ITP001 Axioms: ITP081_7.ax
%------------------------------------------------------------------------------
% File : ITP081_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 : alist.ax [Gau19]
% : HL4081_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 321 ( 129 unt; 131 typ; 0 def)
% Number of atoms : 286 ( 210 equ)
% Maximal formula atoms : 5 ( 0 avg)
% Number of connectives : 102 ( 6 ~; 3 |; 18 &)
% ( 23 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 102 ( 64 >; 38 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 128 ( 128 usr; 8 con; 0-5 aty)
% Number of variables : 940 ( 760 !; 2 ?; 940 :)
% ( 178 !>; 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_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $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_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_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_2Ealist_2EALOOKUP_2E0,type,
c_2Ealist_2EALOOKUP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Ealist_2EALOOKUP_2E1,type,
c_2Ealist_2EALOOKUP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)) > tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2Ealist_2EALOOKUP_2E2,type,
c_2Ealist_2EALOOKUP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)) * A_27b ) > tyop_2Eoption_2Eoption(A_27a) ) ).
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_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_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_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_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Efinite__map_2EFAPPLY_2E0,type,
c_2Efinite__map_2EFAPPLY_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Efinite__map_2EFAPPLY_2E2,type,
c_2Efinite__map_2EFAPPLY_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Efinite__map_2EFDOM_2E0,type,
c_2Efinite__map_2EFDOM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Efinite__map_2EFDOM_2E1,type,
c_2Efinite__map_2EFDOM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_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_2Elist_2EFILTER_2E0,type,
c_2Elist_2EFILTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EFILTER_2E2,type,
c_2Elist_2EFILTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
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_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_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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
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_2Ewhile_2ELEAST_2E0,type,
c_2Ewhile_2ELEAST_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Ewhile_2ELEAST_2E1,type,
c_2Ewhile_2ELEAST_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).
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_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_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_2Eoption_2EOPTION__MAP_2E0,type,
c_2Eoption_2EOPTION__MAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))) ).
tff(c_2Eoption_2EOPTION__MAP_2E1,type,
c_2Eoption_2EOPTION__MAP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)) ) ).
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_2Elist_2ESET__TO__LIST_2E0,type,
c_2Elist_2ESET__TO__LIST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2ESET__TO__LIST_2E1,type,
c_2Elist_2ESET__TO__LIST_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Elist_2Elist(A_27a) ) ).
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_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_2Esorting_2ESTABLE_2E0,type,
c_2Esorting_2ESTABLE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)) ).
tff(c_2Esorting_2ESTABLE_2E2,type,
c_2Esorting_2ESTABLE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).
tff(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > A_27a ) ).
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_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
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_2Ealist_2Ealist__range_2E0,type,
c_2Ealist_2Ealist__range_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ealist_2Ealist__range_2E1,type,
c_2Ealist_2Ealist__range_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ealist_2Ealist__to__fmap_2E0,type,
c_2Ealist_2Ealist__to__fmap_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)) ).
tff(c_2Ealist_2Ealist__to__fmap_2E1,type,
c_2Ealist_2Ealist__to__fmap_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).
tff(c_2Ealist_2Efmap__to__alist_2E0,type,
c_2Ealist_2Efmap__to__alist_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Ealist_2Efmap__to__alist_2E1,type,
c_2Ealist_2Efmap__to__alist_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).
tff(c_2Erelation_2Einv__image_2E0,type,
c_2Erelation_2Einv__image_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Erelation_2Einv__image_2E2,type,
c_2Erelation_2Einv__image_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,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_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_2Erelation_2Etotal_2E0,type,
c_2Erelation_2Etotal_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etotal_2E1,type,
c_2Erelation_2Etotal_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Etransitive_2E0,type,
c_2Erelation_2Etransitive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Etransitive_2E1,type,
c_2Erelation_2Etransitive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_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_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_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: A_27b,X1_2E0: A_27d] : ( c_2Epair_2E_2C_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),c_2Epair_2E_2C_2E0(A_27b,A_27d),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_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),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_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ealist_2EALOOKUP_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: A_27a] : ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ealist_2EALOOKUP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27d_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))] : ( c_2Ealist_2EALOOKUP_2E1(A_27d,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Ealist_2EALOOKUP_2E0(A_27d,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ealist_2EALOOKUP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Ealist_2EALOOKUP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Ealist_2EALOOKUP_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),c_2Ealist_2EALOOKUP_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),c_2Ealist_2EALOOKUP_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))] : ( c_2Ealist_2EALOOKUP_2E1(A_27d,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Ealist_2EALOOKUP_2E0(A_27d,A_27c),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_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(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(arityeq2_2Ec_2Elist_2ECONS_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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27c,A_27d),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(A_27c,A_27d)),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_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EEL_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_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EEL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_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(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(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(arityeq2_2Ec_2Elist_2EFILTER_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_2EFILTER_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_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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EFILTER_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Elist_2EFILTER_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Elist_2EFILTER_2E0(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_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(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(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_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_2EFLOOKUP_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Efinite__map_2EFLOOKUP_2E0(A_27c,A_27d),X0_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_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_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_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__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_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(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(arityeq2_2Ec_2Epred__set_2EIMAGE_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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),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_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_2Ewhile_2ELEAST_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ewhile_2ELEAST_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E0,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_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_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_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EMAP_2E0(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),c_2Elist_2EMAP_2E0(A_27b,A_27d),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_27c_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27d))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),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_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,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_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EMAP__KEYS_2E0(A_27a,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27d)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27b,A_27d),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27d),tyop_2Efinite__map_2Efmap(A_27b,A_27d)),c_2Efinite__map_2EMAP__KEYS_2E0(A_27a,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Eoption_2EOPTION__MAP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] : ( c_2Eoption_2EOPTION__MAP_2E1(A_27b,A_27d,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MAP_2E0(A_27b,A_27d),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Esorting_2EPERM_2E0(A_27a),X0_2E0),X1_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(arityeq1_2Ec_2Elist_2EREVERSE_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_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EREVERSE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2ESET__TO__LIST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E0(A_27a),X0_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_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_2Esorting_2ESTABLE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Esorting_2ESTABLE_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_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Esorting_2ESTABLE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Eoption_2ETHE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),A_27b,c_2Eoption_2ETHE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Emin_2Ebool),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_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27b,A_27c,tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E0(A_27a,A_27d),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(arityeq1_2Ec_2Ealist_2Ealist__range_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ealist_2Ealist__range_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ealist_2Ealist__range_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ealist_2Ealist__to__fmap_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Ealist_2Ealist__to__fmap_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Ealist_2Ealist__to__fmap_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27d))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27d,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27d)),tyop_2Efinite__map_2Efmap(A_27b,A_27d),c_2Ealist_2Ealist__to__fmap_2E0(A_27b,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Efinite__map_2Efmap(A_27c,A_27a),c_2Ealist_2Ealist__to__fmap_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Efinite__map_2Efmap(A_27c,A_27b),c_2Ealist_2Ealist__to__fmap_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Efinite__map_2Efmap(A_27c,A_27d),c_2Ealist_2Ealist__to__fmap_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ealist_2Efmap__to__alist_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Ealist_2Efmap__to__alist_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Ealist_2Efmap__to__alist_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Ealist_2Efmap__to__alist_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Ealist_2Efmap__to__alist_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Einv__image_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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a)] : ( c_2Erelation_2Einv__image_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27d_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27d)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Eoption_2Eoption(A_27d),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Eoption_2Eoption(A_27d),tyop_2Eoption_2Eoption(A_27b)),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_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27d)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2Eoption__CASE_2E0(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etotal_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_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_2Ealist_2Efmap__to__alist__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)))] :
( ! [V0s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0s_2E0),V1k_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V0s_2E0,V1k_2E0)) )
=> ! [V0s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0s_2E0) = c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0s_2E0),c_2Elist_2ESET__TO__LIST_2E1(A_27a,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0s_2E0))) ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__def,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))))] :
( ! [V1k_2E0: A_27a,V2v_2E0: A_27b,V3f_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,V1k_2E0),V2v_2E0),V3f_2E0) = c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,V3f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0)) )
=> ! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0s_2E0) = 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),c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0s_2E0) ) ) ).
tff(thm_2Ealist_2Ealist__range__def,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V1v_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0m_2E0),V1v_2E0))
<=> ? [V2k_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,V0m_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1v_2E0) ) )
=> ( ! [V0m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V1v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0m_2E0),V1v_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1v_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0m_2E0),V1v_2E0)) )
=> ! [V0m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ealist_2Ealist__range_2E1(A_27a,A_27b,V0m_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0m_2E0)) ) ) ) ).
tff(thm_2Ealist_2Efmap__to__alist__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0v_2E0: A_27d,V1t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V2k_2E0: A_27c] :
( ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
& ( c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27d,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(A_27c,A_27d,V2k_2E0,V0v_2E0),V1t_2E0)) = c_2Efinite__map_2EFUPDATE_2E2(A_27c,A_27d,c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27d,V1t_2E0),c_2Epair_2E_2C_2E2(A_27c,A_27d,V2k_2E0,V0v_2E0)) ) ) ).
tff(thm_2Ealist_2EALOOKUP__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( ! [V1q_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a))),V1q_2E0))
& ! [V2x_2E0: A_27b,V3y_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V5q_2E0: A_27b] :
( ( ( V2x_2E0 != V5q_2E0 )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V4t_2E0),V5q_2E0)) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V2x_2E0,V3y_2E0),V4t_2E0)),V5q_2E0)) ) )
=> ! [V6v_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V7v1_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V6v_2E0),V7v1_2E0)) ) ).
tff(thm_2Ealist_2EALOOKUP__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V2x_2E0: A_27b,V4q_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,V2x_2E0),V4q_2E0))
<=> ( V2x_2E0 = V4q_2E0 ) )
=> ( ! [V0q_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),V0q_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
& ! [V1y_2E0: A_27a,V2x_2E0: A_27b,V3t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V4q_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V2x_2E0,V1y_2E0),V3t_2E0),V4q_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,V2x_2E0),V4q_2E0),c_2Eoption_2ESOME_2E1(A_27a,V1y_2E0),c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,V3t_2E0,V4q_2E0)) ) ) ) ).
tff(thm_2Ealist_2EALOOKUP__FAILS,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,V1l_2E0,V0x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> ! [V2k_2E0: A_27b,V3v_2E0: A_27a] :
( 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),V1l_2E0)))
=> ( V2k_2E0 != V0x_2E0 ) ) ) ).
tff(thm_2Ealist_2EALOOKUP__NONE,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1x_2E0: A_27a] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0l_2E0,V1x_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_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),V0l_2E0)))) ) ).
tff(thm_2Ealist_2EALOOKUP__TABULATE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)))] :
( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V2f_2E0),V3k_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V3k_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V3k_2E0)) )
=> ! [V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V2f_2E0),V1l_2E0),V0x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0)) ) ) ) ).
tff(thm_2Ealist_2EALOOKUP__EQ__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27d),V1al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( c_2Efinite__map_2EFLOOKUP_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V1al_2E0)) = c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,V1al_2E0) )
& ( c_2Ealist_2EALOOKUP_2E1(A_27d,A_27c,c_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27d,V0fm_2E0)) = c_2Efinite__map_2EFLOOKUP_2E1(A_27c,A_27d,V0fm_2E0) ) ) ).
tff(thm_2Ealist_2EMEM__fmap__to__alist,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V2fm_2E0))))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2fm_2E0)))
& ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,V2fm_2E0,V1x_2E0) = V0y_2E0 ) ) ) ).
tff(thm_2Ealist_2EMEM__fmap__to__alist__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V1fm_2E0))))
<=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V1fm_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V0p_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V0p_2E0)) ) ) ).
tff(thm_2Ealist_2EMEM__pair__fmap__to__alist__FLOOKUP,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b,V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V2fm_2E0))))
<=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2fm_2E0,V0x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V1y_2E0) ) ) ).
tff(thm_2Ealist_2ELENGTH__fmap__to__alist,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_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_2Ealist_2Efmap__to__alist__to__fmap,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0fm_2E0)) = V0fm_2E0 ) ).
tff(thm_2Ealist_2EALOOKUP__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a,V2v_2E0: A_27b] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0al_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V2v_2E0) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V2v_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0al_2E0))) ) ).
tff(thm_2Ealist_2EALOOKUP__SOME__FAPPLY__alist__to__fmap,axiom,
! [A_27a: $tType,A_27b: $tType,V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a,V2v_2E0: A_27b] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0al_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V2v_2E0) )
=> ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_2E0),V1k_2E0) = V2v_2E0 ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__FAPPLY__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1z_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_2E0))))
=> p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1z_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_2E0),V1z_2E0)),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0al_2E0))) ) ).
tff(thm_2Ealist_2EALOOKUP__MAP,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(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27c,V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(A_27c,A_27b,V2x_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27c,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0)),V1al_2E0)) = c_2Ecombin_2Eo_2E2(A_27c,tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E1(A_27a,A_27b,V0f_2E0),c_2Ealist_2EALOOKUP_2E1(A_27a,A_27c,V1al_2E0)) ) ) ).
tff(thm_2Ealist_2EFDOM__alist__to__fmap,axiom,
! [A_27a: $tType,A_27b: $tType,V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_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),V0al_2E0)) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__prefix,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V1l1_2E0) = c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V2l2_2E0) )
=> ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_2E0,V1l1_2E0)) = c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_2E0,V2l2_2E0)) ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__APPEND,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))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0l1_2E0,V1l2_2E0)) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0l1_2E0),c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V1l2_2E0)) ) ).
tff(thm_2Ealist_2EALOOKUP__prefix,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2k_2E0: A_27a,V3ls2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V1ls_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) )
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1ls_2E0,V3ls2_2E0),V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) ) )
& ( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V1ls_2E0,V2k_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1ls_2E0,V3ls2_2E0),V2k_2E0) = c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V3ls2_2E0,V2k_2E0) ) ) ) ).
tff(thm_2Ealist_2EALOOKUP__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b))] :
( ! [V3v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),F0_2E0,V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3v_2E0) )
=> ! [V0l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2k_2E0: A_27a] : ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0l1_2E0,V1l2_2E0),V2k_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0l1_2E0,V2k_2E0),c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V1l2_2E0,V2k_2E0),F0_2E0) ) ) ).
tff(thm_2Ealist_2EFUPDATE__LIST__EQ__APPEND__REVERSE,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)] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V1fm_2E0,V0ls_2E0) = c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_2E0),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V1fm_2E0))) ) ).
tff(thm_2Ealist_2EFLOOKUP__FUPDATE__LIST__ALOOKUP__SOME,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27a,V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2k_2E0: A_27b,V3fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,V1ls_2E0,V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0v_2E0) )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,V3fm_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V1ls_2E0)),V2k_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0v_2E0) ) ) ).
tff(thm_2Ealist_2EFLOOKUP__FUPDATE__LIST__ALOOKUP__NONE,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V1k_2E0: A_27b,V2fm_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27a)] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27a,A_27b,V0ls_2E0,V1k_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27b,A_27a,V2fm_2E0,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V0ls_2E0)),V1k_2E0) = c_2Efinite__map_2EFLOOKUP_2E2(A_27b,A_27a,V2fm_2E0,V1k_2E0) ) ) ).
tff(thm_2Ealist_2EFUNION__alist__to__fmap,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)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0ls_2E0),V1fm_2E0) = 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)) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))))] :
( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V3x_2E0: A_27a,V4y_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))),F0_2E0,V0f1_2E0),V1f2_2E0),V3x_2E0),V4y_2E0) = c_2Epair_2E_2C_2E2(A_27b,A_27d,app_2E2(A_27a,A_27b,V0f1_2E0,V3x_2E0),app_2E2(A_27c,A_27d,V1f2_2E0,V4y_2E0)) )
=> ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V2al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f1_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27c),V2al_2E0)),c_2Epred__set_2EUNIV_2E0(A_27b)))
=> ( c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27d,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2EUNCURRY_2E1(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))),F0_2E0,V0f1_2E0),V1f2_2E0)),V2al_2E0)) = c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27d,V0f1_2E0,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27d,V1f2_2E0,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27c,V2al_2E0))) ) ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__to__alist,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)))] :
( ! [V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0al_2E0),V1k_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,c_2Eoption_2ETHE_2E1(A_27b,c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0al_2E0,V1k_2E0))) )
=> ! [V0al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_2E0)) = c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0al_2E0),c_2Elist_2ESET__TO__LIST_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),V0al_2E0)))) ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__to__alist__PERM,axiom,
! [A_27a: $tType,A_27b: $tType,V0al_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),V0al_2E0)))
=> p(c_2Esorting_2EPERM_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0al_2E0)),V0al_2E0)) ) ).
tff(thm_2Ealist_2EALOOKUP__LEAST__EL,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0ls_2E0),V1k_2E0),V2n_2E0))
<=> ( c_2Elist_2EEL_2E2(A_27a,V2n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0ls_2E0)) = V1k_2E0 ) )
=> ! [V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a] : ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0ls_2E0,V1k_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V1k_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),V0ls_2E0))),c_2Eoption_2ESOME_2E1(A_27b,c_2Elist_2EEL_2E2(A_27b,c_2Ewhile_2ELEAST_2E1(app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0ls_2E0),V1k_2E0)),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),V0ls_2E0))),c_2Eoption_2ENONE_2E0(A_27b)) ) ) ).
tff(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__MEM,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_2E0: A_27b,V1k_2E0: A_27a,V2al_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),V2al_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1k_2E0,V0v_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V2al_2E0))) )
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V2al_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V0v_2E0) ) ) ).
tff(thm_2Ealist_2EALL__DISTINCT__fmap__to__alist__keys,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_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),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0fm_2E0)))) ).
tff(thm_2Ealist_2Efmap__to__alist__inj,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)] :
( ( c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0f1_2E0) = c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V1f2_2E0) )
=> ( V0f1_2E0 = V1f2_2E0 ) ) ).
tff(thm_2Ealist_2Efmap__to__alist__preserves__FDOM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0fm1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27c)] :
( ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm1_2E0) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27c,V1fm2_2E0) )
=> ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0fm1_2E0)) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27c),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27c,V1fm2_2E0)) ) ) ).
tff(thm_2Ealist_2EPERM__fmap__to__alist,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_2Esorting_2EPERM_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V1fm1_2E0),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0fm2_2E0)))
<=> ( V1fm1_2E0 = V0fm2_2E0 ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__PERM,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))] :
( ( p(c_2Esorting_2EPERM_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0l1_2E0,V1l2_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),V0l1_2E0))) )
=> ( c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0l1_2E0) = c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V1l2_2E0) ) ) ).
tff(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__EL,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0ls_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),V0ls_2E0))) )
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0ls_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1n_2E0,V0ls_2E0))) = c_2Eoption_2ESOME_2E1(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1n_2E0,V0ls_2E0))) ) ) ).
tff(thm_2Ealist_2EALOOKUP__ZIP__MAP__SND,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b),V2k_2E0: A_27c,V3f_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
=> ( c_2Ealist_2EALOOKUP_2E1(A_27d,A_27a,c_2Elist_2EZIP_2E1(A_27a,A_27d,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d),V0l1_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27d,V3f_2E0,V1l2_2E0)))) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Eoption_2Eoption(A_27d),tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E1(A_27b,A_27d,V3f_2E0),c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0)))) ) ) ).
tff(thm_2Ealist_2EALOOKUP__FILTER,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3k_2E0: A_27a,V4v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V3k_2E0),V4v_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3k_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2x_2E0: A_27a] : ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EFILTER_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0)),V1ls_2E0),V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0),c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V1ls_2E0,V2x_2E0),c_2Eoption_2ENONE_2E0(A_27b)) ) ) ).
tff(thm_2Ealist_2EALOOKUP__APPEND__same,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)),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,V0l1_2E0) = c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,V1l2_2E0) )
=> ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0l1_2E0,V2l_2E0)) = c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1l2_2E0,V2l_2E0)) ) ) ).
tff(thm_2Ealist_2EALOOKUP__IN__FRANGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a,V2v_2E0: A_27b] :
( ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0ls_2E0,V1k_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V2v_2E0) )
=> p(c_2Ebool_2EIN_2E2(A_27b,V2v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27a,A_27b,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27b,V0ls_2E0)))) ) ).
tff(thm_2Ealist_2EFRANGE__alist__to__fmap__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27a,V0ls_2E0)),c_2Epred__set_2EIMAGE_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),V0ls_2E0)))) ).
tff(thm_2Ealist_2EIN__FRANGE__alist__to__fmap__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2v_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,V1P_2E0,V2v_2E0)) )
=> ! [V3v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3v_2E0,c_2Efinite__map_2EFRANGE_2E1(A_27b,A_27a,c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27a,V0ls_2E0))))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3v_2E0)) ) ) ).
tff(thm_2Ealist_2Ealist__to__fmap__MAP__matchable,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))))] :
( ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V5x_2E0: A_27a,V6y_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))),F0_2E0,V0f1_2E0),V1f2_2E0),V5x_2E0),V6y_2E0) = c_2Epair_2E_2C_2E2(A_27b,A_27d,app_2E2(A_27a,A_27b,V0f1_2E0,V5x_2E0),app_2E2(A_27c,A_27d,V1f2_2E0,V6y_2E0)) )
=> ! [V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V2al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),V3mal_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27d)),V4v_2E0: tyop_2Efinite__map_2Efmap(A_27b,A_27d)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f1_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27c),V2al_2E0)),c_2Epred__set_2EUNIV_2E0(A_27b)))
& ( V3mal_2E0 = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2EUNCURRY_2E1(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27d)))),F0_2E0,V0f1_2E0),V1f2_2E0)),V2al_2E0) )
& ( V4v_2E0 = c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27b,A_27d,V0f1_2E0,c_2Efinite__map_2Eo__f_2E2(A_27a,A_27c,A_27d,V1f2_2E0,c_2Ealist_2Ealist__to__fmap_2E1(A_27a,A_27c,V2al_2E0))) ) )
=> ( c_2Ealist_2Ealist__to__fmap_2E1(A_27b,A_27d,V3mal_2E0) = V4v_2E0 ) ) ) ).
tff(thm_2Ealist_2EMAP__values__fmap__to__alist,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(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2k_2E0: A_27c,V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0),V2k_2E0),V3v_2E0) = c_2Epair_2E_2C_2E2(A_27c,A_27b,V2k_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3v_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1fm_2E0: tyop_2Efinite__map_2Efmap(A_27c,A_27a)] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0)),c_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27a,V1fm_2E0)) = c_2Ealist_2Efmap__to__alist_2E1(A_27c,A_27b,c_2Efinite__map_2Eo__f_2E2(A_27c,A_27a,A_27b,V0f_2E0,V1fm_2E0)) ) ) ).
tff(thm_2Ealist_2EMAP__KEYS__I,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EMAP__KEYS_2E2(A_27a,A_27a,A_27b,c_2Ecombin_2EI_2E0(A_27a),V0fm_2E0) = V0fm_2E0 ) ).
tff(thm_2Ealist_2Ealist__to__fmap__MAP__values,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(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2k_2E0: A_27c,V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0),V2k_2E0),V3v_2E0) = c_2Epair_2E_2C_2E2(A_27c,A_27b,V2k_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3v_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1al_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27b,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2EUNCURRY_2E1(A_27c,A_27a,tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0,V0f_2E0)),V1al_2E0)) = c_2Efinite__map_2Eo__f_2E2(A_27c,A_27a,A_27b,V0f_2E0,c_2Ealist_2Ealist__to__fmap_2E1(A_27c,A_27a,V1al_2E0)) ) ) ).
tff(thm_2Ealist_2Eset__MAP__FST__fmap__to__alist,axiom,
! [A_27a: $tType,A_27b: $tType,V0fm_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( 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),c_2Ealist_2Efmap__to__alist_2E1(A_27a,A_27b,V0fm_2E0))) = c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V0fm_2E0) ) ).
tff(thm_2Ealist_2Ealookup__distinct__reverse,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a] :
( 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),V0l_2E0)))
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l_2E0),V1k_2E0) = c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V0l_2E0,V1k_2E0) ) ) ).
tff(thm_2Ealist_2Eflookup__fupdate__list,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b))] :
( ! [V3v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),F0_2E0,V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V3v_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1k_2E0: A_27a,V2m_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V2m_2E0,V0l_2E0),V1k_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l_2E0),V1k_2E0),c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,V2m_2E0,V1k_2E0),F0_2E0) ) ) ).
tff(thm_2Ealist_2Efupdate__list__funion,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))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,V0m_2E0,V1l_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1l_2E0),V0m_2E0) ) ).
tff(thm_2Ealist_2Emem__to__flookup,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b,V2l_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),V2l_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V2l_2E0))) )
=> ( c_2Efinite__map_2EFLOOKUP_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V2l_2E0),V0x_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V1y_2E0) ) ) ).
tff(thm_2Ealist_2Ealookup__filter,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))] :
( ! [V2x_2E0: A_27b,V3x_27_2E0: A_27b,V4y_2E0: A_27c] :
( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),F0_2E0,V2x_2E0),V3x_27_2E0),V4y_2E0))
<=> ( V2x_2E0 = V3x_27_2E0 ) )
=> ! [V0f_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),V2x_2E0: A_27b] : ( c_2Ealist_2EALOOKUP_2E2(A_27c,A_27b,V1l_2E0,V2x_2E0) = c_2Ealist_2EALOOKUP_2E2(A_27c,A_27b,c_2Elist_2EFILTER_2E2(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),F0_2E0,V2x_2E0)),V1l_2E0),V2x_2E0) ) ) ).
tff(thm_2Ealist_2Ealookup__stable__sorted,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1sort_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0))
& p(c_2Esorting_2ESTABLE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1sort_2E0,c_2Erelation_2Einv__image_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,V0R_2E0,c_2Epair_2EFST_2E0(A_27a,A_27b)))) )
=> ( c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1sort_2E0,c_2Erelation_2Einv__image_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,V0R_2E0,c_2Epair_2EFST_2E0(A_27a,A_27b))),V3l_2E0),V2x_2E0) = c_2Ealist_2EALOOKUP_2E2(A_27b,A_27a,V3l_2E0,V2x_2E0) ) ) ).
tff(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__PERM__same,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))] :
( ( 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),V0l1_2E0)))
& p(c_2Esorting_2EPERM_2E2(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_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1l2_2E0)))
& ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l1_2E0) = c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1l2_2E0) ) )
=> ( c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,V0l1_2E0) = c_2Ealist_2EALOOKUP_2E1(A_27b,A_27a,V1l2_2E0) ) ) ).
%------------------------------------------------------------------------------