( ap @ V7p_27 @ V14x ) ) ) @ ( ap @ V3f @ V14x ) ) ) )
@ V1v_27 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__FUN__VAR,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1v_27: $i] :
( ( mem @ V1v_27 @ A_27b )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27c @ A_27d ) )
=> ! [V3p: $i] :
( ( mem @ V3p @ ( arr @ A_27d @ A_27a ) )
=> ! [V4g: $i] :
( ( mem @ V4g @ ( arr @ A_27d @ bool ) )
=> ! [V5r: $i] :
( ( mem @ V5r @ ( arr @ A_27d @ A_27e ) )
=> ! [V6p_27: $i] :
( ( mem @ V6p_27 @ ( arr @ A_27c @ A_27b ) )
=> ( ( ! [V7x_27: $i] :
( ( mem @ V7x_27 @ A_27c )
=> ( ( V1v_27
= ( ap @ V6p_27 @ V7x_27 ) )
<=> ( ( ap @ V3p @ ( ap @ V2f @ V7x_27 ) )
= V0v ) ) )
& ! [V8x: $i] :
( ( mem @ V8x @ A_27d )
=> ( ( V0v
= ( ap @ V3p @ V8x ) )
=> ? [V9x_27: $i] :
( ( mem @ V9x_27 @ A_27c )
& ( ( ap @ V2f @ V9x_27 )
= V8x ) ) ) )
& ! [V10x: $i] :
( ( mem @ V10x @ A_27d )
=> ! [V11y: $i] :
( ( mem @ V11y @ A_27d )
=> ( ( ( ap @ V3p @ V10x )
= ( ap @ V3p @ V11y ) )
=> ( V10x = V11y ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27e @ A_27d @ A_27a ) @ V3p ) @ V4g ) @ V5r ) @ V0v )
= ( ap
@ ( ap
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27e @ A_27c @ A_27b ) @ V6p_27 )
@ ( lam @ A_27c
@ ^ [V12x: $i] : ( ap @ V4g @ ( ap @ V2f @ V12x ) ) ) )
@ ( lam @ A_27c
@ ^ [V13x: $i] : ( ap @ V5r @ ( ap @ V2f @ V13x ) ) ) )
@ V1v_27 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V2rows2 ) )
<=> ( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V1rows1 )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V2rows2 ) )
& ( ? [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V3r ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows1 ) ) )
& ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V3r @ V0v ) ) ) )
<=> ? [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V4r ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows2 ) ) )
& ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V4r @ V0v ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__EQUIV__EXPAND,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V2rows2 ) )
<=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V2rows2 ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__1,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V1rows ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__2,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V2rows2 ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V2rows2 ) @ V1rows1 ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__3,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3rows3: $i] :
( ( mem @ V3rows3 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V2rows2 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V2rows2 ) @ V3rows3 ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V3rows3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__MATCH,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1 ) @ V2rows2 ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V1rows1 )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V2rows2 ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__APPEND__SEM,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1: $i] :
( ( mem @ V1rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows2: $i] :
( ( mem @ V2rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows1 ) @ V2rows2 ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Ebool_2ECOND @ A_27b )
@ ( ap @ ( c_2Ebool_2E_3F @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V3r: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V3r ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows1 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V3r @ V0v ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V1rows1 ) )
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V2rows2 ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__APPEND,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows1a: $i] :
( ( mem @ V1rows1a @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rows1b: $i] :
( ( mem @ V2rows1b @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3rows2a: $i] :
( ( mem @ V3rows2a @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V4rows2b: $i] :
( ( mem @ V4rows2b @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows1a ) @ V2rows1b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V3rows2a ) @ V4rows2b ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows1a ) @ V3rows2a ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows1b ) @ V4rows2b ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__CONS__NONE,axiom,
! [A_27a: del,A_27b: del,V0row: $i] :
( ( mem @ V0row @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( ( ap @ V0row @ V1v )
= ( c_2Eoption_2ENONE @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27b @ A_27a ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V0row ) @ V2rows ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27b @ A_27a ) @ V1v ) @ V2rows ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__TRIVIAL__SOUNDNESS__EQUIV,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) )
& ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1rows ) @ V0v ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V1rows ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__TRIVIAL__SOUNDNESS,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) )
& ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1rows ) @ V0v ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V1rows )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V1rows ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT,axiom,
! [A_27a: del,A_27b: del,V0r1: $i] :
( ( mem @ V0r1 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V1r2: $i] :
( ( mem @ V1r2 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rows1: $i] :
( ( mem @ V2rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3rows2: $i] :
( ( mem @ V3rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V4rows3: $i] :
( ( mem @ V4rows3 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27a )
=> ( ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V1r2 @ V5v ) ) )
=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V0r1 @ V5v ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V5v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V0r1 ) @ V3rows2 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r2 ) @ V4rows3 ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V5v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V0r1 ) @ V3rows2 ) ) ) @ V4rows3 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__PMATCH__ROWS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27a @ A_27c ) )
=> ! [V3p_27: $i] :
( ( mem @ V3p_27 @ ( arr @ A_27d @ A_27b ) )
=> ! [V4g_27: $i] :
( ( mem @ V4g_27 @ ( arr @ A_27d @ bool ) )
=> ! [V5r_27: $i] :
( ( mem @ V5r_27 @ ( arr @ A_27d @ A_27c ) )
=> ! [V6rows1: $i] :
( ( mem @ V6rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V7rows2: $i] :
( ( mem @ V7rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V8rows3: $i] :
( ( mem @ V8rows3 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V9v: $i] :
( ( mem @ V9v @ A_27b )
=> ( ! [V10x_27: $i] :
( ( mem @ V10x_27 @ A_27d )
=> ( ( ( V9v
= ( ap @ V3p_27 @ V10x_27 ) )
& ( p @ ( ap @ V4g_27 @ V10x_27 ) ) )
=> ? [V11x: $i] :
( ( mem @ V11x @ A_27a )
& ( ( ap @ V3p_27 @ V10x_27 )
= ( ap @ V0p @ V11x ) )
& ( p @ ( ap @ V1g @ V11x ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V9v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V6rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2r ) ) @ V7rows2 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27d @ A_27b ) @ V3p_27 ) @ V4g_27 ) @ V5r_27 ) ) @ V8rows3 ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V9v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V6rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2r ) ) @ V7rows2 ) ) ) @ V8rows3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__SUBSUMED,axiom,
! [A_27a: del,A_27b: del,V0r1: $i] :
( ( mem @ V0r1 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V1r2: $i] :
( ( mem @ V1r2 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rows1: $i] :
( ( mem @ V2rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3rows2: $i] :
( ( mem @ V3rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V4rows3: $i] :
( ( mem @ V4rows3 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27a )
=> ( ( ! [V6x: $i] :
( ( mem @ V6x @ A_27b )
=> ( ( ( ap @ V0r1 @ V5v )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V6x ) )
=> ( ( ap @ V1r2 @ V5v )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V6x ) ) ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V0r1 @ V5v ) ) )
=> ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V7row: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V7row @ V5v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V3rows2 ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V5v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V0r1 ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V3rows2 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r2 ) @ V4rows3 ) ) ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V5v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows1 ) @ V3rows2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r2 ) @ V4rows3 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__SUBSUMED__PMATCH__ROWS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27a @ A_27c ) )
=> ! [V3p_27: $i] :
( ( mem @ V3p_27 @ ( arr @ A_27d @ A_27b ) )
=> ! [V4g_27: $i] :
( ( mem @ V4g_27 @ ( arr @ A_27d @ bool ) )
=> ! [V5r_27: $i] :
( ( mem @ V5r_27 @ ( arr @ A_27d @ A_27c ) )
=> ! [V6rows1: $i] :
( ( mem @ V6rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V7rows2: $i] :
( ( mem @ V7rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V8rows3: $i] :
( ( mem @ V8rows3 @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V9v: $i] :
( ( mem @ V9v @ A_27b )
=> ( ( ! [V10x: $i] :
( ( mem @ V10x @ A_27a )
=> ( ( ( V9v
= ( ap @ V0p @ V10x ) )
& ( p @ ( ap @ V1g @ V10x ) ) )
=> ? [V11x_27: $i] :
( ( mem @ V11x_27 @ A_27d )
& ( ( ap @ V0p @ V10x )
= ( ap @ V3p_27 @ V11x_27 ) )
& ( p @ ( ap @ V4g_27 @ V11x_27 ) ) ) ) )
& ! [V12x: $i] :
( ( mem @ V12x @ A_27a )
=> ! [V13x_27: $i] :
( ( mem @ V13x_27 @ A_27d )
=> ( ( ( V9v
= ( ap @ V0p @ V12x ) )
& ( ( ap @ V0p @ V12x )
= ( ap @ V3p_27 @ V13x_27 ) )
& ( p @ ( ap @ V1g @ V12x ) )
& ( p @ ( ap @ V4g_27 @ V13x_27 ) ) )
=> ( ( ap @ V2r @ V12x )
= ( ap @ V5r_27 @ V13x_27 ) ) ) ) )
& ! [V14x: $i] :
( ( mem @ V14x @ A_27a )
=> ( ( ( V9v
= ( ap @ V0p @ V14x ) )
& ( p @ ( ap @ V1g @ V14x ) ) )
=> ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) )
@ ^ [V15row: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ ( ap @ V15row @ ( ap @ V0p @ V14x ) ) ) @ ( c_2Eoption_2ENONE @ A_27c ) ) ) )
@ V7rows2 ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V9v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V6rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2r ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V7rows2 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27d @ A_27b ) @ V3p_27 ) @ V4g_27 ) @ V5r_27 ) ) @ V8rows3 ) ) ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V9v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V6rows1 ) @ V7rows2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27d @ A_27b ) @ V3p_27 ) @ V4g_27 ) @ V5r_27 ) ) @ V8rows3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__REMOVE__ARB,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27a @ A_27c ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27b )
=> ! [V4rows: $i] :
( ( mem @ V4rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ( ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( ap @ V2r @ V5x )
= ( c_2Ebool_2EARB @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V3v ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27a @ A_27b ) @ V0p ) @ V1g ) @ V2r ) ) @ V4rows ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V3v ) @ V4rows ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__INTRO__CATCHALL,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27b )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V0v ) @ V1rows )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V0v )
@ ( ap
@ ( ap @ ( c_2Elist_2ESNOC @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
@ ( ap
@ ( ap
@ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27b )
@ ( lam @ A_27b
@ ^ [V2__0: $i] : V2__0 ) )
@ ( lam @ A_27b
@ ^ [V3__0: $i] : c_2Ebool_2ET ) )
@ ( lam @ A_27b
@ ^ [V4__0: $i] : ( c_2Ebool_2EARB @ A_27a ) ) ) )
@ V1rows ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__REMOVE__ARB__NO__OVERLAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27b @ A_27c ) )
=> ! [V4rows1: $i] :
( ( mem @ V4rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V5rows2: $i] :
( ( mem @ V5rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ( ( ! [V6x: $i] :
( ( mem @ V6x @ A_27b )
=> ( ( ap @ V3r @ V6x )
= ( c_2Ebool_2EARB @ A_27c ) ) )
& ! [V7x: $i] :
( ( mem @ V7x @ A_27b )
=> ( ( ( V0v
= ( ap @ V1p @ V7x ) )
& ( p @ ( ap @ V2g @ V7x ) ) )
=> ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) )
@ ^ [V8row: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27c ) ) @ ( ap @ V8row @ ( ap @ V1p @ V7x ) ) ) @ ( c_2Eoption_2ENONE @ A_27c ) ) ) )
@ V5rows2 ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V4rows1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V3r ) ) @ V5rows2 ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V4rows1 ) @ V5rows2 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs: $i] :
( ( mem @ V1rs @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ V1rs ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs ) ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ V1rs ) @ V0v ) ) )
=> ? [V3j: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
& ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ V1rs ) @ V0v ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__NIL,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
<=> $false ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__0,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rs: $i] :
( ( mem @ V2rs @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r ) @ V2rs ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( ( ap @ V1r @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__SUC,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rs: $i] :
( ( mem @ V2rs @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r ) @ V2rs ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) )
<=> ( ( ( ( ap @ V1r @ V0v )
!= ( c_2Eoption_2ENONE @ A_27b ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rs ) ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ V2rs ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__APPEND__LT,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs1: $i] :
( ( mem @ V1rs1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rs2: $i] :
( ( mem @ V2rs2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) @ V2rs2 ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ V1rs1 ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__APPEND__GE,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs1: $i] :
( ( mem @ V1rs1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rs2: $i] :
( ( mem @ V2rs2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3i: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) @ V2rs2 ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
<=> ( ( ~ ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V4r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V4r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V1rs1 ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rs2 ) ) ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ V2rs2 ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
<=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) )
& ! [V4i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) )
& ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V5r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V5r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V1rows ) )
=> ( p @ V2c ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__NIL,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Ebool_2ET ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__SNOC,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V5i: $i] :
( ( mem @ V5i @ bool )
=> ! [V6c_27: $i] :
( ( mem @ V6c_27 @ bool )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ( ( ( ap @ V4r @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) )
=> ( ( p @ V2c )
=> ( p @ V6c_27 ) ) )
=> ( ( ( p @ V2c )
=> ( ( p @ V5i )
=> ( ( ap @ V4r @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V4r ) @ V1rows ) ) @ V6c_27 ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ bool ) @ V5i ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__def,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ V0i ) @ V1p ) @ V2g ) )
<=> ? [V3x: $i] :
( ( mem @ V3x @ A_27b )
& ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V0i ) @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__SNOC__PMATCH__ROW,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4p: $i] :
( ( mem @ V4p @ ( arr @ A_27c @ A_27a ) )
=> ! [V5g: $i] :
( ( mem @ V5g @ ( arr @ A_27c @ bool ) )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( arr @ A_27c @ A_27b ) )
=> ! [V7c_27: $i] :
( ( mem @ V7c_27 @ bool )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27c ) @ V0v ) @ V4p ) @ V5g ) )
=> ( ( p @ V2c )
<=> ( p @ V7c_27 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27b @ A_27c @ A_27a ) @ V4p ) @ V5g ) @ V6r ) ) @ V1rows ) ) @ V7c_27 ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ bool ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V2c ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27c ) @ V0v ) @ V4p ) @ V5g ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__CONS,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1row: $i] :
( ( mem @ V1row @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3c: $i] :
( ( mem @ V3c @ bool )
=> ! [V4i: $i] :
( ( mem @ V4i @ bool )
=> ! [V5infos_27: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1row ) @ V2rows ) ) @ V3c ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V4i ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) ) )
<=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2rows ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) ) )
& ( ( p @ V4i )
=> ( ( ap @ V1row @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) ) )
& ( ( ( ap @ V1row @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V2rows ) @ V3c ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a: del,V0is: tp__c_ty_2Elist_2Elist_o,V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0is ) ) @ V1xs )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ bool @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ bool @ A_27a ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EFILTER @ ( ty_2Epair_2Eprod @ bool @ A_27a ) )
@ ( lam @ ( ty_2Epair_2Eprod @ bool @ A_27a )
@ ^ [V2x: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( c_2Epair_2EFST @ bool @ A_27a ) @ V2x ) ) ) )
@ ( ap @ ( c_2Elist_2EZIP @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0is ) ) @ V1xs ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO__THMS,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ( ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27a ) @ ( c_2Elist_2ENIL @ bool ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V0is: tp__c_ty_2Elist_2Elist_o,V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2xs: $i] :
( ( mem @ V2xs @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2ET ) @ ( inj__c_ty_2Elist_2Elist_o @ V0is ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V1x ) @ V2xs ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V0is ) ) @ V2xs ) ) ) )
& ! [V3is: tp__c_ty_2Elist_2Elist_o,V4x: $i] :
( ( mem @ V4x @ A_27c )
=> ! [V5xs: $i] :
( ( mem @ V5xs @ ( ty_2Elist_2Elist @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27c ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2EF ) @ ( inj__c_ty_2Elist_2Elist_o @ V3is ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27c ) @ V4x ) @ V5xs ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27c ) @ V4x ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ A_27c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3is ) ) @ V5xs ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__ROWS__INFO__EQUIV,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1c: $i] :
( ( mem @ V1c @ bool )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V2rows ) @ V1c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27b ) @ V0v ) @ V2rows ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) @ V2rows ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFO__TO__PMATCH__EQ,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1c: $i] :
( ( mem @ V1c @ bool )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V2rows ) @ V1c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ V2rows )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) @ V2rows ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs: $i] :
( ( mem @ V1rs @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27a @ A_27b ) @ V0v ) @ V1rs ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEXISTS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V2r: $i] : ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ V2r @ V0v ) ) ) )
@ V1rs ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__REWRITES,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) )
<=> $false ) )
& ! [V1v: $i] :
( ( mem @ V1v @ A_27c )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27d ) ) )
=> ! [V3rs: $i] :
( ( mem @ V3rs @ ( ty_2Elist_2Elist @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27d ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27c @ A_27d ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27d ) ) ) @ V2r ) @ V3rs ) ) )
<=> ( ( ( ap @ V2r @ V1v )
!= ( c_2Eoption_2ENONE @ A_27d ) )
| ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27c @ A_27d ) @ V1v ) @ V3rs ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__EXTRACT__IS__EXHAUSTIVE,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ~ ( p @ V2c )
=> ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27a @ A_27b ) @ V0v ) @ V1rows ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__def,axiom,
! [V0ip1: tp__c_ty_2Elist_2Elist_o,V1ip2: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( inj__c_ty_2Elist_2Elist_o @ V0ip1 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1ip2 ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP2 @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V2i1: $i] :
( lam @ bool
@ ^ [V3i2: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2i1 ) @ V3i2 ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V0ip1 ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V1ip2 ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__REWRITE,axiom,
! [V0i1: $i] :
( ( mem @ V0i1 @ bool )
=> ! [V1is1: tp__c_ty_2Elist_2Elist_o,V2i2: $i] :
( ( mem @ V2i2 @ bool )
=> ! [V3is2: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( c_2Elist_2ENIL @ bool ) ) @ ( c_2Elist_2ENIL @ bool ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( c_2Elist_2ENIL @ bool ) ) )
& ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V0i1 ) @ ( inj__c_ty_2Elist_2Elist_o @ V1is1 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V2i2 ) @ ( inj__c_ty_2Elist_2Elist_o @ V3is2 ) ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V0i1 ) @ V2i2 ) ) @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( inj__c_ty_2Elist_2Elist_o @ V1is1 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3is2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__THM,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4c_27: $i] :
( ( mem @ V4c_27 @ bool )
=> ! [V5infos_27: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2c ) @ V4c_27 ) ) @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ__def,axiom,
! [V0ip1: tp__c_ty_2Elist_2Elist_o,V1ip2: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ @ ( inj__c_ty_2Elist_2Elist_o @ V0ip1 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1ip2 ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP2 @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V2i1: $i] :
( lam @ bool
@ ^ [V3i2: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2i1 ) @ V3i2 ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V0ip1 ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V1ip2 ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ__THM,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4c_27: $i] :
( ( mem @ V4c_27 @ bool )
=> ! [V5infos_27: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V4c_27 ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2c ) @ V4c_27 ) ) @ ( ap @ ( ap @ c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V5infos_27 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ bool )
=> ! [V2infos: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) @ V1p ) @ ( inj__c_ty_2Elist_2Elist_o @ V2infos ) ) )
= ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ V1p ) @ ( inj__c_ty_2Elist_2Elist_o @ V2infos ) ) ) ) ) )
& ! [V3v: $i] :
( ( mem @ V3v @ A_27a )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V5rows: $i] :
( ( mem @ V5rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V6p: $i] :
( ( mem @ V6p @ bool )
=> ! [V7infos: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V3v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V4r ) @ V5rows ) ) @ V6p ) @ ( inj__c_ty_2Elist_2Elist_o @ V7infos ) ) )
= ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V3v ) @ V5rows ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V6p ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V4r @ V3v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ bool ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V6p ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V4r @ V3v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V7infos ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Epair_2ESND @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ c_2Ebool_2ET ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2ELENGTH__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( c_2Epair_2ESND @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2p ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EEL1__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Epair_2ESND @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2p ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EEL2__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o,V4i: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Epair_2ESND @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2p ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) )
<=> ( ( ( p @ V2p )
& ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V5r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V5r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) @ V1rows ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) ) @ V1rows ) @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2ELENGTH__STRONGEST__REDUNDANT__ROWS__INFO,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EFST__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ bool )
=> ! [V3infos: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( c_2Epair_2EFST @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX @ A_27a @ A_27b ) @ V0v ) @ V1rows ) @ V2p ) @ ( inj__c_ty_2Elist_2Elist_o @ V3infos ) ) ) )
<=> ( ( p @ V2p )
& ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V4r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V4r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V1rows ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EEL__STRONGEST__REDUNDANT__ROWS__INFO,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rows ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) ) )
<=> ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V3r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V3r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ V1rows ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ V1rows ) @ V0v )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__OK,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rows: $i] :
( ( mem @ V1rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( p
@ ( ap
@ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows )
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V2r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V2r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V1rows ) )
@ ( ap @ ( ap @ ( c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO @ A_27a @ A_27b ) @ V0v ) @ V1rows ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__FULL__DEF,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ V0i ) @ V1p ) @ V2g ) )
<=> ? [V3x: $i] :
( ( mem @ V3x @ A_27b )
& ( V0i
= ( ap @ V1p @ V3x ) )
& ( p @ ( ap @ V2g @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__WEAKEN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27c )
=> ! [V2p: $i] :
( ( mem @ V2p @ ( arr @ A_27b @ A_27c ) )
=> ! [V3g: $i] :
( ( mem @ V3g @ ( arr @ A_27b @ bool ) )
=> ! [V4p_27: $i] :
( ( mem @ V4p_27 @ ( arr @ A_27a @ A_27c ) )
=> ! [V5g_27: $i] :
( ( mem @ V5g_27 @ ( arr @ A_27a @ bool ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27c @ A_27b ) @ V1v ) @ V2p ) @ V3g ) )
=> ( ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ( ( ap @ V4p_27 @ V6x )
= ( ap @ V2p @ ( ap @ V0f @ V6x ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27c @ A_27a ) @ V1v ) @ V4p_27 ) @ V5g_27 ) )
<=> ( p
@ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27c @ A_27a ) @ V1v ) @ V4p_27 )
@ ( lam @ A_27a
@ ^ [V7x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V5g_27 @ V7x ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V3g @ ( ap @ V0f @ V7x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__FALSE,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27b )
=> ~ ( p @ ( ap @ V2g @ V3x ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ V0v ) @ V1p ) @ V2g ) )
<=> $false ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__IMP__REWRITE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ! [V3p_27: $i] :
( ( mem @ V3p_27 @ ( arr @ A_27c @ A_27a ) )
=> ! [V4g_27: $i] :
( ( mem @ V4g_27 @ ( arr @ A_27c @ bool ) )
=> ! [V5RES: $i] :
( ( mem @ V5RES @ bool )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ V0v ) @ V1p ) @ V2g ) )
=> ( ! [V6x: $i] :
( ( mem @ V6x @ A_27b )
=> ( ( p @ ( ap @ V2g @ V6x ) )
=> ( ? [V7x_27: $i] :
( ( mem @ V7x_27 @ A_27c )
& ( ( ap @ V3p_27 @ V7x_27 )
= ( ap @ V1p @ V6x ) )
& ( p @ ( ap @ V4g_27 @ V7x_27 ) ) )
<=> ( p @ V5RES ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27c ) @ V0v ) @ V3p_27 ) @ V4g_27 ) )
<=> ( p @ V5RES ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__CONTRADICT,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs: $i] :
( ( mem @ V1rs @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V2r: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V2r @ V0v ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) )
@ V1rs ) )
=> $false )
=> ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27a @ A_27b ) @ V0v ) @ V1rs ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__EVAL__COND__EX,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27b @ A_27c ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27a @ A_27b ) @ V0i ) @ V1p ) @ V2g ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V3r ) @ V0i )
= ( ap @ ( c_2Eoption_2ESOME @ A_27c )
@ ( ap @ V3r
@ ( ap @ ( c_2Emin_2E_40 @ A_27b )
@ ( lam @ A_27b
@ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V0i ) @ V4x ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__NEQ__NONE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ A_27a ) )
=> ! [V3i: $i] :
( ( mem @ V3i @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2r ) @ V3i )
!= ( c_2Eoption_2ENONE @ A_27a ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__EX @ A_27c @ A_27b ) @ V3i ) @ V0p ) @ V1g ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__DOUBLE__BINDS__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
( ( mem @ V0g @ ( arr @ A_27a @ A_27b ) )
=> ! [V1p1: $i] :
( ( mem @ V1p1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2g1: $i] :
( ( mem @ V2g1 @ ( arr @ A_27a @ bool ) )
=> ! [V3r1: $i] :
( ( mem @ V3r1 @ ( arr @ A_27a @ A_27d ) )
=> ! [V4p2: $i] :
( ( mem @ V4p2 @ ( arr @ A_27b @ A_27c ) )
=> ! [V5g2: $i] :
( ( mem @ V5g2 @ ( arr @ A_27b @ bool ) )
=> ! [V6r2: $i] :
( ( mem @ V6r2 @ ( arr @ A_27b @ A_27d ) )
=> ( ( ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8y: $i] :
( ( mem @ V8y @ A_27a )
=> ( ( ( ap @ V1p1 @ V7x )
= ( ap @ V1p1 @ V8y ) )
=> ( V7x = V8y ) ) ) )
& ! [V9x: $i] :
( ( mem @ V9x @ A_27a )
=> ( ( ap @ V4p2 @ ( ap @ V0g @ V9x ) )
= ( ap @ V1p1 @ V9x ) ) )
& ! [V10x_27: $i] :
( ( mem @ V10x_27 @ A_27b )
=> ( ( p @ ( ap @ V5g2 @ V10x_27 ) )
<=> ? [V11x: $i] :
( ( mem @ V11x @ A_27a )
& ( V10x_27
= ( ap @ V0g @ V11x ) )
& ( p @ ( ap @ V2g1 @ V11x ) ) ) ) )
& ! [V12x: $i] :
( ( mem @ V12x @ A_27a )
=> ( ( ap @ V6r2 @ ( ap @ V0g @ V12x ) )
= ( ap @ V3r1 @ V12x ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27a @ A_27c ) @ V1p1 ) @ V2g1 ) @ V3r1 )
= ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27b @ A_27c ) @ V4p2 ) @ V5g2 ) @ V6r2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EGUARDS__ELIM__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1rs1: $i] :
( ( mem @ V1rs1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V2rs2: $i] :
( ( mem @ V2rs2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3p: $i] :
( ( mem @ V3p @ ( arr @ A_27c @ A_27a ) )
=> ! [V4g: $i] :
( ( mem @ V4g @ ( arr @ A_27c @ bool ) )
=> ! [V5r: $i] :
( ( mem @ V5r @ ( arr @ A_27c @ A_27b ) )
=> ( ! [V6x1: $i] :
( ( mem @ V6x1 @ A_27c )
=> ! [V7x2: $i] :
( ( mem @ V7x2 @ A_27c )
=> ( ( ( ap @ V3p @ V6x1 )
= ( ap @ V3p @ V7x2 ) )
=> ( V6x1 = V7x2 ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27b @ A_27c @ A_27a ) @ V3p ) @ V4g ) @ V5r ) ) @ V2rs2 ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0v )
@ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1rs1 )
@ ( ap
@ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( ap
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27b @ A_27c @ A_27a ) @ V3p )
@ ( lam @ A_27c
@ ^ [V8x: $i] : c_2Ebool_2ET ) )
@ ( lam @ A_27c
@ ^ [V9x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ V4g @ V9x ) ) @ ( ap @ V5r @ V9x ) ) @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ ( ap @ V3p @ V9x ) ) @ V2rs2 ) ) ) ) )
@ V2rs2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27b @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ bool ) )
=> ! [V2row: $i] :
( ( mem @ V2row @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27c )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V2row ) @ V3v )
= ( ap
@ ( ap
@ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ( ap @ ( c_2Eoption_2Esome @ A_27b )
@ ( lam @ A_27b
@ ^ [V4x: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c ) @ V0p ) @ V1g ) @ V3v ) @ V4x ) ) ) )
@ ( c_2Eoption_2ENONE @ A_27a ) )
@ ( lam @ A_27b
@ ^ [V5x: $i] : ( ap @ ( ap @ V2row @ V5x ) @ V5x ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__FLATTEN__THM__SINGLE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ! [V3rows: $i] :
( ( mem @ V3rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) )
=> ( ! [V4x: $i] :
( ( mem @ V4x @ A_27b )
=> ( p
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27b @ A_27c ) @ V4x )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V5r: $i] : ( ap @ V5r @ V4x ) ) )
@ V3rows ) ) ) )
=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS @ A_27a @ A_27c ) @ V0v )
@ ( ap
@ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g )
@ ( lam @ A_27b
@ ^ [V6x: $i] :
( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V6x )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V7r: $i] : ( ap @ V7r @ V6x ) ) )
@ V3rows ) ) ) ) )
@ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V8r: $i] : ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V8r ) ) )
@ V3rows ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__FLATTEN__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ A_27a )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27b @ A_27a ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27b @ bool ) )
=> ! [V3rows1: $i] :
( ( mem @ V3rows1 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V4rows2: $i] :
( ( mem @ V4rows2 @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) )
=> ! [V5rows: $i] :
( ( mem @ V5rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) ) )
=> ( ! [V6x: $i] :
( ( mem @ V6x @ A_27b )
=> ( p
@ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27b @ A_27c ) @ V6x )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V7r: $i] : ( ap @ V7r @ V6x ) ) )
@ V5rows ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v )
@ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V3rows1 )
@ ( ap
@ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g )
@ ( lam @ A_27b
@ ^ [V8x: $i] :
( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27b ) @ V8x )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V9r: $i] : ( ap @ V9r @ V8x ) ) )
@ V5rows ) ) ) ) )
@ V4rows2 ) ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27c @ A_27a ) @ V0v )
@ ( ap
@ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ V3rows1 )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ( lam @ ( arr @ A_27b @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
@ ^ [V10r: $i] : ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27c @ A_27b @ A_27a ) @ V1p ) @ V2g ) @ V10r ) ) )
@ V5rows ) ) )
@ V4rows2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ A_27b ) )
=> ( ! [V1x1: $i] :
( ( mem @ V1x1 @ A_27a )
=> ! [V2x2: $i] :
( ( mem @ V2x2 @ A_27a )
=> ( ( ( ap @ V0p @ V1x1 )
= ( ap @ V0p @ V2x2 ) )
=> ( V1x1 = V2x2 ) ) ) )
=> ! [V3g: $i] :
( ( mem @ V3g @ ( arr @ A_27a @ bool ) )
=> ! [V4p_27: $i] :
( ( mem @ V4p_27 @ ( arr @ A_27c @ A_27a ) )
=> ! [V5g_27: $i] :
( ( mem @ V5g_27 @ ( arr @ A_27a @ ( arr @ A_27c @ bool ) ) )
=> ! [V6r_27: $i] :
( ( mem @ V6r_27 @ ( arr @ A_27a @ ( arr @ A_27c @ A_27d ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27d @ A_27a @ A_27b ) @ V0p ) @ V3g )
@ ( lam @ A_27a
@ ^ [V7x: $i] : ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27a ) @ V4p_27 ) @ ( ap @ V5g_27 @ V7x ) ) @ ( ap @ V6r_27 @ V7x ) ) ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27b )
@ ( lam @ A_27c
@ ^ [V8x: $i] : ( ap @ V0p @ ( ap @ V4p_27 @ V8x ) ) ) )
@ ( lam @ A_27c
@ ^ [V9x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V3g @ ( ap @ V4p_27 @ V9x ) ) ) @ ( ap @ ( ap @ V5g_27 @ ( ap @ V4p_27 @ V9x ) ) @ V9x ) ) ) )
@ ( lam @ A_27c
@ ^ [V10x: $i] : ( ap @ ( ap @ V6r_27 @ ( ap @ V4p_27 @ V10x ) ) @ V10x ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ__def,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V1r ) @ V2rows ) )
<=> ( ~ ( ( ( ap @ V1r @ V0i )
!= ( c_2Eoption_2ENONE @ A_27b ) ) )
| ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEXISTS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) )
@ ^ [V3row: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ V3row @ V0i ) ) @ ( c_2Eoption_2ENONE @ A_27b ) ) ) ) )
@ V2rows ) )
& ( ( ap @ ( c_2Eoption_2ETHE @ A_27b ) @ ( ap @ V1r @ V0i ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27a ) @ V0i ) @ V2rows ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ__FIRST__ROW,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2r_27: $i] :
( ( mem @ V2r_27 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V3rows: $i] :
( ( mem @ V3rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ( ( ( ap @ V2r_27 @ V0i )
!= ( c_2Eoption_2ENONE @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V1r ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V2r_27 ) @ V3rows ) ) )
<=> ( ( ( ap @ V1r @ V0i )
!= ( c_2Eoption_2ENONE @ A_27b ) )
=> ( ( ap @ V1r @ V0i )
= ( ap @ V2r_27 @ V0i ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ__NIL,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V1r ) @ ( c_2Elist_2ENIL @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) )
<=> ( ( ( ap @ V1r @ V0i )
!= ( c_2Eoption_2ENONE @ A_27b ) )
=> $false ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ__NOT__FIRST__ROW,axiom,
! [A_27a: del,A_27b: del,V0i: $i] :
( ( mem @ V0i @ A_27a )
=> ! [V1r_27: $i] :
( ( mem @ V1r_27 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V1r_27 ) @ V2rows ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V3r ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ V1r_27 ) @ V2rows ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27a @ A_27b ) @ V0i ) @ V3r ) @ V2rows ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__PRED__UNROLL__NIL,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ A_27b ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27c )
=> ( ( ap @ V0P @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27c ) @ V1v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) )
= ( ap @ V0P @ ( c_2Ebool_2EARB @ A_27a ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__PRED__UNROLL__CONS,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2r: $i] :
( ( mem @ V2r @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ! [V3rows: $i] :
( ( mem @ V3rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V2r ) @ V3rows ) ) ) )
<=> ( ( ( ( ap @ V2r @ V1v )
!= ( c_2Eoption_2ENONE @ A_27a ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ V2r @ V1v ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27b @ A_27a ) @ V1v ) @ V2r ) @ V3rows ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ V3rows ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__EXPAND__PRED__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2rows__before: $i] :
( ( mem @ V2rows__before @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ V0P ) @ V1v ) @ V2rows__before ) @ ( c_2Elist_2ENIL @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) )
<=> ( ~ ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27b @ A_27a ) @ V1v ) @ ( ap @ ( c_2Elist_2EREVERSE @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V2rows__before ) ) )
=> ( p @ ( ap @ V0P @ ( c_2Ebool_2EARB @ A_27a ) ) ) ) ) ) ) )
& ! [V3P: $i] :
( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
=> ! [V4v: $i] :
( ( mem @ V4v @ A_27b )
=> ! [V5rows__before: $i] :
( ( mem @ V5rows__before @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ! [V7rows__after: $i] :
( ( mem @ V7rows__after @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ V3P ) @ V4v ) @ V5rows__before ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V6r ) @ V7rows__after ) ) )
<=> ( ( ( ( ap @ V6r @ V4v )
!= ( c_2Eoption_2ENONE @ A_27a ) )
=> ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
@ ( lam @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ^ [V8r_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V8r_27 @ V4v ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V8r_27 @ V4v ) ) @ ( ap @ V6r @ V4v ) ) ) ) )
@ V5rows__before ) )
=> ( p @ ( ap @ V3P @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ V6r @ V4v ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ V3P ) @ V4v ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V6r ) @ V5rows__before ) ) @ V7rows__after ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXPAND__PRED__THM__GEN,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2rows__before: $i] :
( ( mem @ V2rows__before @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ! [V3rows__after: $i] :
( ( mem @ V3rows__after @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ V0P ) @ V1v ) @ V2rows__before ) @ V3rows__after ) )
<=> ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
@ ( lam @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ^ [V4r: $i] : ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__COND__NOT__EX__OR__EQ @ A_27b @ A_27a ) @ V1v ) @ V4r ) @ V3rows__after ) ) )
@ V2rows__before ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ V3rows__after ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__EXPAND__PRED__THM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27b ) @ V1v ) @ V2rows ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__EXPAND__PRED @ A_27a @ A_27b ) @ V0P ) @ V1v ) @ ( c_2Elist_2ENIL @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) @ V2rows ) ) ) ) ) ) ).
thf(ax_thm_2EpatternMatches_2EPMATCH__ROW__LIFT__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
=> ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__LIFT @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1r )
= ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27c @ A_27b ) @ V0f ) @ ( ap @ V1r @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__LIFT__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27c )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27c @ A_27a ) @ V1v ) @ V2rows ) )
=> ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27a @ A_27c ) @ V1v ) @ V2rows ) )
= ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH @ A_27b @ A_27c ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__LIFT @ A_27c @ A_27b @ A_27a ) @ V0f ) ) @ V2rows ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__ROW__LIFT__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27c @ A_27d ) )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27c @ bool ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( arr @ A_27c @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__LIFT @ A_27d @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27c @ A_27d ) @ V1p ) @ V2g ) @ V3r ) )
= ( ap @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW @ A_27b @ A_27c @ A_27d ) @ V1p ) @ V2g )
@ ( lam @ A_27c
@ ^ [V4x: $i] : ( ap @ V0f @ ( ap @ V3r @ V4x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__LIFT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27c )
=> ! [V2rows: $i] :
( ( mem @ V2rows @ ( ty_2Elist_2Elist @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27c @ A_27a ) @ V1v ) @ V2rows ) )
=> ( p @ ( ap @ ( ap @ ( c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ A_27c @ A_27b ) @ V1v ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) @ ( ap @ ( c_2EpatternMatches_2EPMATCH__ROW__LIFT @ A_27c @ A_27b @ A_27a ) @ V0f ) ) @ V2rows ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------