ITP001 Axioms: ITP065_7.ax
%------------------------------------------------------------------------------
% File : ITP065_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 : finite_map.ax [Gau19]
% : HL4065_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 751 ( 337 unt; 219 typ; 0 def)
% Number of atoms : 974 ( 617 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 476 ( 34 ~; 13 |; 122 &)
% ( 88 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 190 ( 108 >; 82 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 215 ( 215 usr; 14 con; 0-7 aty)
% Number of variables : 2922 (2563 !; 28 ?;2922 :)
% ( 331 !>; 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(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( $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_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
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_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Ecombin_2EASSOC_2E0,type,
c_2Ecombin_2EASSOC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2EASSOC_2E1,type,
c_2Ecombin_2EASSOC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EBIJ_2E0,type,
c_2Epred__set_2EBIJ_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_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EBIJ_2E3,type,
c_2Epred__set_2EBIJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ecombin_2EC_2E0,type,
c_2Ecombin_2EC_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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ecombin_2EC_2E1,type,
c_2Ecombin_2EC_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)) ) ).
tff(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).
tff(c_2Ecombin_2ECOMM_2E0,type,
c_2Ecombin_2ECOMM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2ECOMM_2E1,type,
c_2Ecombin_2ECOMM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2ECOMPL_2E0,type,
c_2Epred__set_2ECOMPL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ECOMPL_2E1,type,
c_2Epred__set_2ECOMPL_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,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_2EDELETE_2E0,type,
c_2Epred__set_2EDELETE_2E0:
!>[A_27a: $tType] : 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_2Epred__set_2EDELETE_2E2,type,
c_2Epred__set_2EDELETE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_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_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_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_2Epred__set_2EDISJOINT_2E0,type,
c_2Epred__set_2EDISJOINT_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_2EDISJOINT_2E2,type,
c_2Epred__set_2EDISJOINT_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_2Efinite__map_2EDRESTRICT_2E0,type,
c_2Efinite__map_2EDRESTRICT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(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_2EDRESTRICT_2E2,type,
c_2Efinite__map_2EDRESTRICT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > 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_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(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_2E1,type,
c_2Efinite__map_2EFAPPLY_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( 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_2EFCARD_2E0,type,
c_2Efinite__map_2EFCARD_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum) ).
tff(c_2Efinite__map_2EFCARD_2E1,type,
c_2Efinite__map_2EFCARD_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Enum_2Enum ) ).
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_2Efinite__map_2EFDOM_2E2,type,
c_2Efinite__map_2EFDOM_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efinite__map_2EFEMPTY_2E0,type,
c_2Efinite__map_2EFEMPTY_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Efinite__map_2Efmap(A_27a,A_27b) ).
tff(c_2Efinite__map_2EFEVERY_2E0,type,
c_2Efinite__map_2EFEVERY_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2EFEVERY_2E2,type,
c_2Efinite__map_2EFEVERY_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > 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_2Efinite__map_2EFLOOKUP_2E0,type,
c_2Efinite__map_2EFLOOKUP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))) ).
tff(c_2Efinite__map_2EFLOOKUP_2E1,type,
c_2Efinite__map_2EFLOOKUP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)) ) ).
tff(c_2Efinite__map_2EFLOOKUP_2E2,type,
c_2Efinite__map_2EFLOOKUP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > tyop_2Eoption_2Eoption(A_27b) ) ).
tff(c_2Efinite__map_2EFMAP__MAP2_2E0,type,
c_2Efinite__map_2EFMAP__MAP2_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2EFMAP__MAP2_2E2,type,
c_2Efinite__map_2EFMAP__MAP2_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Efinite__map_2EFMERGE_2E0,type,
c_2Efinite__map_2EFMERGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a)))) ).
tff(c_2Efinite__map_2EFMERGE_2E1,type,
c_2Efinite__map_2EFMERGE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) > tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a))) ) ).
tff(c_2Efinite__map_2EFMERGE_2E3,type,
c_2Efinite__map_2EFMERGE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) * tyop_2Efinite__map_2Efmap(A_27b,A_27a) * tyop_2Efinite__map_2Efmap(A_27b,A_27a) ) > tyop_2Efinite__map_2Efmap(A_27b,A_27a) ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E1,type,
c_2Elist_2EFOLDL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) ).
tff(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Elist_2EFOLDL2_2E0,type,
c_2Elist_2EFOLDL2_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)))) ).
tff(c_2Elist_2EFOLDL2_2E4,type,
c_2Elist_2EFOLDL2_2E4:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))) * A_27a * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > A_27a ) ).
tff(c_2Elist_2EFOLDR_2E0,type,
c_2Elist_2EFOLDR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDR_2E3,type,
c_2Elist_2EFOLDR_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Efinite__map_2EFRANGE_2E0,type,
c_2Efinite__map_2EFRANGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2EFRANGE_2E1,type,
c_2Efinite__map_2EFRANGE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Efinite__map_2EFUNION_2E0,type,
c_2Efinite__map_2EFUNION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2EFUNION_2E2,type,
c_2Efinite__map_2EFUNION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
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_2Efinite__map_2EFUPDATE_2E0,type,
c_2Efinite__map_2EFUPDATE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2EFUPDATE_2E2,type,
c_2Efinite__map_2EFUPDATE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Efinite__map_2EFUPDATE__LIST_2E0,type,
c_2Efinite__map_2EFUPDATE__LIST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2EFUPDATE__LIST_2E2,type,
c_2Efinite__map_2EFUPDATE__LIST_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_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_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
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_2EINJ_2E0,type,
c_2Epred__set_2EINJ_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_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINJ_2E3,type,
c_2Epred__set_2EINJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Esum_2EINL_2E0,type,
c_2Esum_2EINL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINL_2E1,type,
c_2Esum_2EINL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
tff(c_2Esum_2EINR_2E0,type,
c_2Esum_2EINR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINR_2E1,type,
c_2Esum_2EINR_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
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_2Epred__set_2EINTER_2E0,type,
c_2Epred__set_2EINTER_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_2EINTER_2E2,type,
c_2Epred__set_2EINTER_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_2Esum_2EISL_2E0,type,
c_2Esum_2EISL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Esum_2EISL_2E1,type,
c_2Esum_2EISL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Esum_2Esum(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Epred__set_2ELINV_2E0,type,
c_2Epred__set_2ELINV_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_2Emin_2Efun(A_27b,A_27a))) ).
tff(c_2Epred__set_2ELINV_2E2,type,
c_2Epred__set_2ELINV_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Elist_2ELIST__REL_2E0,type,
c_2Elist_2ELIST__REL_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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Elist_2ELIST__REL_2E3,type,
c_2Elist_2ELIST__REL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > 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_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Elist_2EMAP2_2E0,type,
c_2Elist_2EMAP2_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Elist_2EMAP2_2E3,type,
c_2Elist_2EMAP2_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27c) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Efinite__map_2EMAP__KEYS_2E0,type,
c_2Efinite__map_2EMAP__KEYS_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))) ).
tff(c_2Efinite__map_2EMAP__KEYS_2E2,type,
c_2Efinite__map_2EMAP__KEYS_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) > tyop_2Efinite__map_2Efmap(A_27b,A_27c) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eoption_2EOPTION__BIND_2E0,type,
c_2Eoption_2EOPTION__BIND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Eoption_2EOPTION__BIND_2E2,type,
c_2Eoption_2EOPTION__BIND_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Eoption_2EOPTREL_2E0,type,
c_2Eoption_2EOPTREL_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_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Eoption_2EOPTREL_2E3,type,
c_2Eoption_2EOPTREL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Eoption_2Eoption(A_27a) * tyop_2Eoption_2Eoption(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Esum_2EOUTL_2E0,type,
c_2Esum_2EOUTL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27a) ).
tff(c_2Esum_2EOUTL_2E1,type,
c_2Esum_2EOUTL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Esum_2Esum(A_27a,A_27b) > A_27a ) ).
tff(c_2Esorting_2EPERM_2E0,type,
c_2Esorting_2EPERM_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Esorting_2EPERM_2E2,type,
c_2Esorting_2EPERM_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EREVERSE_2E0,type,
c_2Elist_2EREVERSE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EREVERSE_2E1,type,
c_2Elist_2EREVERSE_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Efinite__map_2ERRESTRICT_2E0,type,
c_2Efinite__map_2ERRESTRICT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2ERRESTRICT_2E2,type,
c_2Efinite__map_2ERRESTRICT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Elist_2ESNOC_2E0,type,
c_2Elist_2ESNOC_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_2ESNOC_2E2,type,
c_2Elist_2ESNOC_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Efinite__map_2ESUBMAP_2E0,type,
c_2Efinite__map_2ESUBMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2ESUBMAP_2E2,type,
c_2Efinite__map_2ESUBMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,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_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2ESUM__IMAGE_2E0,type,
c_2Epred__set_2ESUM__IMAGE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)) ).
tff(c_2Epred__set_2ESUM__IMAGE_2E2,type,
c_2Epred__set_2ESUM__IMAGE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_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_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
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_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Elist_2EZIP_2E0,type,
c_2Elist_2EZIP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Elist_2EZIP_2E1,type,
c_2Elist_2EZIP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).
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_2Efinite__map_2Ef__o_2E0,type,
c_2Efinite__map_2Ef__o_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))) ).
tff(c_2Efinite__map_2Ef__o_2E2,type,
c_2Efinite__map_2Ef__o_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27b,A_27c) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) ).
tff(c_2Efinite__map_2Ef__o__f_2E0,type,
c_2Efinite__map_2Ef__o__f_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(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_2Ef__o__f_2E2,type,
c_2Efinite__map_2Ef__o__f_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27b,A_27c) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) ).
tff(c_2Efinite__map_2Efdomsub_2E0,type,
c_2Efinite__map_2Efdomsub_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).
tff(c_2Efinite__map_2Efdomsub_2E2,type,
c_2Efinite__map_2Efdomsub_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Efinite__map_2Efmap__ABS_2E0,type,
c_2Efinite__map_2Efmap__ABS_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)) ).
tff(c_2Efinite__map_2Efmap__ABS_2E1,type,
c_2Efinite__map_2Efmap__ABS_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Efinite__map_2Efmap__EQ__UPTO_2E0,type,
c_2Efinite__map_2Efmap__EQ__UPTO_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Efinite__map_2Efmap__EQ__UPTO_2E3,type,
c_2Efinite__map_2Efmap__EQ__UPTO_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efinite__map_2Efmap__REP_2E0,type,
c_2Efinite__map_2Efmap__REP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))) ).
tff(c_2Efinite__map_2Efmap__REP_2E1,type,
c_2Efinite__map_2Efmap__REP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)) ) ).
tff(c_2Efinite__map_2Efmap__REP_2E2,type,
c_2Efinite__map_2Efmap__REP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone) ) ).
tff(c_2Efinite__map_2Efmap__inverse_2E0,type,
c_2Efinite__map_2Efmap__inverse_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2Efmap__inverse_2E2,type,
c_2Efinite__map_2Efmap__inverse_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efinite__map_2Efmap__rel_2E0,type,
c_2Efinite__map_2Efmap__rel_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Efinite__map_2Efmap__rel_2E3,type,
c_2Efinite__map_2Efmap__rel_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Efinite__map_2Efmap(A_27c,A_27a) * tyop_2Efinite__map_2Efmap(A_27c,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Efinite__map_2Efmap__size_2E0,type,
c_2Efinite__map_2Efmap__size_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum))) ).
tff(c_2Efinite__map_2Efmap__size_2E3,type,
c_2Efinite__map_2Efmap__size_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Enum_2Enum ) ).
tff(c_2Efinite__map_2Eis__fmap_2E0,type,
c_2Efinite__map_2Eis__fmap_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool) ).
tff(c_2Efinite__map_2Eis__fmap_2E1,type,
c_2Efinite__map_2Eis__fmap_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
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_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).
tff(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_2Eoption_2Esome_2E0,type,
c_2Eoption_2Esome_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2Esome_2E1,type,
c_2Eoption_2Esome_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(A_27a) ) ).
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_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2E_2C_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2E_2C_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27c,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2E_2C_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27c,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2E_2C_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d] : ( c_2Epair_2E_2C_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Epair_2E_2C_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27c,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27d: $tType,A_27e: $tType,X0_2E0: A_27d,X1_2E0: A_27e] : ( c_2Epair_2E_2C_2E2(A_27d,A_27e,X0_2E0,X1_2E0) = app_2E2(A_27e,tyop_2Epair_2Eprod(A_27d,A_27e),app_2E2(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27d,A_27e)),c_2Epair_2E_2C_2E0(A_27d,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2Etyop_2Elist_2Elist_28A_27e_29,axiom,
! [A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Elist_2Elist(A_27d),X1_2E0: tyop_2Elist_2Elist(A_27e)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)),app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)),X0_2E0),X1_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_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_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(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EAPPEND_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2EASSOC_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] : ( c_2Ecombin_2EASSOC_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2EC_2E1(A_27b,A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ecombin_2EC_2E0(A_27b,A_27b,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2ECOMM_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(A_27b,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] : ( c_2Ecombin_2ECOMM_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Ebool_2ECOND_2E0(tyop_2Efinite__map_2Efmap(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X2_2E0: tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)] : ( c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),c_2Ebool_2ECOND_2E0(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,X0_2E0,X1_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)),c_2Epred__set_2EDELETE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_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_2EDIFF_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_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_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_2EDISJOINT_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_2EDISJOINT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EDRESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2EDRESTRICT_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2EDRESTRICT_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2EDRESTRICT_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2EEL_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFAPPLY_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFAPPLY_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Efinite__map_2EFAPPLY_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Efinite__map_2EFAPPLY_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27c,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),c_2Efinite__map_2EFAPPLY_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a),c_2Efinite__map_2EFAPPLY_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: A_27b] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27c,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27c),c_2Efinite__map_2EFAPPLY_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: A_27c] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a),c_2Efinite__map_2EFAPPLY_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b),c_2Efinite__map_2EFAPPLY_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFCARD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFDOM_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2EFDOM_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Efinite__map_2EFDOM_2E1(A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] : ( c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFEVERY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Efinite__map_2EFEVERY_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFEVERY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Efinite__map_2EFEVERY_2E0(A_27a,A_27c),X0_2E0),X1_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_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efinite__map_2EFLOOKUP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efinite__map_2EFLOOKUP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Efinite__map_2EFLOOKUP_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Efinite__map_2EFLOOKUP_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Efinite__map_2EFLOOKUP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: A_27b] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Efinite__map_2EFLOOKUP_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: A_27c] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),c_2Efinite__map_2EFLOOKUP_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),c_2Efinite__map_2EFLOOKUP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFMAP__MAP2_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFMAP__MAP2_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a))),c_2Efinite__map_2EFMERGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFMERGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Efinite__map_2EFMERGE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFMERGE_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFMERGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] : ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b))),c_2Efinite__map_2EFMERGE_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] : ( c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27c_2CA_27d_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d)))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL2_2E4(tyop_2Efinite__map_2Efmap(A_27c,A_27d),A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d))),app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d)))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d)))),c_2Elist_2EFOLDL2_2E0(tyop_2Efinite__map_2Efmap(A_27c,A_27d),A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27d_2CA_27e_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Elist_2EFOLDL2_2E4(tyop_2Efinite__map_2Efmap(A_27d,A_27e),A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27d,A_27e))),app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),c_2Elist_2EFOLDL2_2E0(tyop_2Efinite__map_2Efmap(A_27d,A_27e),A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b))] : ( c_2Elist_2EFOLDR_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Elist_2EFOLDR_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDR_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Elist_2EFOLDR_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EFST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,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_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUNION_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2EFUNION_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFUNION_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2EFUNION_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Efinite__map_2EFUNION_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27a)),c_2Efinite__map_2EFUNION_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2EFUNION_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] : ( c_2Efinite__map_2EFUNION_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),c_2Efinite__map_2EFUNION_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(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)),c_2Efinite__map_2EFUN__FMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2EFUN__FMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2EFUN__FMAP_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2EFUN__FMAP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27c)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2EFUPDATE_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2EFUPDATE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: tyop_2Epair_2Eprod(A_27b,A_27c)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2EFUPDATE_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: tyop_2Epair_2Eprod(A_27c,A_27a)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27a)),c_2Efinite__map_2EFUPDATE_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: tyop_2Epair_2Eprod(A_27c,A_27b)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2EFUPDATE_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0: tyop_2Epair_2Eprod(A_27c,A_27d)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),c_2Efinite__map_2EFUPDATE_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e),X1_2E0: tyop_2Epair_2Eprod(A_27d,A_27e)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27d,A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),c_2Efinite__map_2EFUPDATE_2E0(A_27d,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Efinite__map_2Efmap(A_27c,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Efinite__map_2Efmap(A_27c,A_27a)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27d,A_27e))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27d,A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27d,A_27e)),tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27d,A_27e)),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27d,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27c_20mono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27c,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27c,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27b),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_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,X0_2E0) = app_2E2(A_27b,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E0(A_27b,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E0(A_27b,tyop_2Eone_2Eone),X0_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(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_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_2EINTER_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_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)] : ( c_2Esum_2EISL_2E1(A_27b,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Ebool,c_2Esum_2EISL_2E0(A_27b,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b] : ( c_2Ecombin_2EK_2E1(A_27b,A_27c,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2EK_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27c_29_2Ctyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)))] : ( c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ELINV_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Epred__set_2ELINV_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ELINV_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2ELINV_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_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(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Elist_2EMAP_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27b),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),A_27c),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27b),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP2_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP2_2E3(A_27d,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP2_2E0(A_27d,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Elist_2EMAP2_2E3(A_27d,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP2_2E0(A_27d,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27e_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Elist_2EMAP2_2E3(A_27e,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27e),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27e)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(A_27e))),c_2Elist_2EMAP2_2E0(A_27e,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2EMAP__KEYS_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a)),c_2Efinite__map_2EMAP__KEYS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))] : ( c_2Eoption_2EOPTION__BIND_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__BIND_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Eoption_2EOPTREL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)] : ( c_2Esum_2EOUTL_2E1(A_27b,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),A_27b,c_2Esum_2EOUTL_2E0(A_27b,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Esorting_2EPERM_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Esorting_2EPERM_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2ERRESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2ERRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2ERRESTRICT_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2ERRESTRICT_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ESND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( c_2Epair_2ESND_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ESNOC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2ESUBMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Efinite__map_2ESUBMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2ESUBMAP_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] : ( c_2Efinite__map_2ESUBMAP_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Ebool),c_2Efinite__map_2ESUBMAP_2E0(A_27c,A_27d),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(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d),c_2Epair_2EUNCURRY_2E0(A_27b,A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27e,axiom,
! [A_27b: $tType,A_27c: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27e,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e),c_2Epair_2EUNCURRY_2E0(A_27b,A_27c,A_27e),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Efinite__map_2Efmap_28A_27d_2CA_27e_29,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),c_2Epair_2EUNCURRY_2E0(A_27b,A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)),X0_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_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))] : ( c_2Elist_2EZIP_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e))] : ( c_2Elist_2EZIP_2E1(A_27d,A_27e,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27d,A_27e)),c_2Elist_2EZIP_2E0(A_27d,A_27e),X0_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_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Efinite__map_2Ef__o_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2Ef__o_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Efinite__map_2Ef__o_2E2(A_27c,A_27a,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),c_2Efinite__map_2Ef__o_2E0(A_27c,A_27a,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2Ef__o_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27d)),c_2Efinite__map_2Ef__o_2E0(A_27a,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Efinite__map_2Ef__o_2E2(A_27c,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Efinite__map_2Efmap(A_27c,A_27d)),c_2Efinite__map_2Ef__o_2E0(A_27c,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Efinite__map_2Ef__o__f_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2Ef__o__f_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2Ef__o__f_2E2(A_27b,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2Ef__o__f_2E0(A_27b,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2Ef__o__f_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2Efdomsub_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0: A_27a] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2Efdomsub_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2Efdomsub_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0: A_27b] : ( c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2Efdomsub_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0: A_27c] : ( c_2Efinite__map_2Efdomsub_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Efinite__map_2Efmap(A_27c,A_27a),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27c,A_27a)),c_2Efinite__map_2Efdomsub_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Efinite__map_2Efdomsub_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2Efdomsub_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2Efmap__ABS_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] : ( c_2Efinite__map_2Efmap__ABS_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efmap__ABS_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2Efmap__EQ__UPTO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Efinite__map_2Efmap__EQ__UPTO_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2Efmap__REP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efmap__REP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efinite__map_2Efmap__REP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efmap__REP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2Efmap__REP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efinite__map_2Efmap__REP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Efmap__inverse_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2Efmap__inverse_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Efinite__map_2Efmap__inverse_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2Efmap__rel_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),X2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Efinite__map_2Efmap__rel_2E0(A_27a,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2Efmap__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),X2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] : ( c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool)),c_2Efinite__map_2Efmap__rel_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Efinite__map_2Efmap__size_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efmap__size_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum)),c_2Efinite__map_2Efmap__size_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Efinite__map_2Eis__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] : ( c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),c_2Ecombin_2Eo_2E0(A_27d,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Efinite__map_2Eo__f_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Efinite__map_2Efmap(A_27c,A_27b)),c_2Efinite__map_2Eo__f_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2Eo__f_2E2(A_27b,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),c_2Efinite__map_2Eo__f_2E0(A_27b,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(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)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Efinite__map_2Eo__f_2E2(A_27b,A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27a)),c_2Efinite__map_2Eo__f_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27d)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27d)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27d,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27c_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27c),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27c,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27c,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eoption_2Esome_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E0(A_27a),X0_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_2Efinite__map_2Efmap__inverse__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( p(c_2Efinite__map_2Efmap__inverse_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0))
<=> ! [V2k_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0m1_2E0)))
=> ? [V3v_2E0: A_27b] :
( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0m1_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3v_2E0) )
& ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V1m2_2E0,V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2k_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2EFMAP__MAP2__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),V1m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V1m_2E0),V2x_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V2x_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,V1m_2E0,V2x_2E0))) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),V1m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1m_2E0) = c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V1m_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1m_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27a,A_27b) = c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E0(A_27a,A_27b)) ) ).
tff(thm_2Efinite__map_2ESUBMAP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2EFCARD__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V0fm_2E0) = c_2Epred__set_2ECARD_2E1(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0)) ) ).
tff(thm_2Efinite__map_2EFDOM__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Efinite__map_2EFDOM_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Esum_2EISL_2E1(A_27b,tyop_2Eone_2Eone,c_2Efinite__map_2Efmap__REP_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0)) ) ).
tff(thm_2Efinite__map_2EFAPPLY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Esum_2EOUTL_2E1(A_27b,tyop_2Eone_2Eone,c_2Efinite__map_2Efmap__REP_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0)) ) ).
tff(thm_2Efinite__map_2EFEMPTY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( ! [V0a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),F0_2E0,V0a_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
=> ( c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) = c_2Efinite__map_2Efmap__ABS_2E1(A_27a,A_27b,F0_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))))] :
( ! [V3a_2E0: A_27a,V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3a_2E0),V1x_2E0))
<=> ( V3a_2E0 = V1x_2E0 ) )
=> ( ! [V1x_2E0: A_27a,V2y_2E0: A_27b,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F0_2E0,V1x_2E0),V2y_2E0),V0f_2E0),V3a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3a_2E0),V1x_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V2y_2E0),c_2Efinite__map_2Efmap__REP_2E2(A_27a,A_27b,V0f_2E0,V3a_2E0)) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) = c_2Efinite__map_2Efmap__ABS_2E1(A_27a,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F0_2E0,V1x_2E0),V2y_2E0),V0f_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__ISO__DEF,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efmap__ABS_2E1(A_27a,A_27b,c_2Efinite__map_2Efmap__REP_2E1(A_27a,A_27b,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V1r_2E0))
<=> ( c_2Efinite__map_2Efmap__REP_2E1(A_27a,A_27b,c_2Efinite__map_2Efmap__ABS_2E1(A_27a,A_27b,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Efinite__map_2Efmap__TY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Eis__fmap_2E0(A_27a,A_27b),V0rep_2E0)) ).
tff(thm_2Efinite__map_2Eis__fmap__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V7x_2E0: A_27a,V5a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V7x_2E0),V5a_2E0))
<=> ( V7x_2E0 = V5a_2E0 ) )
=> ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V0x_2E0))
<=> ! [V1is__fmap_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)] :
( ! [V2a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( ( ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V2a0_2E0,V3x_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
| ? [V4f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V5a_2E0: A_27a,V6b_2E0: A_27b] :
( ! [V7x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V2a0_2E0,V7x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V7x_2E0),V5a_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V6b_2E0),app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V4f_2E0,V7x_2E0)) )
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V1is__fmap_27_2E0,V4f_2E0)) ) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V1is__fmap_27_2E0,V2a0_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V1is__fmap_27_2E0,V0x_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),V1r_2E0) )
& ! [V2x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0),V2x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),V1r_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V2x_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUNION__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)) )
& ! [V2x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0),V2x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Efinite__map_2Efmap__domsub,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0fm_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1k_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ) ).
tff(thm_2Efinite__map_2Ef__o__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V0f_2E0))) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0) = c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V1g_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFUN__FMAP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1P_2E0))
=> ( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0)) = V1P_2E0 )
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1P_2E0))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0),V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2ERRESTRICT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
( ! [V2x_2E0: A_27a,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V2x_2E0),V0f_2E0),V1r_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27b,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),V1r_2E0)) ) )
=> ( ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1r_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V2x_2E0),V0f_2E0),V1r_2E0)) )
=> ( ! [V3x_2E0: A_27a,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3x_2E0),V0f_2E0),V1r_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27b,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V1r_2E0)) ) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0)) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1r_2E0)) )
& ! [V3x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V3x_2E0),V0f_2E0),V1r_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V3x_2E0)) ) ) ) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0,V0f_2E0),V1y_2E0))
<=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = V1y_2E0 ) ) )
=> ( ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0f_2E0),V1y_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V1y_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0,V0f_2E0),V1y_2E0)) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0f_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2Eo__f__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0)) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) )
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2Ef__o__f__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,c_2Ebool_2EIN_2E2(A_27b,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V0f_2E0))) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0))) )
& ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0),V3x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V3x_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2EFEVERY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,V1f_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f_2E0)))
=> p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)),c_2Eoption_2ESOME_2E1(A_27b,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0)),c_2Eoption_2ENONE_2E0(A_27b)) ) ).
tff(thm_2Efinite__map_2EFMERGE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool))] :
( ! [V3x_2E0: A_27b,V1f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( p(app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1f_2E0))
<=> ~ p(c_2Ebool_2EIN_2E2(A_27b,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,V1f_2E0))) )
=> ! [V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,V0m_2E0,V1f_2E0,V2g_2E0)) = c_2Epred__set_2EUNION_2E2(A_27b,c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,V1f_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,V2g_2E0)) )
& ! [V3x_2E0: A_27b] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,V0m_2E0,V1f_2E0,V2g_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1f_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,V2g_2E0,V3x_2E0),c_2Ebool_2ECOND_2E3(A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V2g_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,V1f_2E0,V3x_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0m_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,V1f_2E0,V3x_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,V2g_2E0,V3x_2E0)))) ) ) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1fm_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0)) )
& ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1fm_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0)) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,V1fm_2E0,V2x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] :
( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V0R_2E0,V1f1_2E0,V2f2_2E0))
<=> ( ( c_2Efinite__map_2EFDOM_2E1(A_27c,A_27b,V2f2_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27c,A_27a,V1f1_2E0) )
& ! [V3x_2E0: A_27c] :
( p(c_2Ebool_2EIN_2E2(A_27c,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27c,A_27a,V1f1_2E0)))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27c,A_27a,V1f1_2E0,V3x_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27c,A_27b,V2f2_2E0,V3x_2E0))) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2vs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2vs_2E0))
<=> ( ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,V2vs_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,V2vs_2E0)) )
& ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,V2vs_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f1_2E0,V3x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f2_2E0,V3x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__size__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))))] :
( ! [V0kz_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1vz_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0,V0kz_2E0),V1vz_2E0),V2fm_2E0),V3k_2E0) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0kz_2E0,V3k_2E0),app_2E2(A_27b,tyop_2Enum_2Enum,V1vz_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2fm_2E0,V3k_2E0))) )
=> ! [V0kz_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1vz_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efmap__size_2E3(A_27a,A_27b,V0kz_2E0,V1vz_2E0,V2fm_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0,V0kz_2E0),V1vz_2E0),V2fm_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2fm_2E0)) ) ) ).
tff(thm_2Efinite__map_2Efevery__funion,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1m1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2m2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,V1m1_2E0))
& p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,V2m2_2E0)) )
=> p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1m1_2E0,V2m2_2E0))) ) ).
tff(thm_2Efinite__map_2Edrestrict__iter__list,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] :
( ! [V2k_2E0: A_27a,V3m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),F0_2E0,V2k_2E0),V3m_2E0) = c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V3m_2E0,V2k_2E0) )
=> ! [V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),F0_2E0,V0m_2E0,V1l_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0m_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Efinite__map_2Edisjoint__drestrict,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1m_2E0)))
=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1m_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0)) = V1m_2E0 ) ) ).
tff(thm_2Efinite__map_2Efmap__to__list,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
? [V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1l_2E0)))
& ( V0m_2E0 = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1l_2E0) ) ) ).
tff(thm_2Efinite__map_2Efupdate__list__foldl,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] :
( ! [V2env_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3k_2E0: A_27a,V4v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),F1_2E0,V2env_2E0),V3k_2E0),V4v_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2env_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)) )
=> ( ! [V2env_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),F0_2E0,V2env_2E0) = c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),F1_2E0,V2env_2E0)) )
=> ! [V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),F0_2E0,V0m_2E0,V1l_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0m_2E0,V1l_2E0) ) ) ) ).
tff(thm_2Efinite__map_2Efupdate__list__foldr,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))))] :
( ! [V2k_2E0: A_27a,V3v_2E0: A_27b,V4env_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),F0_2E0,V2k_2E0),V3v_2E0),V4env_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V4env_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v_2E0)) )
=> ! [V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EFOLDR_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),F0_2E0),V0m_2E0,V1l_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0m_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__EQ__FUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1kv_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,V1kv_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0fm_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1kv_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) ).
tff(thm_2Efinite__map_2Eflookup__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2v_2E0: A_27b] :
( ( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0))) )
& ( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V2v_2E0) )
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = V2v_2E0 ) ) ) ) ).
tff(thm_2Efinite__map_2Efdom__fupdate__list2,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0kvl_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1fm_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))) ) ).
tff(thm_2Efinite__map_2Efupdate__list__map,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c))))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V4a_2E0: A_27a,V5b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c))),F0_2E0,V1f_2E0),V4a_2E0),V5b_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27c,V4a_2E0,app_2E2(A_27b,A_27c,V1f_2E0,V5b_2E0)) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2x_2E0: A_27a,V3y_2E0: A_27d] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0l_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27c,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27c))),F0_2E0,V1f_2E0)),V0l_2E0)),V2x_2E0) = app_2E2(A_27b,A_27c,V1f_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0l_2E0),V2x_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__sym,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V1x_2E0)) )
=> ! [V3x_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V4y_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V0R_2E0,V3x_2E0,V4y_2E0))
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V0R_2E0,V4y_2E0,V3x_2E0)) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__trans,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0),V3z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V3z_2E0)) )
=> ! [V4x_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V5y_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V6z_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V0R_2E0,V4x_2E0,V5y_2E0))
& p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V0R_2E0,V5y_2E0,V6z_2E0)) )
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V0R_2E0,V4x_2E0,V6z_2E0)) ) ) ).
tff(thm_2Efinite__map_2Ef__o__f__FUPDATE__compose,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2k_2E0: A_27c,V3x_2E0: A_27a,V4v_2E0: A_27b] :
( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0)))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27c,A_27a,V1f2_2E0))) )
=> ( c_2Efinite__map_2Ef__o__f_2E2(A_27c,A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V4v_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27a,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27a,V2k_2E0,V3x_2E0))) = c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27b,c_2Efinite__map_2Ef__o__f_2E2(A_27c,A_27a,A_27b,V0f1_2E0,V1f2_2E0),c_2Epair_2E_2C_2E2(A_27c,A_27b,V2k_2E0,V4v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V2s_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V2s_2E0) )
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3t_2E0,V2s_2E0)) )
=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V3t_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V3t_2E0) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FDOM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)) = V0f_2E0 ) ).
tff(thm_2Efinite__map_2EFRANGE__DRESTRICT__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EDRESTRICT_2E2(A_27b,A_27a,V1fm_2E0,V0s_2E0)),c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0))) ).
tff(thm_2Efinite__map_2EIN__FRANGE__DOMSUB__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27b,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3v_2E0)) )
=> ! [V4v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,V1fm_2E0,V0k_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__DOMSUB__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27b,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,V1fm_2E0,V0k_2E0)),c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0))) ).
tff(thm_2Efinite__map_2EIN__FRANGE__FUNION__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1f1_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3v_2E0)) )
& ! [V4v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V0f2_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) )
=> ! [V5v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFUNION_2E2(A_27b,A_27a,V1f1_2E0,V0f2_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V5v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUNION__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFUNION_2E2(A_27b,A_27a,V1f1_2E0,V0f2_2E0)),c_2Epred__set_2EUNION_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1f1_2E0),c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V0f2_2E0)))) ).
tff(thm_2Efinite__map_2EIN__FRANGE__FUPDATE__LIST__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3v_2E0)) )
& ! [V4v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4v_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),V0ls_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) )
=> ! [V5v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,V1fm_2E0,V0ls_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V5v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUPDATE__LIST__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0ls_2E0)),c_2Epred__set_2EUNION_2E2(A_27b,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V1fm_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V0ls_2E0))))) ).
tff(thm_2Efinite__map_2EIN__FRANGE__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1v_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V1v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0f_2E0)))
<=> ? [V2k_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0f_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V1v_2E0) ) ) ).
tff(thm_2Efinite__map_2EIN__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1v_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V1v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0f_2E0)))
<=> ? [V2k_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2k_2E0) = V1v_2E0 ) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0ls_2E0)))
=> ! [V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_2E0)) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0ls_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__APPLY__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2k_2E0: A_27b,V3v_2E0: A_27a,V4fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27b,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27a),V1ls_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V2k_2E0,V3v_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V1ls_2E0)))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3v_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,V4fm_2E0,V1ls_2E0),V2k_2E0))) ) ).
tff(thm_2Efinite__map_2EFUPDATE__SAME__LIST__APPLY,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm1_2E0,V0kvl_2E0),V3x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm2_2E0,V0kvl_2E0),V3x_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__SAME__APPLY,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1kv_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V2fm2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3fm1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( ( V0x_2E0 = c_2Epair_2EFST_2E1(A_27a,A_27b,V1kv_2E0) )
| ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V3fm1_2E0,V0x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2fm2_2E0,V0x_2E0) ) )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V3fm1_2E0,V1kv_2E0),V0x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2fm2_2E0,V1kv_2E0),V0x_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__HO__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V3k_2E0: A_27b] :
( ( ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V2kvl_2E0)))
& ( V3k_2E0 = c_2Elist_2EEL_2E2(A_27b,V4n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27a),V2kvl_2E0)) )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EEL_2E2(A_27a,V4n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),V2kvl_2E0))))
& ! [V5m_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V5m_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V5m_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V2kvl_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27b,V5m_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27a),V2kvl_2E0)) != V3k_2E0 ) ) )
| ( ~ p(c_2Ebool_2EIN_2E2(A_27b,V3k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27b,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27a),V2kvl_2E0))))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,V1f_2E0,V3k_2E0))) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27a,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,V1f_2E0,V2kvl_2E0),V3k_2E0))) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM__matchable,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v_2E0: A_27b] :
( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))))
& ( V3v_2E0 = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f_2E0,V2k_2E0) ) )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f_2E0,V0kvl_2E0),V2k_2E0) = V3v_2E0 ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FUNION__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s2_2E0,V1s1_2E0))
=> ? [V4h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V3f_2E0,V1s1_2E0),V2g_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V3f_2E0,V0s2_2E0),V4h_2E0) ) ) ).
tff(thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST__paired,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e))),F3_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d)))] :
( ! [V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),V10b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e)),F2_2E0,V1f2_2E0),V10b_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27e,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e)),V1f2_2E0,V10b_2E0)) )
=> ( ! [V5fm_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e),V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),V6b_2E0: A_27a,V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),V7c_2E0: A_27b,V8d_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))))),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)))))),F3_2E0,V5fm_2E0),V0f1_2E0),V6b_2E0),V1f2_2E0),V7c_2E0),V8d_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27d,A_27e,V5fm_2E0,c_2Epair_2E_2C_2E2(A_27d,A_27e,app_2E2(A_27c,A_27d,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d)),V0f1_2E0,V6b_2E0),V7c_2E0),V8d_2E0),app_2E2(A_27c,A_27e,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e)),V1f2_2E0,V6b_2E0),V7c_2E0),V8d_2E0))) )
=> ( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),V5fm_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e),V6b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e))))),F0_2E0,V0f1_2E0),V1f2_2E0),V5fm_2E0),V6b_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e))))),app_2E2(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Efinite__map_2Efmap(A_27d,A_27e)))))),F3_2E0,V5fm_2E0),V0f1_2E0),V6b_2E0),V1f2_2E0)) )
=> ( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),V9b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d)),F1_2E0,V0f1_2E0),V9b_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27d,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d)),V0f1_2E0,V9b_2E0)) )
=> ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),V2bs_2E0: tyop_2Elist_2Elist(A_27a),V3cs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),V4a_2E0: tyop_2Efinite__map_2Efmap(A_27d,A_27e)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,V2bs_2E0) = c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27c),V3cs_2E0) )
=> ( c_2Elist_2EFOLDL2_2E4(tyop_2Efinite__map_2Efmap(A_27d,A_27e),A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27d,A_27e))))),F0_2E0,V0f1_2E0),V1f2_2E0),V4a_2E0,V2bs_2E0,V3cs_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27d,A_27e,V4a_2E0,c_2Elist_2EZIP_2E1(A_27d,A_27e,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e),c_2Elist_2EMAP2_2E3(A_27d,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27d)),F1_2E0,V0f1_2E0),V2bs_2E0,V3cs_2E0),c_2Elist_2EMAP2_2E3(A_27e,A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27e)),F2_2E0,V1f2_2E0),V2bs_2E0,V3cs_2E0)))) ) ) ) ) ) ) ).
tff(thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d))))))] :
( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V5fm_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),V6b_2E0: A_27a,V7c_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d)),app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d))))),F0_2E0,V0f1_2E0),V1f2_2E0),V5fm_2E0),V6b_2E0),V7c_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27d,V5fm_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27d,app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f1_2E0,V6b_2E0),V7c_2E0),app_2E2(A_27b,A_27d,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27d),V1f2_2E0,V6b_2E0),V7c_2E0))) )
=> ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V2bs_2E0: tyop_2Elist_2Elist(A_27a),V3cs_2E0: tyop_2Elist_2Elist(A_27b),V4a_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,V2bs_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V3cs_2E0) )
=> ( c_2Elist_2EFOLDL2_2E4(tyop_2Efinite__map_2Efmap(A_27c,A_27d),A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27c,A_27d))))),F0_2E0,V0f1_2E0),V1f2_2E0),V4a_2E0,V2bs_2E0,V3cs_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27d,V4a_2E0,c_2Elist_2EZIP_2E1(A_27c,A_27d,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP2_2E3(A_27c,A_27a,A_27b,V0f1_2E0,V2bs_2E0,V3cs_2E0),c_2Elist_2EMAP2_2E3(A_27d,A_27a,A_27b,V1f2_2E0,V2bs_2E0,V3cs_2E0)))) ) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT__SAME,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2f1_2E0,V0s_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V0s_2E0) )
<=> ( ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f1_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)) )
& ! [V3x_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f1_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0)) )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f1_2E0,V3x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f2_2E0,V3x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FUNION__SAME,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0fm_2E0,V1s_2E0),V0fm_2E0) = V0fm_2E0 ) ).
tff(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP__gen,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V2s_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V2s_2E0)))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3t_2E0,V2s_2E0)) )
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V3t_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V3t_2E0))) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2k_2E0: A_27a] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V2k_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V2k_2E0)) ) ).
tff(thm_2Efinite__map_2EDOMSUB__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0))) )
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0))) ) ).
tff(thm_2Efinite__map_2ESUBMAP__DOMSUB__gen,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a] : ( c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0f_2E0,V2k_2E0),V1g_2E0) = c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0f_2E0,V2k_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1g_2E0,V2k_2E0)) ) ).
tff(thm_2Efinite__map_2ESUBMAP__mono__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)))
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1g_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)))) ) ).
tff(thm_2Efinite__map_2EIMAGE__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27c,A_27a,V1fm_2E0)) = c_2Efinite__map_2EFRANGE_2E1(A_27c,A_27b,c_2Efinite__map_2Eo__f_2E2(A_27c,A_27a,A_27b,V0f_2E0,V1fm_2E0)) ) ).
tff(thm_2Efinite__map_2EDRESTRICTED__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0),V2s_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V2s_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V2s_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0)))) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s1_2E0,V0s2_2E0))
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2f_2E0,V1s1_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2f_2E0,V0s2_2E0))) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__SUBMAP__gen,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V1f_2E0,V0g_2E0))
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f_2E0,V2P_2E0),V0g_2E0)) ) ).
tff(thm_2Efinite__map_2EIN__FRANGE__o__f__suff,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2P_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V0fm_2E0)))
=> p(app_2E2(A_27c,tyop_2Emin_2Ebool,V2P_2E0,app_2E2(A_27a,A_27c,V1f_2E0,V3v_2E0))) )
=> ! [V4v_2E0: A_27c] :
( p(c_2Ebool_2EIN_2E2(A_27c,V4v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27b,A_27a,A_27c,V1f_2E0,V0fm_2E0))))
=> p(app_2E2(A_27c,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EIN__FRANGE__FUPDATE__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0kv_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3v_2E0)) )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,c_2Epair_2ESND_2E1(A_27b,A_27a,V0kv_2E0))) )
=> ! [V4v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27a,V1fm_2E0,V0kv_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUPDATE__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0kv_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27a,V1fm_2E0,V0kv_2E0)),c_2Epred__set_2EUNION_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,c_2Epair_2ESND_2E1(A_27b,A_27a,V0kv_2E0),c_2Epred__set_2EEMPTY_2E0(A_27a))))) ).
tff(thm_2Efinite__map_2EIN__FRANGE__DRESTRICT__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1fm_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3v_2E0)) )
=> ! [V4v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EDRESTRICT_2E2(A_27b,A_27a,V1fm_2E0,V0s_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUNION__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1g_2E0,V2h_2E0)) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0),V2h_2E0) ) ).
tff(thm_2Efinite__map_2EFUNION__COMM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)))
=> ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1g_2E0,V0f_2E0) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V2f_2E0,V1g_2E0),V0k_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V2f_2E0,V0k_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1g_2E0,V0k_2E0)) ) ).
tff(thm_2Efinite__map_2EFUNION__EQ__IMPL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f3_2E0)))
& ( V1f2_2E0 = V2f3_2E0 ) )
=> ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V2f3_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUNION__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f3_2E0))) )
=> ( ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V2f3_2E0) )
<=> ( V1f2_2E0 = V2f3_2E0 ) ) ) ).
tff(thm_2Efinite__map_2EFEMPTY__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0h_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)))
<=> ( V0h_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUNION__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0)))
& ! [V2f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),V3f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27c,c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,V2f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,V3f2_2E0)))
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27c,A_27d,V3f2_2E0,c_2Efinite__map_2EFUNION_2E2(A_27c,A_27d,V2f1_2E0,V3f2_2E0))) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0))
| ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,V2f3_2E0)) ) )
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1f2_2E0,V2f3_2E0))) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUNION__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
=> ( c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1f2_2E0,V2f3_2E0)) = c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f1_2E0,V2f3_2E0) ) )
& ! [V3f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),V4f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),V5f3_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27c,c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,V3f1_2E0),c_2Epred__set_2EDIFF_2E2(A_27c,c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,V5f3_2E0),c_2Efinite__map_2EFDOM_2E1(A_27c,A_27d,V4f2_2E0))))
=> ( c_2Efinite__map_2ESUBMAP_2E2(A_27c,A_27d,V3f1_2E0,c_2Efinite__map_2EFUNION_2E2(A_27c,A_27d,V4f2_2E0,V5f3_2E0)) = c_2Efinite__map_2ESUBMAP_2E2(A_27c,A_27d,V3f1_2E0,V4f2_2E0) ) ) ) ).
tff(thm_2Efinite__map_2EFUNION__EQ__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0h1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1h2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0h1_2E0,V1h2_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
<=> ( ( V0h1_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
& ( V1h2_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ) ).
tff(thm_2Efinite__map_2EFEVERY__DRESTRICT__COMPL,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2k_2E0: A_27a,V3f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V4P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V4P_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V3f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V0v_2E0)),c_2Epred__set_2ECOMPL_2E1(A_27a,V1s_2E0))))
<=> ( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,V1s_2E0))
=> p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V0v_2E0))) )
& p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V4P_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V3f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2k_2E0,V1s_2E0))))) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__ELIM,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1v_2E0: A_27b,V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V0k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f_2E0,V0k_2E0) = V1v_2E0 ) )
=> ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V0k_2E0,V1v_2E0)) = V2f_2E0 ) ) ).
tff(thm_2Efinite__map_2EFEVERY__STRENGTHEN__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V3P_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)))
& ( ( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V3P_2E0,V2f_2E0))
& p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V3P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0))) )
=> p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V3P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFMAP__MAP2__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27a,V1v_2E0: A_27c,V2m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V3f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] : ( c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V3f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27c,V2m_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V0x_2E0,V1v_2E0))) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V3f_2E0,V2m_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,V3f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V0x_2E0,V1v_2E0)))) ) ).
tff(thm_2Efinite__map_2EFMAP__MAP2__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] : ( c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2EFMAP__MAP2__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V1f_2E0,V0m_2E0)) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V0m_2E0) )
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V0m_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFMAP__MAP2_2E2(A_27a,A_27b,A_27c,V1f_2E0,V0m_2E0),V2x_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V2x_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,V0m_2E0,V2x_2E0))) ) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__PURGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__DISJ__ELIM,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a,V2v_2E0: A_27b,V3ck_2E0: A_27a,V4cv_2E0: A_27b] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3ck_2E0,V4cv_2E0)) )
<=> ( ( V1k_2E0 = V3ck_2E0 )
& ( V2v_2E0 = V4cv_2E0 )
& ( ( V0fm_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
| ? [V5v_27_2E0: A_27b] : ( V0fm_2E0 = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V5v_27_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__ELIM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),V1k_2E0: A_27a,V2v_2E0: A_27b,V3ck_2E0: A_27a,V4cv_2E0: A_27b,V5nv_2E0: A_27b] :
( ? [V6fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V6fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3ck_2E0,V4cv_2E0)) )
& p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V6fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V5nv_2E0)))) )
<=> ( ( V1k_2E0 = V3ck_2E0 )
& ( V2v_2E0 = V4cv_2E0 )
& p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3ck_2E0,V5nv_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFMEQ__ENUMERATE__CASES,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,V2p_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1kvl_2E0) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1kvl_2E0))) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__SAME__KEYS__UNWIND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2kvl1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3kvl2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0f1_2E0,V2kvl1_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f2_2E0,V3kvl2_2E0) )
& ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V2kvl1_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V3kvl2_2E0) )
& p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V2kvl1_2E0))) )
=> ( ( V2kvl1_2E0 = V3kvl2_2E0 )
& ! [V4kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V4kvl_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V2kvl1_2E0) )
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0f1_2E0,V4kvl_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f2_2E0,V4kvl_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__SAME__UPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f1_2E0,V0kvl_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2f2_2E0,V0kvl_2E0) )
<=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f1_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)))) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2f2_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFDOM__FUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0kvl_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1fm_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))) ) ).
tff(thm_2Efinite__map_2EFUPD11__SAME__UPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v_2E0: A_27b] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v_2E0)) )
<=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2k_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2k_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ) ) ).
tff(thm_2Efinite__map_2EFUPD__SAME__KEY__UNWIND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v1_2E0: A_27b,V4v2_2E0: A_27b] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v1_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V4v2_2E0)) )
=> ( ( V3v1_2E0 = V4v2_2E0 )
& ! [V5v_2E0: A_27b] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V5v_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V5v_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EFUPD11__SAME__BASE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2v1_2E0: A_27b,V3k2_2E0: A_27a,V4v2_2E0: A_27b] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V2v1_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k2_2E0,V4v2_2E0)) )
<=> ( ( ( V1k1_2E0 = V3k2_2E0 )
& ( V2v1_2E0 = V4v2_2E0 ) )
| ( ( V1k1_2E0 != V3k2_2E0 )
& p(c_2Ebool_2EIN_2E2(A_27a,V1k1_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V3k2_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
& ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V2v1_2E0)) = V0f_2E0 )
& ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k2_2E0,V4v2_2E0)) = V0f_2E0 ) ) ) ) ).
tff(thm_2Efinite__map_2ESAME__KEY__UPDATES__DIFFER,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v1_2E0: A_27b,V4v2_2E0: A_27b] :
( ( V3v1_2E0 != V4v2_2E0 )
=> ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v1_2E0)) != c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V4v2_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUPD11__SAME__NEW__KEY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v1_2E0: A_27b,V4v2_2E0: A_27b] :
( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0)))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0))) )
=> ( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v1_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V4v2_2E0)) )
<=> ( ( V0f1_2E0 = V1f2_2E0 )
& ( V3v1_2E0 = V4v2_2E0 ) ) ) ) ).
tff(thm_2Efinite__map_2EFUPD11__SAME__KEY__AND__BASE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a,V2v1_2E0: A_27b,V3v2_2E0: A_27b] :
( ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v1_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V3v2_2E0)) )
<=> ( V2v1_2E0 = V3v2_2E0 ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0,V0xs_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V0xs_2E0),V1x_2E0) ) ).
tff(thm_2Efinite__map_2EFOLDL__FUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))))] :
( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V4fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V5k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c)))),F0_2E0,V0f1_2E0),V1f2_2E0),V4fm_2E0),V5k_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27c,V4fm_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27c,app_2E2(A_27a,A_27b,V0f1_2E0,V5k_2E0),app_2E2(A_27a,A_27c,V1f2_2E0,V5k_2E0))) )
=> ( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V6k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),F1_2E0,V0f1_2E0),V1f2_2E0),V6k_2E0) = c_2Epair_2E_2C_2E2(A_27b,A_27c,app_2E2(A_27a,A_27b,V0f1_2E0,V6k_2E0),app_2E2(A_27a,A_27c,V1f2_2E0,V6k_2E0)) )
=> ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2ls_2E0: tyop_2Elist_2Elist(A_27a),V3a_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27b,A_27c)))),F0_2E0,V0f1_2E0),V1f2_2E0),V3a_2E0,V2ls_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27c,V3a_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),F1_2E0,V0f1_2E0),V1f2_2E0),V2ls_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a,V3v_2E0: A_27b,V4n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0kvl_2E0)))
& ( V2k_2E0 = c_2Elist_2EEL_2E2(A_27a,V4n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)) )
& ( V3v_2E0 = c_2Elist_2EEL_2E2(A_27b,V4n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V0kvl_2E0)) )
& ! [V5m_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V5m_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V5m_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0kvl_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27a,V5m_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)) != V2k_2E0 ) ) )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f_2E0,V0kvl_2E0),V2k_2E0) = V3v_2E0 ) ) ).
tff(thm_2Efinite__map_2EFEVERY__FUPDATE__LIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)))
=> ( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V2P_2E0,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0kvl_2E0)))
<=> ( p(c_2Elist_2EEVERY_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2P_2E0,V0kvl_2E0))
& p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V2P_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1fm_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0)))))) ) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2k_2E0: A_27a,V3fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1kvl_2E0))))
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V3fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V0v_2E0)),V1kvl_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V3fm_2E0,V1kvl_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2k_2E0: A_27a,V3fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1kvl_2E0))))
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V3fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V0v_2E0)),V1kvl_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V3fm_2E0,V1kvl_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V0v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1kvl1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1kvl1_2E0,V0kvl2_2E0)) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V1kvl1_2E0),V0kvl2_2E0) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0kvl_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2k_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0kvl_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1f_2E0,V0kvl_2E0),V2k_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f_2E0,V2k_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = V0f_2E0 )
& ! [V1h_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V2t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1h_2E0,V2t_2E0)) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,V1h_2E0),V2t_2E0) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1g_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) = V3y_2E0 )
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0))) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V1g_2E0,V2h_2E0)) )
=> p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V2h_2E0)) ) ).
tff(thm_2Efinite__map_2ESUBMAP__ANTISYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V1g_2E0,V0f_2E0)) )
<=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__REFL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V0f_2E0)) ).
tff(thm_2Efinite__map_2ESUBMAP__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0f_2E0)) ).
tff(thm_2Efinite__map_2Efmap__EXT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( V0f_2E0 = V1g_2E0 )
<=> ( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) )
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) ) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) )
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) ) ) )
<=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Efinite__map_2Efmap__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) )
& ( c_2Efinite__map_2EFAPPLY_2E1(A_27a,A_27b,V0f_2E0) = c_2Efinite__map_2EFAPPLY_2E1(A_27a,A_27b,V1g_2E0) ) )
<=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Efinite__map_2ENOT__FDOM__FAPPLY__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1x_2E0) ) ) ).
tff(thm_2Efinite__map_2EFM__PULL__APART,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0)))
=> ? [V2fm0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3v_2E0: A_27b] :
( ( V0fm_2E0 = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2fm0_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V3v_2E0)) )
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V1k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2fm0_2E0))) ) ) ).
tff(thm_2Efinite__map_2Efmap__INDUCT,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)))
& ! [V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V1f_2E0))
=> ! [V2x_2E0: A_27a,V3y_2E0: A_27b] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f_2E0)))
=> p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)))) ) ) )
=> ! [V4f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V4f_2E0)) ) ).
tff(thm_2Efinite__map_2EFCARD__SUC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1n_2E0: tyop_2Enum_2Enum] :
( ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V0f_2E0) = c_2Enum_2ESUC_2E1(V1n_2E0) )
<=> ? [V2f_27_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3x_2E0: A_27a,V4y_2E0: A_27b] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f_27_2E0)))
& ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V2f_27_2E0) = V1n_2E0 )
& ( V0f_2E0 = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2f_27_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V4y_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EFCARD__0__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V0f_2E0) = c_2Enum_2E0_2E0 )
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ).
tff(thm_2Efinite__map_2EFCARD__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b] : ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V1a_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0)),c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V0fm_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,V0fm_2E0))) ) ).
tff(thm_2Efinite__map_2EFCARD__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Efinite__map_2EFCARD_2E1(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Efinite__map_2EFDOM__FINITE,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0))) ).
tff(thm_2Efinite__map_2EFDOM__F__FEMPTY1,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ! [V1a_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(A_27a,V1a_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ).
tff(thm_2Efinite__map_2EFDOM__EQ__EMPTY__SYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Epred__set_2EEMPTY_2E0(A_27a) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) )
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ).
tff(thm_2Efinite__map_2EFDOM__EQ__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ).
tff(thm_2Efinite__map_2Efmap__SIMPLE__INDUCT,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)))
& ! [V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V1f_2E0))
=> ! [V2x_2E0: A_27a,V3y_2E0: A_27b] : p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)))) ) )
=> ! [V4f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V4f_2E0)) ) ).
tff(thm_2Efinite__map_2EFDOM__EQ__FDOM__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ! [V2y_2E0: A_27b] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0))) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0) ) ) ).
tff(thm_2Efinite__map_2ENOT__EQ__FEMPTY__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b] : ( c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) != c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)) ) ).
tff(thm_2Efinite__map_2EFAPPLY__FUPDATE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V3x_2E0: A_27a,V1a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1a_2E0))
<=> ( V3x_2E0 = V1a_2E0 ) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)),V3x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1a_2E0),V2b_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFDOM__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0))) = c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)) ) ).
tff(thm_2Efinite__map_2EFDOM__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Efinite__map_2EFUPDATE__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27b] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V3c_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V3c_2E0)) ) ).
tff(thm_2Efinite__map_2EFUPDATE__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27a,V4d_2E0: A_27b] :
( ( V1a_2E0 != V3c_2E0 )
=> ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3c_2E0,V4d_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3c_2E0,V4d_2E0)),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)) ) ) ).
tff(thm_2Efinite__map_2ENOT__EQ__FAPPLY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1a_2E0: A_27a,V2x_2E0: A_27a,V3y_2E0: A_27b] :
( ( V1a_2E0 != V2x_2E0 )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1a_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0f_2E0,V1a_2E0) ) ) ).
tff(thm_2Efinite__map_2EFAPPLY__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)),V1x_2E0) = V2y_2E0 ) ).
tff(thm_2Efinite__map_2Eis__fmap__cases,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V5x_2E0: A_27a,V3a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V5x_2E0),V3a_2E0))
<=> ( V5x_2E0 = V3a_2E0 ) )
=> ! [V0a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V0a0_2E0))
<=> ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V0a0_2E0,V1x_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
| ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V3a_2E0: A_27a,V4b_2E0: A_27b] :
( ! [V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V0a0_2E0,V5x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V5x_2E0),V3a_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V4b_2E0),app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V2f_2E0,V5x_2E0)) )
& p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V2f_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2Eis__fmap__strongind,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))))] :
( ! [V1a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),F0_2E0,V1a_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
=> ( ! [V5x_2E0: A_27a,V3a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V5x_2E0),V3a_2E0))
<=> ( V5x_2E0 = V3a_2E0 ) )
=> ( ! [V3a_2E0: A_27a,V4b_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V3a_2E0),V4b_2E0),V2f_2E0),V5x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V5x_2E0),V3a_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V4b_2E0),app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V2f_2E0,V5x_2E0)) )
=> ! [V0is__fmap_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,F0_2E0))
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V3a_2E0: A_27a,V4b_2E0: A_27b] :
( ( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V2f_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,V2f_2E0)) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V3a_2E0),V4b_2E0),V2f_2E0))) ) )
=> ! [V6a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V6a0_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,V6a0_2E0)) ) ) ) ) ) ).
tff(thm_2Efinite__map_2Eis__fmap__ind,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))))] :
( ! [V1a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),F0_2E0,V1a_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
=> ( ! [V5x_2E0: A_27a,V3a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V5x_2E0),V3a_2E0))
<=> ( V5x_2E0 = V3a_2E0 ) )
=> ( ! [V3a_2E0: A_27a,V4b_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V3a_2E0),V4b_2E0),V2f_2E0),V5x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V5x_2E0),V3a_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V4b_2E0),app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V2f_2E0,V5x_2E0)) )
=> ! [V0is__fmap_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,F0_2E0))
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V3a_2E0: A_27a,V4b_2E0: A_27b] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,V2f_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V3a_2E0),V4b_2E0),V2f_2E0))) ) )
=> ! [V6a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V6a0_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool,V0is__fmap_27_2E0,V6a0_2E0)) ) ) ) ) ) ).
tff(thm_2Efinite__map_2Eis__fmap__rules,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))))] :
( ! [V0a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),F0_2E0,V0a_2E0) = c_2Esum_2EINR_2E1(A_27b,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
=> ( ! [V4x_2E0: A_27a,V2a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V4x_2E0),V2a_2E0))
<=> ( V4x_2E0 = V2a_2E0 ) )
=> ( ! [V2a_2E0: A_27a,V3b_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V2a_2E0),V3b_2E0),V1f_2E0),V4x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V4x_2E0),V2a_2E0),c_2Esum_2EINL_2E1(A_27b,tyop_2Eone_2Eone,V3b_2E0),app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),V1f_2E0,V4x_2E0)) )
=> ( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,F0_2E0))
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2a_2E0: A_27a,V3b_2E0: A_27b] :
( p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,V1f_2E0))
=> p(c_2Efinite__map_2Eis__fmap_2E1(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),F1_2E0,V2a_2E0),V3b_2E0),V1f_2E0))) ) ) ) ) ) ).
tff(thm_2Efinite__map_2EFUNION__FEMPTY__1,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0g_2E0) = V0g_2E0 ) ).
tff(thm_2Efinite__map_2EFUNION__FEMPTY__2,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = V0f_2E0 ) ).
tff(thm_2Efinite__map_2EFUNION__FUPDATE__1,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1g_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)) ) ).
tff(thm_2Efinite__map_2EFUNION__FUPDATE__2,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1g_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)),c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0))) ) ).
tff(thm_2Efinite__map_2EEQ__FDOM__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( V1f_2E0 = V0g_2E0 )
<=> ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V1f_2E0,V0g_2E0))
& ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0g_2E0) ) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUPDATE__EQN,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V2f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0))))
<=> ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f_2E0)))
| ( ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f_2E0,V1x_2E0) = V0y_2E0 )
& p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f_2E0))) ) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0r_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1r_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1r_2E0),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0)) ) ).
tff(thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1r_2E0))
=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1r_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1r_2E0,V2x_2E0)),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFDOM__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27c] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),V1r_2E0) ) ).
tff(thm_2Efinite__map_2ENOT__FDOM__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0)))
=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) = V0f_2E0 ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0),V0f_2E0)) ).
tff(thm_2Efinite__map_2EDRESTRICT__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0),V2Q_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1P_2E0,V2Q_2E0)) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__IS__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2EFUPDATE__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) ) ).
tff(thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1r_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1r_2E0),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))),V1r_2E0)),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))),V1r_2E0))) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V0f_2E0 ) ).
tff(thm_2Efinite__map_2ESUBMAP__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0),V0f_2E0)) ).
tff(thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V2s1_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V3s2_2E0) )
<=> ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f1_2E0,V2s1_2E0),V1f2_2E0))
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f2_2E0,V3s2_2E0),V0f1_2E0))
& ( c_2Epred__set_2EINTER_2E2(A_27a,V2s1_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,V3s2_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EFDOM__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27c] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)) ) ).
tff(thm_2Efinite__map_2EFMERGE__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1m1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2m2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V3k_2E0: A_27b] : ( c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,V0m_2E0,V1m1_2E0,V2m2_2E0),V3k_2E0) = c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,V0m_2E0,c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,V1m1_2E0,V3k_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27a,V2m2_2E0,V3k_2E0)) ) ).
tff(thm_2Efinite__map_2ESUBMAP__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1f_2E0,V0k_2E0),V1f_2E0)) ).
tff(thm_2Efinite__map_2Efmap__CASES,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
| ? [V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( V0f_2E0 = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1g_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__NOT__IN__DOM,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1fm_2E0)))
=> ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1fm_2E0,V0k_2E0) = V1fm_2E0 ) ) ).
tff(thm_2Efinite__map_2Eo__f__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: A_27c,V1k_2E0: A_27a,V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V3f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V3f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27c,V2fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V1k_2E0,V0v_2E0))) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V3f_2E0,V2fm_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,app_2E2(A_27c,A_27b,V3f_2E0,V0v_2E0))) ) ).
tff(thm_2Efinite__map_2EDOMSUB__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0k2_2E0: A_27a,V1k1_2E0: A_27a,V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V2fm_2E0,V1k1_2E0),V0k2_2E0) = c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V2fm_2E0,V0k2_2E0),V1k1_2E0) ) ).
tff(thm_2Efinite__map_2EDOMSUB__IDEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1fm_2E0,V0k_2E0),V0k_2E0) = c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V1fm_2E0,V0k_2E0) ) ).
tff(thm_2Efinite__map_2Eo__f__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0k_2E0: A_27a,V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V1g_2E0,V2fm_2E0),V0k_2E0) = c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V1g_2E0,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27c,V2fm_2E0,V0k_2E0)) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUPDATE__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a,V2v_2E0: A_27b] : ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0))) = c_2Epred__set_2EINSERT_2E2(A_27b,V2v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0))) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FLOOKUP__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1k1_2E0: A_27a,V2k2_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0))
<=> ( V1k1_2E0 = V2k2_2E0 ) )
=> ! [V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k1_2E0),V2k2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0),c_2Eoption_2ENONE_2E0(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FLOOKUP__NEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a] :
( ( V1k1_2E0 != V2k2_2E0 )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k1_2E0),V2k2_2E0) = c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0),V1k_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FAPPLY__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1k1_2E0: A_27a,V2k2_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0))
<=> ( V1k1_2E0 = V2k2_2E0 ) )
=> ! [V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k1_2E0),V2k2_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V2k2_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FAPPLY__NEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a] :
( ( V1k1_2E0 != V2k2_2E0 )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k1_2E0),V2k2_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FAPPLY,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0),V1k_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1k_2E0) ) ).
tff(thm_2Efinite__map_2EFDOM__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0)) = c_2Epred__set_2EDELETE_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0),V1k_2E0) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FUPDATE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1k1_2E0: A_27a,V2k2_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0))
<=> ( V1k1_2E0 = V2k2_2E0 ) )
=> ! [V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a,V3v_2E0: A_27b] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V3v_2E0)),V2k2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V3v_2E0))) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FUPDATE__NEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k1_2E0: A_27a,V2k2_2E0: A_27a,V3v_2E0: A_27b] :
( ( V1k1_2E0 != V2k2_2E0 )
=> ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V3v_2E0)),V2k2_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V2k2_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k1_2E0,V3v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a,V2v_2E0: A_27b] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0)),V1k_2E0) = c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V0fm_2E0,V1k_2E0) ) ).
tff(thm_2Efinite__map_2EDOMSUB__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a] : ( c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0k_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2Ef__o__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0h_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27d)] :
( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V1g_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V4y_2E0) )
<=> ( V3x_2E0 = V4y_2E0 ) )
& ! [V5x_2E0: A_27c,V6y_2E0: A_27c] :
( ( app_2E2(A_27c,A_27a,V0h_2E0,V5x_2E0) = app_2E2(A_27c,A_27a,V0h_2E0,V6y_2E0) )
<=> ( V5x_2E0 = V6y_2E0 ) ) )
=> ( c_2Efinite__map_2Ef__o_2E2(A_27c,A_27a,A_27d,c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27d,V2f_2E0,V1g_2E0),V0h_2E0) = c_2Efinite__map_2Ef__o_2E2(A_27c,A_27b,A_27d,V2f_2E0,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V1g_2E0,V0h_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFINITE__PRED__11,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0g_2E0),V3f_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0g_2E0,V4x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V3f_2E0))) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0g_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0g_2E0,V2y_2E0) )
<=> ( V1x_2E0 = V2y_2E0 ) )
=> ! [V3f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0g_2E0),V3f_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EFAPPLY__f__o,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V0f_2E0))) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0))))
=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0))))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0),V3x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27c,V0f_2E0,app_2E2(A_27a,A_27b,V1g_2E0,V3x_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2Ef__o__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))] :
( ! [V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V4x_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V3g_2E0),V0fm_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,V4x_2E0,c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27c,A_27a,V3g_2E0,V4x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0))) )
=> ( ! [V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V6x_2E0: A_27c,V1k_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F4_2E0,V3g_2E0),V6x_2E0),V1k_2E0))
<=> ( app_2E2(A_27c,A_27a,V3g_2E0,V6x_2E0) = V1k_2E0 ) )
=> ( ! [V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V1k_2E0: A_27a,V6x_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F2_2E0,V3g_2E0),V1k_2E0),V6x_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,V6x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F4_2E0,V3g_2E0),V6x_2E0),V1k_2E0)) )
=> ( ! [V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V5x_2E0: A_27c,V1k_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V3g_2E0),V5x_2E0),V1k_2E0))
<=> ( app_2E2(A_27c,A_27a,V3g_2E0,V5x_2E0) = V1k_2E0 ) )
=> ( ! [V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V1k_2E0: A_27a,V5x_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F1_2E0,V3g_2E0),V1k_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V3g_2E0),V5x_2E0),V1k_2E0)) )
=> ! [V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a,V2v_2E0: A_27b,V3g_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27c,c_2Epred__set_2EGSPEC_2E1(A_27c,A_27c,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F0_2E0,V3g_2E0),V0fm_2E0))))
& p(c_2Epred__set_2EFINITE_2E1(A_27c,c_2Epred__set_2EGSPEC_2E1(A_27c,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F1_2E0,V3g_2E0),V1k_2E0)))) )
=> ( c_2Efinite__map_2Ef__o_2E2(A_27c,A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0)),V3g_2E0) = c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27c,c_2Ecombin_2EC_2E1(A_27b,A_27b,A_27b,c_2Ecombin_2EK_2E0(A_27b,A_27b)),c_2Efinite__map_2Ef__o_2E2(A_27c,A_27a,A_27b,V0fm_2E0,V3g_2E0),c_2Efinite__map_2EFUN__FMAP_2E2(A_27c,A_27b,c_2Ecombin_2EK_2E1(A_27b,A_27c,V2v_2E0),c_2Epred__set_2EGSPEC_2E1(A_27c,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),F2_2E0,V3g_2E0),V1k_2E0)))) ) ) ) ) ) ) ) ).
tff(thm_2Efinite__map_2Ef__o__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27c),V0g_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c) ) ).
tff(thm_2Efinite__map_2EFDOM__f__o,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V1g_2E0),V0f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V1g_2E0,V3x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V0f_2E0))) )
=> ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,V0f_2E0))) )
=> ! [V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1g_2E0),V0f_2E0))))
=> ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Ef__o_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0)) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V1g_2E0),V0f_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__FUN__FMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2P_2E0))
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V1f_2E0,V2P_2E0),V0k_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V0k_2E0,V2P_2E0),c_2Eoption_2ESOME_2E1(A_27b,app_2E2(A_27a,A_27b,V1f_2E0,V0k_2E0)),c_2Eoption_2ENONE_2E0(A_27b)) ) ) ).
tff(thm_2Efinite__map_2EFDOM__FMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = V1s_2E0 ) ) ).
tff(thm_2Efinite__map_2EFRANGE__FMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1P_2E0))
=> ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1P_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUN__FMAP__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2ERRESTRICT__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1r_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),V1r_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1r_2E0),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,V0f_2E0,V1r_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),c_2Efinite__map_2ERRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))),V1r_2E0)) ) ).
tff(thm_2Efinite__map_2ERRESTRICT__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2ERRESTRICT_2E2(A_27b,A_27a,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a),V0r_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1fm1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm2_2E0)))
=> ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1fm1_2E0,V0fm2_2E0)) = c_2Epred__set_2EUNION_2E2(A_27b,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V1fm1_2E0),c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0fm2_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFRANGE__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27a,V1f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1f_2E0)))
<=> ? [V2k_2E0: A_27b] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V1f_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0v_2E0) ) ) ).
tff(thm_2Efinite__map_2Eo__f__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27a,V1g_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,V1g_2E0)))
=> p(c_2Ebool_2EIN_2E2(A_27c,app_2E2(A_27a,A_27c,V2f_2E0,V0x_2E0),c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27b,A_27a,A_27c,V2f_2E0,V1g_2E0)))) ) ).
tff(thm_2Efinite__map_2EFINITE__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0fm_2E0))) ).
tff(thm_2Efinite__map_2ESUBMAP__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V0f_2E0),c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,V1g_2E0))) ) ).
tff(thm_2Efinite__map_2EFRANGE__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1x_2E0: A_27a,V2y_2E0: A_27b] : ( c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0))) = c_2Epred__set_2EINSERT_2E2(A_27b,V2y_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))))) ) ).
tff(thm_2Efinite__map_2EFRANGE__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__o__f,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))] :
( ! [V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V3v_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V2f_2E0),V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27a,app_2E2(A_27c,A_27a,V2f_2E0,V3v_2E0)) )
=> ! [V0k_2E0: A_27b,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2Eo__f_2E2(A_27b,A_27c,A_27a,V2f_2E0,V1fm_2E0),V0k_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27c,tyop_2Eoption_2Eoption(A_27a),c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27c,V1fm_2E0,V0k_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V2f_2E0)) ) ) ).
tff(thm_2Efinite__map_2Eo__f__o__f,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27d),V1g_2E0: tyop_2Emin_2Efun(A_27d,A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V2f_2E0,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27d,A_27c,V1g_2E0,V0h_2E0)) = c_2Efinite__map_2Eo__f_2E2(A_27a,A_27d,A_27b,c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,V2f_2E0,V1g_2E0),V0h_2E0) ) ).
tff(thm_2Efinite__map_2EFEVERY__o__f,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))] :
( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V3x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2f_2E0),V3x_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool,V1P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,c_2Epair_2EFST_2E1(A_27a,A_27b,V3x_2E0),app_2E2(A_27b,A_27c,V2f_2E0,c_2Epair_2ESND_2E1(A_27a,A_27b,V3x_2E0)))) )
=> ! [V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27c,V1P_2E0,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V2f_2E0,V0m_2E0)) = c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2f_2E0),V0m_2E0) ) ) ).
tff(thm_2Efinite__map_2Eo__f__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ).
tff(thm_2Efinite__map_2Eo__f__FAPPLY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFDOM__o__f,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0)) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) ) ).
tff(thm_2Efinite__map_2Eo__f__FDOM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1g_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0)) ) ).
tff(thm_2Efinite__map_2Ef__o__f__FEMPTY__2,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27c)] : ( c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c) ) ).
tff(thm_2Efinite__map_2Ef__o__f__FEMPTY__1,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Ef__o__f_2E2(A_27a,A_27b,A_27c,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27c),V0f_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c) ) ).
tff(thm_2Efinite__map_2EFEVERY__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1k_2E0: A_27a,V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V3P_2E0,V2f_2E0))
& ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2f_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) ) )
=> p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V3P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V0v_2E0))) ) ).
tff(thm_2Efinite__map_2EFEVERY__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2x_2E0: A_27a,V3y_2E0: A_27b] :
( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0))))
<=> ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)))
& p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))))) ) ) ).
tff(thm_2Efinite__map_2EFEVERY__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b))) ).
tff(thm_2Efinite__map_2EFLOOKUP__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2k_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0fm_2E0,V1s_2E0),V2k_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V2k_2E0,V1s_2E0),c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0fm_2E0,V2k_2E0),c_2Eoption_2ENONE_2E0(A_27b)) ) ).
tff(thm_2Efinite__map_2Efmap__eq__flookup,axiom,
! [A_27a: $tType,A_27b: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( V1f1_2E0 = V0f2_2E0 )
<=> ! [V2x_2E0: A_27a] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V1f1_2E0,V2x_2E0) = c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V0f2_2E0,V2x_2E0) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__EXT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( V1f1_2E0 = V0f2_2E0 )
<=> ( c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27b,V1f1_2E0) = c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27b,V0f2_2E0) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] :
( ! [V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),F0_2E0,V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3v_2E0) )
=> ! [V0k_2E0: A_27b,V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2f1_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2EFUNION_2E2(A_27b,A_27a,V2f1_2E0,V1f2_2E0),V0k_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V2f1_2E0,V0k_2E0),c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V1f2_2E0,V0k_2E0),F0_2E0) ) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUPDATE__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V2f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V2f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0))))
<=> ( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2f_2E0,V1x_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
| ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2f_2E0,V1x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0y_2E0) ) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1k_2E0: A_27a,V2g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V3f_2E0,V2g_2E0))
& ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V3f_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) ) )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2g_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__UPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V2k1_2E0: A_27b,V1k2_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0,V2k1_2E0),V1k2_2E0))
<=> ( V2k1_2E0 = V1k2_2E0 ) )
=> ! [V0v_2E0: A_27a,V1k2_2E0: A_27b,V2k1_2E0: A_27b,V3fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27a,V3fm_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27a,V2k1_2E0,V0v_2E0)),V1k2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0,V2k1_2E0),V1k2_2E0),c_2Eoption_2ESOME_2E1(A_27a,V0v_2E0),c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V3fm_2E0,V1k2_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: A_27b] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a),V0k_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ).
tff(thm_2Efinite__map_2EFMERGE__EQ__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V0m_2E0,V2f_2E0,V1g_2E0) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
<=> ( ( V2f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
& ( V1g_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) ) ) ) ).
tff(thm_2Efinite__map_2EFMERGE__DRESTRICT,axiom,
! [A_27a: $tType,A_27b: $tType,V0vs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1st2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2st1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V3f_2E0,V2st1_2E0,V1st2_2E0),V0vs_2E0) = c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V3f_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2st1_2E0,V0vs_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1st2_2E0,V0vs_2E0)) ) ).
tff(thm_2Efinite__map_2EFMERGE__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2EASSOC_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFMERGE_2E1(A_27b,A_27a,V0m_2E0)) = c_2Ecombin_2EASSOC_2E1(A_27b,V0m_2E0) ) ).
tff(thm_2Efinite__map_2EFMERGE__COMM,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Ecombin_2ECOMM_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFMERGE_2E1(A_27b,A_27a,V0m_2E0)) = c_2Ecombin_2ECOMM_2E1(A_27b,A_27b,V0m_2E0) ) ).
tff(thm_2Efinite__map_2EFMERGE__NO__CHANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V0m_2E0,V2f1_2E0,V1f2_2E0) = V2f1_2E0 )
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f1_2E0)))
& ( app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),V0m_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f1_2E0,V3x_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f2_2E0,V3x_2E0)) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f1_2E0,V3x_2E0) ) ) ) )
& ( ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V0m_2E0,V2f1_2E0,V1f2_2E0) = V1f2_2E0 )
<=> ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2f1_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
& ( app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),V0m_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2f1_2E0,V4x_2E0)),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f2_2E0,V4x_2E0)) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V1f2_2E0,V4x_2E0) ) ) ) ) ) ).
tff(thm_2Efinite__map_2EFUNION__FMERGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0f1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f2_2E0)))
=> ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V2m_2E0,V0f1_2E0,V1f2_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f1_2E0,V1f2_2E0) ) ) ).
tff(thm_2Efinite__map_2EFMERGE__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))] :
( ! [V0x_2E0: A_27b,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0,V0x_2E0),V1y_2E0) = V0x_2E0 )
=> ( c_2Efinite__map_2EFUNION_2E0(A_27a,A_27b) = c_2Efinite__map_2EFMERGE_2E1(A_27b,A_27a,F0_2E0) ) ) ).
tff(thm_2Efinite__map_2EFDOM__FMERGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] : ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,c_2Efinite__map_2EFMERGE_2E3(A_27a,A_27b,V0m_2E0,V1f_2E0,V2g_2E0)) = c_2Epred__set_2EUNION_2E2(A_27b,c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,V1f_2E0),c_2Efinite__map_2EFDOM_2E1(A_27b,A_27a,V2g_2E0)) ) ).
tff(thm_2Efinite__map_2EFMERGE__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V0m_2E0,V1f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = V1f_2E0 )
& ( c_2Efinite__map_2EFMERGE_2E3(A_27b,A_27a,V0m_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1f_2E0) = V1f_2E0 ) ) ).
tff(thm_2Efinite__map_2EFUNION__IDEMPOT,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0fm_2E0,V0fm_2E0) = V0fm_2E0 ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0h_2E0,V1s1_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0h_2E0,V2s2_2E0)) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0h_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s1_2E0,V2s2_2E0)) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__EQ__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1h1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1h1_2E0),c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2h2_2E0)))
& ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1h1_2E0,V2h2_2E0) = V0h_2E0 ) )
=> ( V2h2_2E0 = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0h_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1h1_2E0))) ) ) ).
tff(thm_2Efinite__map_2EIN__FDOM__FOLDR__UNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1hL_2E0: tyop_2Elist_2Elist(tyop_2Efinite__map_2Efmap(A_27a,A_27b))] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Elist_2EFOLDR_2E3(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E0(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1hL_2E0))))
<=> ? [V2h_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1hL_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2h_2E0))) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__FUNION__DRESTRICT__COMPL,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0))) = V1f_2E0 ) ).
tff(thm_2Efinite__map_2EDRESTRICT__IDEMPOT,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1vs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0s_2E0,V1vs_2E0),V1vs_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V0s_2E0,V1vs_2E0) ) ).
tff(thm_2Efinite__map_2ESUBMAP__FUNION__ABSORPTION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))
<=> ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0) = V1g_2E0 ) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__witness,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)))] :
( ! [V0m_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool,F0_2E0,V0m_2E0))
<=> ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27b,A_27c,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),V0m_2E0,V1f_2E0),V2fm_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V2fm_2E0)) )
& ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V1f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V2fm_2E0),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V2fm_2E0)))
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27b,A_27c,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),V0m_2E0,V1f_2E0),V2fm_2E0),app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0)) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27c,V2fm_2E0,V3x_2E0) ) ) ) ) )
=> ( ! [V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),F1_2E0,V4f_2E0),V5fm_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V4f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V5fm_2E0),c_2Epred__set_2EUNIV_2E0(A_27b)),c_2Efinite__map_2Ef__o__f_2E2(A_27b,A_27a,A_27c,V5fm_2E0,c_2Efinite__map_2EFUN__FMAP_2E2(A_27b,A_27a,c_2Epred__set_2ELINV_2E2(A_27a,A_27b,V4f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V5fm_2E0)),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V4f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V5fm_2E0)))),c_2Efinite__map_2EFUN__FMAP_2E2(A_27b,A_27c,c_2Ebool_2EARB_2E0(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V4f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V5fm_2E0)))) )
=> p(c_2Ebool_2ELET_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool,F0_2E0,F1_2E0)) ) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27c)) = c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27c) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V2k_2E0: A_27a,V3v_2E0: A_27c] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2k_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0)),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27c,V1fm_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27c,V2k_2E0,V3v_2E0))) = c_2Efinite__map_2EFUPDATE_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1fm_2E0),c_2Epair_2E_2C_2E2(A_27b,A_27c,app_2E2(A_27a,A_27b,V0f_2E0,V2k_2E0),V3v_2E0)) ) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__using__LINV,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1fm_2E0) = c_2Efinite__map_2Ef__o__f_2E2(A_27b,A_27a,A_27c,V1fm_2E0,c_2Efinite__map_2EFUN__FMAP_2E2(A_27b,A_27a,c_2Epred__set_2ELINV_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0)),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm_2E0)))) ) ) ).
tff(thm_2Efinite__map_2EMAP__KEYS__BIJ__LINV,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
=> ( c_2Efinite__map_2EMAP__KEYS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Efinite__map_2EMAP__KEYS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,A_27a,c_2Epred__set_2ELINV_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),V0t_2E0)) = V0t_2E0 ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__MAP__KEYS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1k_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1k_2E0),V2f_2E0),V0m_2E0),V3x_2E0))
<=> ( ( V1k_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) )
& p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V0m_2E0))) ) )
=> ! [V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1k_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V0m_2E0),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,V0m_2E0),V1k_2E0) = c_2Eoption_2EOPTION__BIND_2E2(A_27c,A_27a,c_2Eoption_2Esome_2E1(A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1k_2E0),V2f_2E0),V0m_2E0)),c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27c,V0m_2E0)) ) ) ) ).
tff(thm_2Efinite__map_2EFLOOKUP__MAP__KEYS__MAPPED,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1k_2E0: A_27a,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,V0m_2E0),app_2E2(A_27a,A_27b,V2f_2E0,V1k_2E0)) = c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27c,V0m_2E0,V1k_2E0) ) ) ).
tff(thm_2Efinite__map_2EDRESTRICT__MAP__KEYS__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2EDRESTRICT_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,V1fm_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0)) = c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27c,V1fm_2E0,V0s_2E0)) ) ) ).
tff(thm_2Efinite__map_2EDOMSUB__MAP__KEYS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: A_27a,V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Efinite__map_2Efdomsub_2E2(A_27b,A_27c,c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,V1fm_2E0),app_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0)) = c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27c,V2f_2E0,c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27c,V1fm_2E0,V0s_2E0)) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FUPDATE__same,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v2_2E0: A_27b,V1v1_2E0: A_27a,V2k_2E0: A_27c,V3f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V4f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V5R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V5R_2E0,V4f1_2E0,V3f2_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5R_2E0,V1v1_2E0),V0v2_2E0)) )
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V5R_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27a,V4f1_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27a,V2k_2E0,V1v1_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27b,V3f2_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27b,V2k_2E0,V0v2_2E0)))) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FUPDATE__LIST__same,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1ls1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),V2ls2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),V3f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V4f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b)] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V0R_2E0,V3f1_2E0,V4f2_2E0))
& ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),A_27c,c_2Epair_2EFST_2E0(A_27c,A_27a),V1ls1_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),A_27c,c_2Epair_2EFST_2E0(A_27c,A_27b),V2ls2_2E0) )
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27c,A_27a),V1ls1_2E0),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27c,A_27b),V2ls2_2E0))) )
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V0R_2E0,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27a,V3f1_2E0,V1ls1_2E0),c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27c,A_27b,V4f2_2E0,V2ls2_2E0))) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V0R_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27c,A_27a),c_2Efinite__map_2EFEMPTY_2E0(A_27c,A_27b))) ).
tff(thm_2Efinite__map_2Efmap__rel__FEMPTY2,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V1R_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a),V0f_2E0))
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a) ) )
& ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V1R_2E0,V0f_2E0,c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a)))
<=> ( V0f_2E0 = c_2Efinite__map_2EFEMPTY_2E0(A_27b,A_27a) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__refl,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V2x_2E0),V2x_2E0))
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27a,A_27b,V1R_2E0,V0x_2E0,V0x_2E0)) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FUNION__rels,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f4_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V1f3_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V3f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V4R_2E0,V3f1_2E0,V2f2_2E0))
& p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V4R_2E0,V1f3_2E0,V0f4_2E0)) )
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V4R_2E0,c_2Efinite__map_2EFUNION_2E2(A_27c,A_27a,V3f1_2E0,V1f3_2E0),c_2Efinite__map_2EFUNION_2E2(A_27c,A_27b,V2f2_2E0,V0f4_2E0))) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FUPDATE__I,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v2_2E0: A_27b,V1v1_2E0: A_27a,V2k_2E0: A_27c,V3f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V4f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V5R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V5R_2E0,c_2Efinite__map_2Efdomsub_2E2(A_27c,A_27a,V4f1_2E0,V2k_2E0),c_2Efinite__map_2Efdomsub_2E2(A_27c,A_27b,V3f2_2E0,V2k_2E0)))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5R_2E0,V1v1_2E0),V0v2_2E0)) )
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V5R_2E0,c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27a,V4f1_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27a,V2k_2E0,V1v1_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27b,V3f2_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27b,V2k_2E0,V0v2_2E0)))) ) ).
tff(thm_2Efinite__map_2Efmap__rel__mono,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2R2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V4x_2E0: A_27a,V5y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R1_2E0,V4x_2E0),V5y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R2_2E0,V4x_2E0),V5y_2E0)) )
=> ( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V3R1_2E0,V1f1_2E0,V0f2_2E0))
=> p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V2R2_2E0,V1f1_2E0,V0f2_2E0)) ) ) ).
tff(thm_2Efinite__map_2Efmap__rel__OPTREL__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V2R_2E0,V1f1_2E0,V0f2_2E0))
<=> ! [V3k_2E0: A_27c] : p(c_2Eoption_2EOPTREL_2E3(A_27a,A_27b,V2R_2E0,c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27a,V1f1_2E0,V3k_2E0),c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27b,V0f2_2E0,V3k_2E0))) ) ).
tff(thm_2Efinite__map_2Efmap__rel__FLOOKUP__imp,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27b),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Efinite__map_2Efmap__rel_2E3(A_27a,A_27b,A_27c,V2R_2E0,V1f1_2E0,V0f2_2E0))
=> ( ! [V3k_2E0: A_27c] :
( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27a,V1f1_2E0,V3k_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27b,V0f2_2E0,V3k_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) )
& ! [V4k_2E0: A_27c,V5v1_2E0: A_27a] :
( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27a,V1f1_2E0,V4k_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V5v1_2E0) )
=> ? [V6v2_2E0: A_27b] :
( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27c,A_27b,V0f2_2E0,V4k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V6v2_2E0) )
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R_2E0,V5v1_2E0),V6v2_2E0)) ) ) ) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO______EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V0f1_2E0,V1f2_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
<=> ( V0f1_2E0 = V1f2_2E0 ) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO______EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0vs_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V1f_2E0,V1f_2E0,V0vs_2E0)) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2ks_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3k_2E0: A_27a,V4v_2E0: A_27b] :
( p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2ks_2E0))
=> p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)),c_2Epred__set_2EDELETE_2E2(A_27a,V2ks_2E0,V3k_2E0))) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH______NO__DELETE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2ks_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3k_2E0: A_27a,V4v_2E0: A_27b] :
( p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2ks_2E0))
=> p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V1f2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)),V2ks_2E0)) ) ).
tff(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__SING,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2ks_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3k_2E0: A_27a,V4v_2E0: A_27b] :
( p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2ks_2E0))
=> p(c_2Efinite__map_2Efmap__EQ__UPTO_2E3(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0f1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,V4v_2E0)),V1f2_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V3k_2E0,V2ks_2E0))) ) ).
tff(thm_2Efinite__map_2Eo__f__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1f1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V2f_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27c,V1f1_2E0,V0f2_2E0)) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V2f_2E0,V1f1_2E0),c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27b,V2f_2E0,V0f2_2E0)) ) ).
tff(thm_2Efinite__map_2EFDOM__FOLDR__DOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))] :
( ! [V2k_2E0: A_27a,V3m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),F0_2E0,V2k_2E0),V3m_2E0) = c_2Efinite__map_2Efdomsub_2E2(A_27a,A_27b,V3m_2E0,V2k_2E0) )
=> ! [V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),F0_2E0,V1fm_2E0,V0ls_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1fm_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0)) ) ) ).
tff(thm_2Efinite__map_2EFEVERY__SUBMAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V2P_2E0,V1fm_2E0))
& p(c_2Efinite__map_2ESUBMAP_2E2(A_27a,A_27b,V0fm0_2E0,V1fm_2E0)) )
=> p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V2P_2E0,V0fm0_2E0)) ) ).
tff(thm_2Efinite__map_2EFEVERY__ALL__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Efinite__map_2EFEVERY_2E2(A_27a,A_27b,V0P_2E0,V1f_2E0))
<=> ! [V2k_2E0: A_27a,V3v_2E0: A_27b] :
( ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V1f_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3v_2E0) )
=> p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2k_2E0,V3v_2E0))) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__CANCEL,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2ls2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ! [V3k_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0ls1_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V3k_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V2ls2_2E0)))) )
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0ls1_2E0),V2ls2_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V2ls2_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__EQ__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1kv_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V0fm_2E0,V1kv_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1kv_2E0),V0fm_2E0) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__APPEND__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0l1_2E0)),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1l2_2E0))))
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V0l1_2E0),V1l2_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V1l2_2E0),V0l1_2E0) ) ) ).
tff(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__PERM,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1ls_27_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0ls_2E0)))
& p(c_2Esorting_2EPERM_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_2E0,V1ls_27_2E0)) )
=> ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V0ls_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2fm_2E0,V1ls_27_2E0) ) ) ).
%------------------------------------------------------------------------------