ITP001 Axioms: ITP103_7.ax
%------------------------------------------------------------------------------
% File : ITP103_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : tc.ax [Gau19]
% : HL4103_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 177 ( 58 unt; 87 typ; 0 def)
% Number of atoms : 148 ( 82 equ)
% Maximal formula atoms : 10 ( 0 avg)
% Number of connectives : 63 ( 5 ~; 8 |; 18 &)
% ( 19 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 88 ( 45 >; 43 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 85 ( 85 usr; 6 con; 0-5 aty)
% Number of variables : 370 ( 271 !; 5 ?; 370 :)
% ( 94 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Efinite__map_2Efmap,type,
tyop_2Efinite__map_2Efmap: ( $tType * $tType ) > $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EEMPTY__REL_2E0,type,
c_2Erelation_2EEMPTY__REL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Efinite__map_2EFAPPLY_2E0,type,
c_2Efinite__map_2EFAPPLY_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Efinite__map_2EFAPPLY_2E2,type,
c_2Efinite__map_2EFAPPLY_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Efinite__map_2EFDOM_2E0,type,
c_2Efinite__map_2EFDOM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2EFDOM_2E1,type,
c_2Efinite__map_2EFDOM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Etc_2EFMAP__TO__RELN_2E0,type,
c_2Etc_2EFMAP__TO__RELN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Etc_2EFMAP__TO__RELN_2E1,type,
c_2Etc_2EFMAP__TO__RELN_2E1:
!>[A_27a: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2EFMAP__TO__RELN_2E2,type,
c_2Etc_2EFMAP__TO__RELN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Efinite__map_2EFUN__FMAP_2E0,type,
c_2Efinite__map_2EFUN__FMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2EFUN__FMAP_2E2,type,
c_2Efinite__map_2EFUN__FMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Erelation_2EO_2E0,type,
c_2Erelation_2EO_2E0:
!>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2EO_2E2,type,
c_2Erelation_2EO_2E2:
!>[A_27g: $tType,A_27h: $tType,A_27k: $tType] : ( ( tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERDOM_2E0,type,
c_2Erelation_2ERDOM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERDOM_2E1,type,
c_2Erelation_2ERDOM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Etc_2ERELN__TO__FMAP_2E0,type,
c_2Etc_2ERELN__TO__FMAP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Etc_2ERELN__TO__FMAP_2E1,type,
c_2Etc_2ERELN__TO__FMAP_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERTC_2E0,type,
c_2Erelation_2ERTC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERTC_2E1,type,
c_2Erelation_2ERTC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ERTC_2E3,type,
c_2Erelation_2ERTC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERUNION_2E0,type,
c_2Erelation_2ERUNION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2ERUNION_2E2,type,
c_2Erelation_2ERUNION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Erelation_2ETC_2E0,type,
c_2Erelation_2ETC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ETC_2E1,type,
c_2Erelation_2ETC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2ETC__ITER_2E0,type,
c_2Etc_2ETC__ITER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2ETC__ITER_2E2,type,
c_2Etc_2ETC__ITER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) > tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2ETC__MOD_2E0,type,
c_2Etc_2ETC__MOD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2ETC__MOD_2E2,type,
c_2Etc_2ETC__MOD_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2ETC__MOD_2E3,type,
c_2Etc_2ETC__MOD_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Etc_2E_5E_7C_2E0,type,
c_2Etc_2E_5E_7C_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2E_5E_7C_2E2,type,
c_2Etc_2E_5E_7C_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2E_5E_7C_2E3,type,
c_2Etc_2E_5E_7C_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Etc_2E_5E_7C_2E4,type,
c_2Etc_2E_5E_7C_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etc_2E_5E_7C_5E_2E0,type,
c_2Etc_2E_5E_7C_5E_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2E_5E_7C_5E_2E2,type,
c_2Etc_2E_5E_7C_5E_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Efinite__map_2Eo__f_2E0,type,
c_2Efinite__map_2Eo__f_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))) ).
tff(c_2Efinite__map_2Eo__f_2E2,type,
c_2Efinite__map_2Eo__f_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) ).
tff(c_2Etc_2EsubTC_2E0,type,
c_2Etc_2EsubTC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2EsubTC_2E2,type,
c_2Etc_2EsubTC_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2EsubTC_2E3,type,
c_2Etc_2EsubTC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Etc_2EsubTC_2E4,type,
c_2Etc_2EsubTC_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Etc_2E_7C_5E_2E0,type,
c_2Etc_2E_7C_5E_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Etc_2E_7C_5E_2E2,type,
c_2Etc_2E_7C_5E_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Etc_2E_7C_5E_2E4,type,
c_2Etc_2E_7C_5E_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFAPPLY_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etc_2EFMAP__TO__RELN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Etc_2EFMAP__TO__RELN_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2EFMAP__TO__RELN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Etc_2EFMAP__TO__RELN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Etc_2EFMAP__TO__RELN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Efinite__map_2EFUN__FMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EO_2E0(A_27a,A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERDOM_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Etc_2ERELN__TO__FMAP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2ERELN__TO__FMAP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Etc_2ERELN__TO__FMAP_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERTC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ERTC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERUNION_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERUNION_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2ETC__ITER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2ETC__ITER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2ETC__ITER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2ETC__MOD_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2ETC__MOD_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2ETC__MOD_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Etc_2ETC__MOD_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2ETC__MOD_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2ETC__MOD_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Etc_2E_5E_7C_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2E_5E_7C_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_5E_7C_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Etc_2E_5E_7C_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a] : ( c_2Etc_2E_5E_7C_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_5E_7C_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Etc_2E_5E_7C_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Etc_2E_5E_7C_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_5E_7C_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2E_5E_7C_5E_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2E_5E_7C_5E_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_5E_7C_5E_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Efinite__map_2Eo__f_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2EsubTC_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2EsubTC_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2EsubTC_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Etc_2EsubTC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a] : ( c_2Etc_2EsubTC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2EsubTC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Etc_2EsubTC_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Etc_2EsubTC_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2EsubTC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Etc_2E_7C_5E_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2E_7C_5E_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_7C_5E_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Etc_2E_7C_5E_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Etc_2E_7C_5E_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etc_2E_7C_5E_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Etc_2EDRESTR,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a,V3b_2E0: A_27a] :
( p(c_2Etc_2E_5E_7C_2E4(A_27a,V0R_2E0,V1s_2E0,V2a_2E0,V3b_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2a_2E0),V3b_2E0)) ) ) ).
tff(thm_2Etc_2ERRESTR,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a,V3b_2E0: A_27a] :
( p(c_2Etc_2E_7C_5E_2E4(A_27a,V0R_2E0,V1s_2E0,V2a_2E0,V3b_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2a_2E0),V3b_2E0)) ) ) ).
tff(thm_2Etc_2EBRESTR,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0) = c_2Etc_2E_7C_5E_2E2(A_27a,c_2Etc_2E_5E_7C_2E2(A_27a,V0R_2E0,V1s_2E0),V1s_2E0) ) ).
tff(thm_2Etc_2EsubTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(c_2Etc_2EsubTC_2E4(A_27a,V0R_2E0,V1s_2E0,V2x_2E0,V3y_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
| ? [V4a_2E0: A_27a,V5b_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0),V4a_2E0,V5b_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4a_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5b_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V4a_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5b_2E0),V3y_2E0)) ) ) ) ).
tff(thm_2Etc_2EFMAP__TO__RELN,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] : ( c_2Etc_2EFMAP__TO__RELN_2E2(A_27a,V0f_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V1x_2E0),c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ).
tff(thm_2Etc_2ERELN__TO__FMAP,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2ERELN__TO__FMAP_2E1(A_27a,V0R_2E0) = c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)) ) ).
tff(thm_2Etc_2ETC__MOD,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1rx_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ra_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2ETC__MOD_2E3(A_27a,V0x_2E0,V1rx_2E0,V2ra_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2ra_2E0),c_2Epred__set_2EUNION_2E2(A_27a,V2ra_2E0,V1rx_2E0),V2ra_2E0) ) ).
tff(thm_2Etc_2ETC__ITER,axiom,
! [A_27a: $tType] :
( ! [V0r_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2ETC__ITER_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0r_2E0) = V0r_2E0 )
& ! [V1x_2E0: A_27a,V2d_2E0: tyop_2Elist_2Elist(A_27a),V3r_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2ETC__ITER_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2d_2E0),V3r_2E0) = c_2Etc_2ETC__ITER_2E2(A_27a,V2d_2E0,c_2Efinite__map_2Eo__f_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etc_2ETC__MOD_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3r_2E0,V1x_2E0)),V3r_2E0)) ) ) ).
tff(thm_2Etc_2EDRESTR__IN,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] : ( c_2Etc_2E_5E_7C_2E3(A_27a,V0R_2E0,V1s_2E0,V2a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2a_2E0),c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ).
tff(thm_2Etc_2EDRESTR__EMPTY,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2E_5E_7C_2E2(A_27a,V0R_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Erelation_2EEMPTY__REL_2E0(A_27a) ) ).
tff(thm_2Etc_2EDRESTR__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2E_5E_7C_2E2(A_27a,V0R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)) = V0R_2E0 ) ).
tff(thm_2Etc_2EREMPTY__RRESTR,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2E_7C_5E_2E2(A_27a,c_2Erelation_2EEMPTY__REL_2E0(A_27a),V0s_2E0) = c_2Erelation_2EEMPTY__REL_2E0(A_27a) ) ).
tff(thm_2Etc_2EO__REMPTY__O,axiom,
! [A_27a: $tType] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,V0R_2E0,c_2Erelation_2EEMPTY__REL_2E0(A_27a)) = c_2Erelation_2EEMPTY__REL_2E0(A_27a) )
& ! [V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,c_2Erelation_2EEMPTY__REL_2E0(A_27a),V1R_2E0) = c_2Erelation_2EEMPTY__REL_2E0(A_27a) ) ) ).
tff(thm_2Etc_2EsubTC__thm,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V1s_2E0) = c_2Erelation_2ERUNION_2E2(A_27a,A_27a,V0R_2E0,c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,V0R_2E0,c_2Erelation_2EO_2E2(A_27a,A_27a,A_27a,c_2Etc_2E_5E_7C_2E2(A_27a,c_2Erelation_2ERTC_2E1(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0)),V1s_2E0),V0R_2E0))) ) ).
tff(thm_2Etc_2EsubTC__EMPTY,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = V0R_2E0 ) ).
tff(thm_2Etc_2ERTC__INSERT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a,V3w_2E0: A_27a,V4z_2E0: A_27a] :
( p(c_2Erelation_2ERTC_2E3(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2a_2E0,V1s_2E0)),V3w_2E0,V4z_2E0))
<=> ( p(c_2Erelation_2ERTC_2E3(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0),V3w_2E0,V4z_2E0))
| ( ( ( V2a_2E0 = V3w_2E0 )
| ? [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0),V3w_2E0,V5x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V2a_2E0)) ) )
& ( ( V2a_2E0 = V4z_2E0 )
| ? [V6y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2a_2E0),V6y_2E0))
& p(c_2Erelation_2ERTC_2E3(A_27a,c_2Etc_2E_5E_7C_5E_2E2(A_27a,V0R_2E0,V1s_2E0),V6y_2E0,V4z_2E0)) ) ) ) ) ) ).
tff(thm_2Etc_2EsubTC__INSERT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2q_2E0: A_27a,V3x_2E0: A_27a,V4y_2E0: A_27a] :
( p(c_2Etc_2EsubTC_2E4(A_27a,V0R_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2q_2E0,V1s_2E0),V3x_2E0,V4y_2E0))
<=> ( p(c_2Etc_2EsubTC_2E4(A_27a,V0R_2E0,V1s_2E0,V3x_2E0,V4y_2E0))
| ( p(c_2Etc_2EsubTC_2E4(A_27a,V0R_2E0,V1s_2E0,V3x_2E0,V2q_2E0))
& p(c_2Etc_2EsubTC_2E4(A_27a,V0R_2E0,V1s_2E0,V2q_2E0,V4y_2E0)) ) ) ) ).
tff(thm_2Etc_2EsubTC__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)) = c_2Erelation_2ETC_2E1(A_27a,V0R_2E0) ) ).
tff(thm_2Etc_2EsubTC__INSERT__COR,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3a_2E0: A_27a] : ( c_2Etc_2EsubTC_2E3(A_27a,V0R_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V1s_2E0),V3a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Etc_2EsubTC_2E3(A_27a,V0R_2E0,V1s_2E0,V3a_2E0)),c_2Epred__set_2EUNION_2E2(A_27a,c_2Etc_2EsubTC_2E3(A_27a,V0R_2E0,V1s_2E0,V3a_2E0),c_2Etc_2EsubTC_2E3(A_27a,V0R_2E0,V1s_2E0,V2x_2E0)),c_2Etc_2EsubTC_2E3(A_27a,V0R_2E0,V1s_2E0,V3a_2E0)) ) ).
tff(thm_2Etc_2ERDOM__SUBSET__FDOM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V0f_2E0)),c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))) ).
tff(thm_2Etc_2EFINITE__RDOM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V0f_2E0)))) ).
tff(thm_2Etc_2EFDOM__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)))
=> ( c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etc_2ERELN__TO__FMAP_2E1(A_27a,V0R_2E0)) = c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0) ) ) ).
tff(thm_2Etc_2ERELN__TO__FMAP__TO__RELN__ID,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)))
=> ( c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,c_2Etc_2ERELN__TO__FMAP_2E1(A_27a,V0R_2E0)) = V0R_2E0 ) ) ).
tff(thm_2Etc_2ERDOM__subTC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erelation_2ERDOM_2E1(A_27a,A_27a,c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V1s_2E0)) = c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0) ) ).
tff(thm_2Etc_2ENOT__IN__RDOM,axiom,
! [A_27a: $tType,V0Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] :
( ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0,V1x_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0Q_2E0))) ) ).
tff(thm_2Etc_2ETC__MOD__EMPTY__ID,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1ra_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Etc_2ETC__MOD_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(thm_2Etc_2EI__o__f,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27b,c_2Ecombin_2EI_2E0(A_27b),V0f_2E0) = V0f_2E0 ) ).
tff(thm_2Etc_2EsubTC__MAX__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)))
=> ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V1s_2E0)) = c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V1s_2E0) ) ) ).
tff(thm_2Etc_2EsubTC__SUPERSET__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0),V1s_2E0)) = c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)) ) ) ).
tff(thm_2Etc_2EsubTC__FDOM,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Etc_2EsubTC_2E2(A_27a,V1R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V1R_2E0)) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V0g_2E0) )
=> ( c_2Etc_2EsubTC_2E2(A_27a,V1R_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0)) = c_2Etc_2EsubTC_2E2(A_27a,V1R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V1R_2E0)) ) ) ).
tff(thm_2Etc_2ESUBSET__FDOM__LEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V1s_2E0) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V2f_2E0) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0))) ) ).
tff(thm_2Etc_2EsubTC__FDOM__RDOM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V1f_2E0) )
=> ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Erelation_2ERDOM_2E1(A_27a,A_27a,V0R_2E0)) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V1f_2E0) ) ) ).
tff(thm_2Etc_2ETC__MOD__LEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0)))
& ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V1s_2E0) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V3f_2E0) ) )
=> ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V1s_2E0)) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,c_2Efinite__map_2Eo__f_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etc_2ETC__MOD_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0,V2x_2E0)),V3f_2E0)) ) ) ).
tff(thm_2Etc_2ETC__ITER__THM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1d_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ( c_2Epred__set_2EUNION_2E2(A_27a,V3s_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1d_2E0)) = c_2Efinite__map_2EFDOM_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0) )
& ( c_2Etc_2EsubTC_2E2(A_27a,V0R_2E0,V3s_2E0) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,V2f_2E0) ) )
=> ( c_2Erelation_2ETC_2E1(A_27a,V0R_2E0) = c_2Etc_2EFMAP__TO__RELN_2E1(A_27a,c_2Etc_2ETC__ITER_2E2(A_27a,V1d_2E0,V2f_2E0)) ) ) ).
%------------------------------------------------------------------------------