ITP001 Axioms: ITP053_7.ax
%------------------------------------------------------------------------------
% File : ITP053_7 : TPTP v9.0.0. 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 : sorting.ax [Gau19]
% : HL4053_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 372 ( 119 unt; 144 typ; 0 def)
% Number of atoms : 516 ( 218 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 301 ( 13 ~; 5 |; 98 &)
% ( 44 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 122 ( 73 >; 49 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 141 ( 141 usr; 16 con; 0-7 aty)
% Number of variables : 1065 ( 916 !; 9 ?;1065 :)
% ( 140 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_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_23_23_2E0,type,
c_2Epair_2E_23_23_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))) ).
tff(c_2Epair_2E_23_23_2E2,type,
c_2Epair_2E_23_23_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)) ) ).
tff(c_2Epair_2E_23_23_2E3,type,
c_2Epair_2E_23_23_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Epair_2Eprod(A_27c,A_27d) ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E1,type,
c_2Earithmetic_2E_2B_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_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_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_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_2E1,type,
c_2Emin_2E_3D_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ecombin_2EASSOC_2E0,type,
c_2Ecombin_2EASSOC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2EASSOC_2E1,type,
c_2Ecombin_2EASSOC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2ECOMM_2E0,type,
c_2Ecombin_2ECOMM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2ECOMM_2E1,type,
c_2Ecombin_2ECOMM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) > tyop_2Emin_2Ebool ) ).
tff(c_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_2E1,type,
c_2Elist_2ECONS_2E1:
!>[A_27a: $tType] : ( 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_2Erich__list_2ECOUNT__LIST_2E0,type,
c_2Erich__list_2ECOUNT__LIST_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)) ).
tff(c_2Erich__list_2ECOUNT__LIST_2E1,type,
c_2Erich__list_2ECOUNT__LIST_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Erelation_2EEQC_2E0,type,
c_2Erelation_2EEQC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2EEQC_2E1,type,
c_2Erelation_2EEQC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_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_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_2Elist_2EGENLIST_2E0,type,
c_2Elist_2EGENLIST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EGENLIST_2E2,type,
c_2Elist_2EGENLIST_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELAST_2E0,type,
c_2Elist_2ELAST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2ELAST_2E1,type,
c_2Elist_2ELAST_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_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_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Esorting_2EPART_2E0,type,
c_2Esorting_2EPART_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))))) ).
tff(c_2Esorting_2EPART_2E4,type,
c_2Esorting_2EPART_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ) ).
tff(c_2Esorting_2EPART3_2E0,type,
c_2Esorting_2EPART3_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))))) ).
tff(c_2Esorting_2EPART3_2E3,type,
c_2Esorting_2EPART3_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ) ).
tff(c_2Esorting_2EPARTITION_2E0,type,
c_2Esorting_2EPARTITION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Esorting_2EPARTITION_2E2,type,
c_2Esorting_2EPARTITION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ) ).
tff(c_2Esorting_2EPERM_2E0,type,
c_2Esorting_2EPERM_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Esorting_2EPERM_2E1,type,
c_2Esorting_2EPERM_2E1:
!>[A_27a: $tType] : ( 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_2Esorting_2EPERM__SINGLE__SWAP_2E0,type,
c_2Esorting_2EPERM__SINGLE__SWAP_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__SINGLE__SWAP_2E2,type,
c_2Esorting_2EPERM__SINGLE__SWAP_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Esorting_2EQSORT_2E0,type,
c_2Esorting_2EQSORT_2E0:
!>[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))) ).
tff(c_2Esorting_2EQSORT_2E2,type,
c_2Esorting_2EQSORT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Esorting_2EQSORT3_2E0,type,
c_2Esorting_2EQSORT3_2E0:
!>[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))) ).
tff(c_2Esorting_2EQSORT3_2E2,type,
c_2Esorting_2EQSORT3_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Erich__list_2EREPLICATE_2E0,type,
c_2Erich__list_2EREPLICATE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Erich__list_2EREPLICATE_2E2,type,
c_2Erich__list_2EREPLICATE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a ) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Erelation_2ERTC_2E0,type,
c_2Erelation_2ERTC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERTC_2E1,type,
c_2Erelation_2ERTC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_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_2Esorting_2ESORTED_2E0,type,
c_2Esorting_2ESORTED_2E0:
!>[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_2Emin_2Ebool)) ).
tff(c_2Esorting_2ESORTED_2E2,type,
c_2Esorting_2ESORTED_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Esorting_2ESORTS_2E0,type,
c_2Esorting_2ESORTS_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_2ESORTS_2E2,type,
c_2Esorting_2ESORTS_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_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_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Elist_2ESUM_2E0,type,
c_2Elist_2ESUM_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ESUM_2E1,type,
c_2Elist_2ESUM_2E1: tyop_2Elist_2Elist(tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2ESUM__IMAGE_2E0,type,
c_2Epred__set_2ESUM__IMAGE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)) ).
tff(c_2Epred__set_2ESUM__IMAGE_2E2,type,
c_2Epred__set_2ESUM__IMAGE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Erelation_2ETC_2E0,type,
c_2Erelation_2ETC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ETC_2E1,type,
c_2Erelation_2ETC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2ETC_2E3,type,
c_2Erelation_2ETC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_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_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_2Erelation_2Eantisymmetric_2E0,type,
c_2Erelation_2Eantisymmetric_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_2Eantisymmetric_2E1,type,
c_2Erelation_2Eantisymmetric_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Ecount_2E0,type,
c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2Ecount_2E1,type,
c_2Epred__set_2Ecount_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eequivalence_2E0,type,
c_2Erelation_2Eequivalence_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_2Eequivalence_2E1,type,
c_2Erelation_2Eequivalence_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
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_2Erelation_2Eirreflexive_2E0,type,
c_2Erelation_2Eirreflexive_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_2Eirreflexive_2E1,type,
c_2Erelation_2Eirreflexive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > 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_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_23_23_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Epair_2E_23_23_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_23_23_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))] : ( c_2Epair_2E_23_23_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Epair_2E_23_23_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),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_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Emin_2E_3D_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_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(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EAPPEND_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EASSOC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Ebool_2ECOND_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Elist_2ECONS_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2ECONS_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2ECOUNT__LIST_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Erich__list_2ECOUNT__LIST_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,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(arityeq1_2Ec_2Erelation_2EEQC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EEQC_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFILTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EFOLDR_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EGENLIST_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EHD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EHD_2E0(A_27a),X0_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_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELAST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ELAST_2E0(A_27a),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(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(A_27b,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Esorting_2EPART_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPART_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Esorting_2EPART_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Esorting_2EPART3_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPART3_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Esorting_2EPART3_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EPARTITION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPARTITION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Esorting_2EPARTITION_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esorting_2EPERM_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E1(A_27a,X0_2E0) = 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) ) ).
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_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Esorting_2EPERM_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Esorting_2EPERM_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esorting_2EPERM_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Esorting_2EPERM_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EPERM__SINGLE__SWAP_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__SINGLE__SWAP_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__SINGLE__SWAP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EQSORT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(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)),c_2Esorting_2EQSORT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EQSORT3_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EQSORT3_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(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)),c_2Esorting_2EQSORT3_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EREPLICATE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),c_2Erich__list_2EREPLICATE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERTC_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(tyop_2Elist_2Elist(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_2Elist_2ESET__TO__LIST_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Elist_2ESET__TO__LIST_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESET__TO__LIST_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2ESORTED_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2ESORTED_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Esorting_2ESORTED_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2ESORTED_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Esorting_2ESORTED_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Esorting_2ESORTED_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2ESORTED_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esorting_2ESORTED_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Esorting_2ESORTED_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2ESORTS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: 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))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2ESORTS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(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),c_2Esorting_2ESORTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2ESTABLE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: 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))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2ESTABLE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(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),c_2Esorting_2ESTABLE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ESUM_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Elist_2ESUM_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erelation_2ETC_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Epair_2EUNCURRY_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),c_2Epair_2EUNCURRY_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),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_2Erelation_2Eantisymmetric_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_2Eantisymmetric_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_2Eantisymmetric_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eequivalence_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eequivalence_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27b_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(A_27b,A_27a)] : ( c_2Erelation_2Einv__image_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(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(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)] : ( c_2Erelation_2Einv__image_2E2(A_27b,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E0(A_27b,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eirreflexive_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_2Eirreflexive_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_2Eirreflexive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_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_2Erelation_2Etransitive_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2Etransitive_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E0(tyop_2Elist_2Elist(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_2Esorting_2EPERM__DEF,axiom,
! [A_27a: $tType,V0L1_2E0: tyop_2Elist_2Elist(A_27a),V1L2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0L1_2E0,V1L2_2E0))
<=> ! [V2x_2E0: A_27a] : ( c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V2x_2E0),V0L1_2E0) = c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V2x_2E0),V1L2_2E0) ) ) ).
tff(thm_2Esorting_2ESORTS__DEF,axiom,
! [A_27a: $tType,V0f_2E0: 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))),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Esorting_2ESORTS_2E2(A_27a,V0f_2E0,V1R_2E0))
<=> ! [V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V2l_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(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)),V0f_2E0,V1R_2E0),V2l_2E0)))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V1R_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(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)),V0f_2E0,V1R_2E0),V2l_2E0))) ) ) ).
tff(thm_2Esorting_2EPART__DEF,axiom,
! [A_27a: $tType] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a),V1l1_2E0,V2l2_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V1l1_2E0,V2l2_2E0) )
& ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4h_2E0: A_27a,V5rst_2E0: tyop_2Elist_2Elist(A_27a),V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPART_2E4(A_27a,V3P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5rst_2E0),V6l1_2E0,V7l2_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V4h_2E0),c_2Esorting_2EPART_2E4(A_27a,V3P_2E0,V5rst_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V6l1_2E0),V7l2_2E0),c_2Esorting_2EPART_2E4(A_27a,V3P_2E0,V5rst_2E0,V6l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V7l2_2E0))) ) ) ).
tff(thm_2Esorting_2EPARTITION__DEF,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPARTITION_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,V1l_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) ) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__DEF,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,V0l1_2E0,V1l2_2E0))
<=> ? [V2x1_2E0: tyop_2Elist_2Elist(A_27a),V3x2_2E0: tyop_2Elist_2Elist(A_27a),V4x3_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V3x2_2E0),V4x3_2E0) )
& ( V1l2_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V4x3_2E0),V3x2_2E0) ) ) ) ).
tff(thm_2Esorting_2ESTABLE__DEF,axiom,
! [A_27a: $tType,V0sort_2E0: 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))),V1r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Esorting_2ESTABLE_2E2(A_27a,V0sort_2E0,V1r_2E0))
<=> ( p(c_2Esorting_2ESORTS_2E2(A_27a,V0sort_2E0,V1r_2E0))
& ! [V2p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2p_2E0,V3x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2p_2E0,V4y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1r_2E0,V3x_2E0),V4y_2E0)) )
=> ! [V5l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V2p_2E0,V5l_2E0) = c_2Elist_2EFILTER_2E2(A_27a,V2p_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(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)),V0sort_2E0,V1r_2E0),V5l_2E0)) ) ) ) ) ).
tff(thm_2Esorting_2EPART3__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V4hd_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2R_2E0),V3h_2E0),V4hd_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3h_2E0),V4hd_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4hd_2E0),V3h_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1h_2E0: A_27a] : ( c_2Esorting_2EPART3_2E3(A_27a,V0R_2E0,V1h_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0(A_27a),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a))) )
& ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V4hd_2E0: A_27a,V5tl_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3h_2E0,c_2Elist_2ECONS_2E2(A_27a,V4hd_2E0,V5tl_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2R_2E0),V3h_2E0),V4hd_2E0),c_2Epair_2E_23_23_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_23_23_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E1(A_27a,V4hd_2E0),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a))),c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3h_2E0,V5tl_2E0)),c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4hd_2E0),V3h_2E0),c_2Epair_2E_23_23_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E1(A_27a,V4hd_2E0),c_2Epair_2E_23_23_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a))),c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3h_2E0,V5tl_2E0)),c_2Epair_2E_23_23_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_23_23_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E1(A_27a,V4hd_2E0)),c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3h_2E0,V5tl_2E0)))) ) ) ) ).
tff(thm_2Esorting_2EPERM__REFL,axiom,
! [A_27a: $tType,V0L_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM_2E2(A_27a,V0L_2E0,V0L_2E0)) ).
tff(thm_2Esorting_2EPERM__INTRO,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0x_2E0 = V1y_2E0 )
=> p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,V1y_2E0)) ) ).
tff(thm_2Esorting_2EPERM__transitive,axiom,
! [A_27a: $tType] : p(c_2Erelation_2Etransitive_2E1(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM_2E0(A_27a))) ).
tff(thm_2Esorting_2EPERM__TRANS,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a),V2z_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,V1y_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V1y_2E0,V2z_2E0)) )
=> p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,V2z_2E0)) ) ).
tff(thm_2Esorting_2EPERM__SYM,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V1l2_2E0,V0l1_2E0) ) ).
tff(thm_2Esorting_2EPERM__CONG,axiom,
! [A_27a: $tType,V0L1_2E0: tyop_2Elist_2Elist(A_27a),V1L2_2E0: tyop_2Elist_2Elist(A_27a),V2L3_2E0: tyop_2Elist_2Elist(A_27a),V3L4_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V0L1_2E0,V2L3_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V1L2_2E0,V3L4_2E0)) )
=> p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0L1_2E0,V1L2_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V2L3_2E0,V3L4_2E0))) ) ).
tff(thm_2Esorting_2EPERM__MONO,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V0l1_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1l2_2E0))) ) ).
tff(thm_2Esorting_2EPERM__CONS__IFF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2l1_2E0),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V2l1_2E0,V1l2_2E0) ) ).
tff(thm_2Esorting_2EPERM__NIL,axiom,
! [A_27a: $tType,V0L_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V0L_2E0,c_2Elist_2ENIL_2E0(A_27a)))
<=> ( V0L_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) )
& ( p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0L_2E0))
<=> ( V0L_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).
tff(thm_2Esorting_2EPERM__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V1L_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a))))
<=> ( V1L_2E0 = c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) )
& ( p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)),V1L_2E0))
<=> ( V1L_2E0 = c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ) ).
tff(thm_2Esorting_2EPERM__CONS__EQ__APPEND,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27a),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a] :
( p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V0t_2E0),V1L_2E0))
<=> ? [V3M_2E0: tyop_2Elist_2Elist(A_27a),V4N_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V1L_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V3M_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V4N_2E0)) )
& p(c_2Esorting_2EPERM_2E2(A_27a,V0t_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3M_2E0,V4N_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V0l1_2E0))) ).
tff(thm_2Esorting_2ECONS__PERM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a),V2M_2E0: tyop_2Elist_2Elist(A_27a),V3N_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V1L_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2M_2E0,V3N_2E0)))
=> p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1L_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V2M_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V3N_2E0)))) ) ).
tff(thm_2Esorting_2EAPPEND__PERM__SYM,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Elist_2Elist(A_27a),V1B_2E0: tyop_2Elist_2Elist(A_27a),V2C_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0A_2E0,V1B_2E0),V2C_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1B_2E0,V0A_2E0),V2C_2E0)) ) ).
tff(thm_2Esorting_2EPERM__SPLIT__IF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1Q_2E0),V3x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
<=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1Q_2E0),V2l_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27a,V2l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2l_2E0),c_2Elist_2EFILTER_2E2(A_27a,V1Q_2E0,V2l_2E0)))) ) ) ).
tff(thm_2Esorting_2EPERM__SPLIT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM_2E2(A_27a,V1l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0),c_2Elist_2EFILTER_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1l_2E0)))) ).
tff(thm_2Esorting_2EFILTER__EQ__REP,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l_2E0) = c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l_2E0)),V0x_2E0) ) ).
tff(thm_2Esorting_2EFILTER__EQ__LENGTHS__EQ,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V2l1_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l2_2E0)) )
=> ( c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V2l1_2E0) = c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__alt,axiom,
! [A_27a: $tType,V0L1_2E0: tyop_2Elist_2Elist(A_27a),V1L2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0L1_2E0,V1L2_2E0))
<=> ! [V2x_2E0: A_27a] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V2x_2E0),V0L1_2E0)) = c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V2x_2E0),V1L2_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__IND,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
( ( p(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),V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V1x_2E0: A_27a,V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(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),V0P_2E0,V2l1_2E0),V3l2_2E0))
=> p(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),V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l1_2E0)),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V3l2_2E0))) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(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),V0P_2E0,V6l1_2E0),V7l2_2E0))
=> p(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),V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,V6l1_2E0))),c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V7l2_2E0)))) )
& ! [V8l1_2E0: tyop_2Elist_2Elist(A_27a),V9l2_2E0: tyop_2Elist_2Elist(A_27a),V10l3_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(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),V0P_2E0,V8l1_2E0),V9l2_2E0))
& p(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),V0P_2E0,V9l2_2E0),V10l3_2E0)) )
=> p(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),V0P_2E0,V8l1_2E0),V10l3_2E0)) ) )
=> ! [V11l1_2E0: tyop_2Elist_2Elist(A_27a),V12l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V11l1_2E0,V12l2_2E0))
=> p(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),V0P_2E0,V11l1_2E0),V12l2_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__SWAP__AT__FRONT,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,V3l1_2E0)),c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l2_2E0))) = c_2Esorting_2EPERM_2E2(A_27a,V3l1_2E0,V2l2_2E0) ) ).
tff(thm_2Esorting_2EPERM__SWAP__L__AT__FRONT,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: tyop_2Elist_2Elist(A_27a),V3y_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x_2E0,V3y_2E0),V1l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V3y_2E0,V2x_2E0),V0l2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V0l2_2E0) ) ).
tff(thm_2Esorting_2EPERM__STRONG__IND,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
( ( p(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),V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V1x_2E0: A_27a,V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V2l1_2E0,V3l2_2E0))
& p(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),V0P_2E0,V2l1_2E0),V3l2_2E0)) )
=> p(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),V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l1_2E0)),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V3l2_2E0))) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V6l1_2E0,V7l2_2E0))
& p(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),V0P_2E0,V6l1_2E0),V7l2_2E0)) )
=> p(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),V0P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,V6l1_2E0))),c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V7l2_2E0)))) )
& ! [V8l1_2E0: tyop_2Elist_2Elist(A_27a),V9l2_2E0: tyop_2Elist_2Elist(A_27a),V10l3_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V8l1_2E0,V9l2_2E0))
& p(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),V0P_2E0,V8l1_2E0),V9l2_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V9l2_2E0,V10l3_2E0))
& p(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),V0P_2E0,V9l2_2E0),V10l3_2E0)) )
=> p(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),V0P_2E0,V8l1_2E0),V10l3_2E0)) ) )
=> ! [V11l1_2E0: tyop_2Elist_2Elist(A_27a),V12l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V11l1_2E0,V12l2_2E0))
=> p(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),V0P_2E0,V11l1_2E0),V12l2_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__LENGTH,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__MEM__EQ,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__LIST__TO__SET,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0) ) ) ).
tff(thm_2Esorting_2ESORTED__IND,axiom,
! [A_27a: $tType,V0P_2E0: 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_2Emin_2Ebool))] :
( ( ! [V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V1R_2E0),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3x_2E0: A_27a] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2R_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Elist_2ENIL_2E0(A_27a))))
& ! [V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5x_2E0: A_27a,V6y_2E0: A_27a,V7rst_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4R_2E0),c_2Elist_2ECONS_2E2(A_27a,V6y_2E0,V7rst_2E0)))
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4R_2E0),c_2Elist_2ECONS_2E2(A_27a,V5x_2E0,c_2Elist_2ECONS_2E2(A_27a,V6y_2E0,V7rst_2E0)))) ) )
=> ! [V8v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V9v1_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V8v_2E0),V9v1_2E0)) ) ).
tff(thm_2Esorting_2ESORTED__DEF,axiom,
! [A_27a: $tType] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2ESORTED_2E2(A_27a,V2R_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a))) = c_2Ebool_2ET_2E0 )
& ! [V3y_2E0: A_27a,V4x_2E0: A_27a,V5rst_2E0: tyop_2Elist_2Elist(A_27a),V6R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V6R_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ECONS_2E2(A_27a,V3y_2E0,V5rst_2E0))))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6R_2E0,V4x_2E0),V3y_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V6R_2E0,c_2Elist_2ECONS_2E2(A_27a,V3y_2E0,V5rst_2E0))) ) ) ) ).
tff(thm_2Esorting_2ESORTED__EQ,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> ( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1L_2E0)))
<=> ( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1L_2E0))
& ! [V3y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1L_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) ) ) ) ) ).
tff(thm_2Esorting_2ESORTED__APPEND,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L1_2E0: tyop_2Elist_2Elist(A_27a),V2L2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1L1_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V2L2_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1L1_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2L2_2E0))) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0)) ) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1L1_2E0,V2L2_2E0))) ) ).
tff(thm_2Esorting_2EPART__LENGTH,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a),V4p_2E0: tyop_2Elist_2Elist(A_27a),V5q_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V4p_2E0,V5q_2E0) = c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,V1L_2E0,V2l1_2E0,V3l2_2E0) )
=> ( c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1L_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V4p_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V5q_2E0)) ) ) ).
tff(thm_2Esorting_2EPART__LENGTH__LEM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a),V4p_2E0: tyop_2Elist_2Elist(A_27a),V5q_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V4p_2E0,V5q_2E0) = c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,V1L_2E0,V2l1_2E0,V3l2_2E0) )
=> ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V4p_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1L_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0))))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V5q_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1L_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0)))) ) ) ).
tff(thm_2Esorting_2EPARTs__HAVE__PROP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2A_2E0: tyop_2Elist_2Elist(A_27a),V3B_2E0: tyop_2Elist_2Elist(A_27a),V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V2A_2E0,V3B_2E0) = c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,V1L_2E0,V4l1_2E0,V5l2_2E0) )
& ! [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V4l1_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V6x_2E0)) )
& ! [V7x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V7x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V5l2_2E0)))
=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V7x_2E0)) ) )
=> ( ! [V8z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V8z_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2A_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V8z_2E0)) )
& ! [V9z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V9z_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3B_2E0)))
=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V9z_2E0)) ) ) ) ).
tff(thm_2Esorting_2EPART__MEM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2a1_2E0: tyop_2Elist_2Elist(A_27a),V3a2_2E0: tyop_2Elist_2Elist(A_27a),V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V2a1_2E0,V3a2_2E0) = c_2Esorting_2EPART_2E4(A_27a,V0P_2E0,V1L_2E0,V4l1_2E0,V5l2_2E0) )
=> ! [V6x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1L_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,V5l2_2E0)))) = c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2a1_2E0,V3a2_2E0))) ) ) ).
tff(thm_2Esorting_2EQSORT__IND,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V10y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2ord_2E0),V3h_2E0),V10y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ord_2E0,V10y_2E0),V3h_2E0) )
=> ( ! [V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V7y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ord_2E0),V3h_2E0),V7y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ord_2E0,V7y_2E0),V3h_2E0) )
=> ! [V0P_2E0: 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_2Emin_2Ebool))] :
( ( ! [V1ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V1ord_2E0),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V4t_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ! [V5l1_2E0: tyop_2Elist_2Elist(A_27a),V6l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V5l1_2E0,V6l2_2E0) = c_2Esorting_2EPARTITION_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2ord_2E0),V3h_2E0),V4t_2E0) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2ord_2E0),V6l2_2E0)) )
& ! [V8l1_2E0: tyop_2Elist_2Elist(A_27a),V9l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V8l1_2E0,V9l2_2E0) = c_2Esorting_2EPARTITION_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2ord_2E0),V3h_2E0),V4t_2E0) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2ord_2E0),V8l1_2E0)) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2ord_2E0),c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V4t_2E0))) ) )
=> ! [V11v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V12v1_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V11v_2E0),V12v1_2E0)) ) ) ) ).
tff(thm_2Esorting_2EQSORT__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),F0_2E0,V2ord_2E0),V3h_2E0),V4l1_2E0),V5l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Esorting_2EQSORT_2E2(A_27a,V2ord_2E0,V4l1_2E0),c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Esorting_2EQSORT_2E2(A_27a,V2ord_2E0,V5l2_2E0)) )
=> ( ! [V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a,V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2ord_2E0),V3h_2E0),V6y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ord_2E0,V6y_2E0),V3h_2E0) )
=> ( ! [V0ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2EQSORT_2E2(A_27a,V0ord_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1t_2E0: tyop_2Elist_2Elist(A_27a),V2ord_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3h_2E0: A_27a] : ( c_2Esorting_2EQSORT_2E2(A_27a,V2ord_2E0,c_2Elist_2ECONS_2E2(A_27a,V3h_2E0,V1t_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),F0_2E0,V2ord_2E0),V3h_2E0)),c_2Esorting_2EPARTITION_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2ord_2E0),V3h_2E0),V1t_2E0)) ) ) ) ) ).
tff(thm_2Esorting_2EQSORT__MEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Esorting_2EQSORT_2E2(A_27a,V0R_2E0,V1L_2E0))) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1L_2E0)) ) ).
tff(thm_2Esorting_2EQSORT__PERM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM_2E2(A_27a,V1L_2E0,c_2Esorting_2EQSORT_2E2(A_27a,V0R_2E0,V1L_2E0))) ).
tff(thm_2Esorting_2EQSORT__SORTED,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Esorting_2EQSORT_2E2(A_27a,V0R_2E0,V1L_2E0))) ) ).
tff(thm_2Esorting_2EQSORT__SORTS,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> p(c_2Esorting_2ESORTS_2E2(A_27a,c_2Esorting_2EQSORT_2E0(A_27a),V0R_2E0)) ) ).
tff(thm_2Esorting_2EPERM__APPEND__IFF,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V1l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V2l2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0) )
& ! [V3l_2E0: tyop_2Elist_2Elist(A_27a),V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V4l1_2E0,V3l_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V5l2_2E0,V3l_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V4l1_2E0,V5l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__SYM,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,V1l2_2E0,V0l1_2E0) ) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__I,axiom,
! [A_27a: $tType,V0x3_2E0: tyop_2Elist_2Elist(A_27a),V1x2_2E0: tyop_2Elist_2Elist(A_27a),V2x1_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V1x2_2E0),V0x3_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V0x3_2E0),V1x2_2E0))) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__APPEND,axiom,
! [A_27a: $tType,V0x3_2E0: tyop_2Elist_2Elist(A_27a),V1x2_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x2_2E0,V0x3_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0x3_2E0,V1x2_2E0))) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__REFL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,V0l_2E0,V0l_2E0)) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1N_2E0: tyop_2Elist_2Elist(A_27a),V2M_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,V2M_2E0,V1N_2E0))
=> p(c_2Esorting_2EPERM__SINGLE__SWAP_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2M_2E0),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1N_2E0))) ) ).
tff(thm_2Esorting_2EPERM__SINGLE__SWAP__TC__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1M_2E0: tyop_2Elist_2Elist(A_27a),V2N_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erelation_2ETC_2E3(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM__SINGLE__SWAP_2E0(A_27a),V1M_2E0,V2N_2E0))
=> p(c_2Erelation_2ETC_2E3(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM__SINGLE__SWAP_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1M_2E0),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2N_2E0))) ) ).
tff(thm_2Esorting_2EPERM__TC,axiom,
! [A_27a: $tType] : ( c_2Esorting_2EPERM_2E0(A_27a) = c_2Erelation_2ETC_2E1(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM__SINGLE__SWAP_2E0(A_27a)) ) ).
tff(thm_2Esorting_2EPERM__RTC,axiom,
! [A_27a: $tType] : ( c_2Esorting_2EPERM_2E0(A_27a) = c_2Erelation_2ERTC_2E1(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM__SINGLE__SWAP_2E0(A_27a)) ) ).
tff(thm_2Esorting_2EPERM__EQC,axiom,
! [A_27a: $tType] : ( c_2Esorting_2EPERM_2E0(A_27a) = c_2Erelation_2EEQC_2E1(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM__SINGLE__SWAP_2E0(A_27a)) ) ).
tff(thm_2Esorting_2EPERM__lifts__transitive__relations,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( ! [V2x1_2E0: tyop_2Elist_2Elist(A_27a),V3x2_2E0: tyop_2Elist_2Elist(A_27a),V4x3_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V3x2_2E0),V4x3_2E0))),app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2x1_2E0,V4x3_2E0),V3x2_2E0))))
& p(c_2Erelation_2Etransitive_2E1(A_27b,V1Q_2E0)) )
=> ! [V5x_2E0: tyop_2Elist_2Elist(A_27a),V6y_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V5x_2E0,V6y_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,V5x_2E0)),app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,V6y_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__lifts__equalities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)] :
( ! [V1x1_2E0: tyop_2Elist_2Elist(A_27a),V2x2_2E0: tyop_2Elist_2Elist(A_27a),V3x3_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V2x2_2E0),V3x3_2E0)) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V3x3_2E0),V2x2_2E0)) )
=> ! [V4x_2E0: tyop_2Elist_2Elist(A_27a),V5y_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V4x_2E0,V5y_2E0))
=> ( app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,V4x_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,V0f_2E0,V5y_2E0) ) ) ) ).
tff(thm_2Esorting_2EPERM__lifts__invariants,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( ! [V1x1_2E0: tyop_2Elist_2Elist(A_27a),V2x2_2E0: tyop_2Elist_2Elist(A_27a),V3x3_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V2x2_2E0),V3x3_2E0)))
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V3x3_2E0),V2x2_2E0))) )
=> ! [V4x_2E0: tyop_2Elist_2Elist(A_27a),V5y_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V4x_2E0,V5y_2E0)) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V5y_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__lifts__monotonicities,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] :
( ! [V1x1_2E0: tyop_2Elist_2Elist(A_27a),V2x2_2E0: tyop_2Elist_2Elist(A_27a),V3x3_2E0: tyop_2Elist_2Elist(A_27a)] :
? [V4x1_27_2E0: tyop_2Elist_2Elist(A_27b),V5x2_27_2E0: tyop_2Elist_2Elist(A_27b),V6x3_27_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V2x2_2E0),V3x3_2E0)) = c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2EAPPEND_2E2(A_27b,V4x1_27_2E0,V5x2_27_2E0),V6x3_27_2E0) )
& ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0f_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1x1_2E0,V3x3_2E0),V2x2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2EAPPEND_2E2(A_27b,V4x1_27_2E0,V6x3_27_2E0),V5x2_27_2E0) ) )
=> ! [V7x_2E0: tyop_2Elist_2Elist(A_27a),V8y_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V7x_2E0,V8y_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0f_2E0,V7x_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0f_2E0,V8y_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__EQUIVALENCE,axiom,
! [A_27a: $tType] : p(c_2Erelation_2Eequivalence_2E1(tyop_2Elist_2Elist(A_27a),c_2Esorting_2EPERM_2E0(A_27a))) ).
tff(thm_2Esorting_2EPERM__EQUIVALENCE__ALT__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,V1y_2E0))
<=> ( c_2Esorting_2EPERM_2E1(A_27a,V0x_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V1y_2E0) ) ) ).
tff(thm_2Esorting_2EALL__DISTINCT__PERM,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l1_2E0) = c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__ALL__DISTINCT,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0l1_2E0))
& p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1l2_2E0))
& ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)) ) )
=> p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0)) ) ).
tff(thm_2Esorting_2EALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V0ls_2E0,c_2Elist_2ESET__TO__LIST_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0ls_2E0))) ) ).
tff(thm_2Esorting_2EPERM__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l1_2E0),c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l2_2E0))) ) ).
tff(thm_2Esorting_2EPERM__SUM,axiom,
! [V0l1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] :
( p(c_2Esorting_2EPERM_2E2(tyop_2Enum_2Enum,V0l1_2E0,V1l2_2E0))
=> ( c_2Elist_2ESUM_2E1(V0l1_2E0) = c_2Elist_2ESUM_2E1(V1l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__FILTER,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l1_2E0),c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2l2_2E0))) ) ).
tff(thm_2Esorting_2EPERM__REVERSE,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Esorting_2EPERM_2E2(A_27a,V0ls_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V0ls_2E0))) ).
tff(thm_2Esorting_2EPERM__REVERSE__EQ,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1l1_2E0),V0l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V0l2_2E0) )
& ( c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V0l2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V0l2_2E0) ) ) ).
tff(thm_2Esorting_2EFOLDR__PERM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3e_2E0: A_27a] :
( ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
& p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0)) )
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0))
=> ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V3e_2E0,V1l1_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V3e_2E0,V2l2_2E0) ) ) ) ).
tff(thm_2Esorting_2EPERM__SET__TO__LIST__count__COUNT__LIST,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Esorting_2EPERM_2E2(tyop_2Enum_2Enum,c_2Elist_2ESET__TO__LIST_2E1(tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(V0n_2E0)),c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0))) ).
tff(thm_2Esorting_2ESUM__IMAGE__count__SUM__GENLIST,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,V1f_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)) = c_2Elist_2ESUM_2E1(c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,V1f_2E0,V0n_2E0)) ) ).
tff(thm_2Esorting_2ESUM__IMAGE__count__MULT,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))] :
( ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1k_2E0: tyop_2Enum_2Enum,V4m_2E0: tyop_2Enum_2Enum,V5x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0,V3f_2E0),V1k_2E0),V4m_2E0),V5x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V3f_2E0,c_2Earithmetic_2E_2B_2E2(V5x_2E0,c_2Earithmetic_2E_2A_2E2(V1k_2E0,V4m_2E0))) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum,V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ! [V4m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4m_2E0,V0n_2E0))
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2g_2E0,V4m_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0,V3f_2E0),V1k_2E0),V4m_2E0),c_2Epred__set_2Ecount_2E1(V1k_2E0)) ) )
=> ( c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,V3f_2E0,c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2E_2A_2E2(V1k_2E0,V0n_2E0))) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,V2g_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)) ) ) ) ).
tff(thm_2Esorting_2Esum__of__sums,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V2a_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V2a_2E0),V3m_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0,V3m_2E0),c_2Epred__set_2Ecount_2E1(V2a_2E0)) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V2a_2E0: tyop_2Enum_2Enum,V4m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F1_2E0,V0f_2E0),V2a_2E0),V4m_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0,c_2Earithmetic_2EDIV_2E2(V4m_2E0,V2a_2E0)),c_2Earithmetic_2EMOD_2E2(V4m_2E0,V2a_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1b_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V2a_2E0),c_2Epred__set_2Ecount_2E1(V1b_2E0)) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F1_2E0,V0f_2E0),V2a_2E0),c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2E_2A_2E2(V2a_2E0,V1b_2E0))) ) ) ) ).
tff(thm_2Esorting_2ESORTED__NIL,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a))) ).
tff(thm_2Esorting_2ESORTED__SING,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a] : p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a)))) ).
tff(thm_2Esorting_2ESORTED__TL,axiom,
! [A_27a: $tType,V0xs_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V2R_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0xs_2E0)))
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V2R_2E0,V0xs_2E0)) ) ).
tff(thm_2Esorting_2ESORTED__EL__SUC,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1ls_2E0))
<=> ! [V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2ESUC_2E1(V2n_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V1ls_2E0)),c_2Elist_2EEL_2E2(A_27a,c_2Enum_2ESUC_2E1(V2n_2E0),V1ls_2E0))) ) ) ).
tff(thm_2Esorting_2ESORTED__EL__LESS,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> ! [V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1ls_2E0))
<=> ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V3n_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0))) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2EEL_2E2(A_27a,V2m_2E0,V1ls_2E0)),c_2Elist_2EEL_2E2(A_27a,V3n_2E0,V1ls_2E0))) ) ) ) ).
tff(thm_2Esorting_2ESORTED__APPEND__IFF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L1_2E0: tyop_2Elist_2Elist(A_27a),V2L2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1L1_2E0,V2L2_2E0)))
<=> ( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1L1_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V2L2_2E0))
& ( ( V1L1_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
| ( V2L2_2E0 = c_2Elist_2ENIL_2E0(A_27a) )
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,c_2Elist_2ELAST_2E1(A_27a,V1L1_2E0)),c_2Elist_2EHD_2E1(A_27a,V2L2_2E0))) ) ) ) ).
tff(thm_2Esorting_2EMEM__PERM,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l1_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l2_2E0)) ) ) ).
tff(thm_2Esorting_2ESORTED__PERM__EQ,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0)) )
=> ! [V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1l1_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V2l2_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0)) )
=> ( V1l1_2E0 = V2l2_2E0 ) ) ) ).
tff(thm_2Esorting_2EQSORT__eq__if__PERM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Eantisymmetric_2E1(A_27a,V0R_2E0)) )
=> ! [V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EQSORT_2E2(A_27a,V0R_2E0,V1l1_2E0) = c_2Esorting_2EQSORT_2E2(A_27a,V0R_2E0,V2l2_2E0) )
<=> p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V2l2_2E0)) ) ) ).
tff(thm_2Esorting_2ESORTED__FILTER,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1ls_2E0: tyop_2Elist_2Elist(A_27a),V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1ls_2E0)) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2EFILTER_2E2(A_27a,V2P_2E0,V1ls_2E0))) ) ).
tff(thm_2Esorting_2EALL__DISTINCT__SORTED__WEAKEN,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
& ( V3x_2E0 != V4y_2E0 ) )
=> ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_27_2E0,V3x_2E0),V4y_2E0) ) )
& p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V2ls_2E0))
& p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V2ls_2E0)) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V1R_27_2E0,V2ls_2E0)) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND__C,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V0l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V1l1_27_2E0) )
=> ( ( c_2Esorting_2EPERM_2E1(A_27a,V2l2_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V3l2_27_2E0) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_27_2E0,V3l2_27_2E0)) ) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V2l1_27_2E0) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2l1_27_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2l2_2E0))) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l1_2E0),V2l2_2E0)) ) ).
tff(thm_2Esorting_2EPERM__FUN__SWAP__AT__FRONT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ECONS_2E2(A_27a,V1y_2E0,V2l_2E0))) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1y_2E0,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2l_2E0))) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS__11__SWAP__AT__FRONT,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l2_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,V3l2_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS__11__APPEND,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l3_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2l2_2E0,V3l3_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2l2_2E0,c_2Elist_2ECONS_2E2(A_27a,V0y_2E0,V3l3_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS__APPEND__1,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l2_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l2_2E0,V0l_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS__APPEND__2,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l2_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V3l2_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND__APPEND__1,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l3_2E0: tyop_2Elist_2Elist(A_27a),V3l4_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V0l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V2l3_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V3l4_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l3_2E0,V3l4_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND__APPEND__2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l3_2E0: tyop_2Elist_2Elist(A_27a),V3l4_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V0l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V2l3_2E0)) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V3l4_2E0,V0l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l4_2E0,V2l3_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V0l1_2E0)) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONS__IFF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V2l1_27_2E0) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V2l1_27_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__APPEND__IFF,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V1l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V2l2_2E0) )
=> ( c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V1l1_2E0)) = c_2Esorting_2EPERM_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V2l2_2E0)) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__CONG,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E1(A_27a,V0l1_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V1l1_27_2E0) )
=> ( ( c_2Esorting_2EPERM_2E1(A_27a,V2l2_2E0) = c_2Esorting_2EPERM_2E1(A_27a,V3l2_27_2E0) )
=> ( c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V2l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_27_2E0,V3l2_27_2E0) ) ) ) ).
tff(thm_2Esorting_2EPERM__CONG__2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V1l1_27_2E0))
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V2l2_2E0,V3l2_27_2E0))
=> ( c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V2l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V1l1_27_2E0,V3l2_27_2E0) ) ) ) ).
tff(thm_2Esorting_2EPERM__CONG__APPEND__IFF,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a),V4l2_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V2l1_27_2E0)))
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V3l2_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V4l2_27_2E0)))
=> ( c_2Esorting_2EPERM_2E2(A_27a,V1l1_2E0,V3l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V2l1_27_2E0,V4l2_27_2E0) ) ) ) ).
tff(thm_2Esorting_2EPERM__CONG__APPEND__IFF2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l1_27_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_27_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a),V4l2_27_2E0: tyop_2Elist_2Elist(A_27a),V5l2_27_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_27_2E0,V2l1_27_27_2E0)))
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V3l2_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V4l2_27_2E0,V5l2_27_27_2E0)))
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V1l1_27_2E0,V4l2_27_2E0))
=> ( c_2Esorting_2EPERM_2E2(A_27a,V0l1_2E0,V3l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V2l1_27_27_2E0,V5l2_27_27_2E0) ) ) ) ) ).
tff(thm_2Esorting_2EPERM__FUN__SPLIT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l1_27_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V3l2_2E0)))
=> ( p(c_2Esorting_2EPERM_2E2(A_27a,V2l1_27_2E0,V1l1_2E0))
=> p(c_2Esorting_2EPERM_2E2(A_27a,V0l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_27_2E0,V3l2_2E0))) ) ) ).
tff(thm_2Esorting_2EPERM__REWR,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1r_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2EPERM_2E2(A_27a,V0l_2E0,V1r_2E0))
=> ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,V2l1_2E0),V3l2_2E0) = c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1r_2E0,V2l1_2E0),V3l2_2E0) ) ) ).
tff(thm_2Esorting_2EPERM__TO__APPEND__SIMPS,axiom,
! [A_27a: $tType,A_27b: $tType,V0zs_2E0: tyop_2Elist_2Elist(A_27a),V1ys_2E0: tyop_2Elist_2Elist(A_27a),V2xs_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a,V4r2_2E0: tyop_2Elist_2Elist(A_27a),V5r1_2E0: tyop_2Elist_2Elist(A_27a),V6r_2E0: tyop_2Elist_2Elist(A_27a),V7l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V7l_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V5r1_2E0),V4r2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V7l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,V4r2_2E0)) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V7l_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4r2_2E0))) = c_2Esorting_2EPERM_2E2(A_27a,V7l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,V4r2_2E0)) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,V1ys_2E0),V0zs_2E0),V6r_2E0) = c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1ys_2E0,V0zs_2E0)),V6r_2E0) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V1ys_2E0),V0zs_2E0),V6r_2E0) = c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1ys_2E0,V0zs_2E0)),V6r_2E0) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V7l_2E0),V6r_2E0) = c_2Esorting_2EPERM_2E2(A_27a,V7l_2E0,V6r_2E0) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,V7l_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,V5r1_2E0),V4r2_2E0)) = c_2Esorting_2EPERM_2E2(A_27a,V7l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,V4r2_2E0)) )
& ( c_2Esorting_2EPERM_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,V7l_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,V4r2_2E0))) = c_2Esorting_2EPERM_2E2(A_27a,V7l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V5r1_2E0,V4r2_2E0)) )
& ( c_2Esorting_2EPERM_2E2(A_27b,c_2Elist_2ENIL_2E0(A_27b),c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2ENIL_2E0(A_27b),c_2Elist_2ENIL_2E0(A_27b))) = c_2Ebool_2ET_2E0 )
& ( c_2Esorting_2EPERM_2E2(A_27a,V2xs_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a))) = c_2Ebool_2ET_2E0 )
& ( c_2Esorting_2EPERM_2E2(A_27a,V2xs_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2EAPPEND_2E2(A_27a,V2xs_2E0,c_2Elist_2ENIL_2E0(A_27a)))) = c_2Ebool_2ET_2E0 ) ) ).
tff(thm_2Esorting_2EPART3__FILTER,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2hd_2E0: A_27a,V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2hd_2E0),V4x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V2hd_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2hd_2E0),V4x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2hd_2E0: A_27a,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2hd_2E0),V3x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V2hd_2E0))
& ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2hd_2E0),V3x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2hd_2E0: A_27a,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2hd_2E0),V5x_2E0))
<=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V2hd_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1tl_2E0: tyop_2Elist_2Elist(A_27a),V2hd_2E0: A_27a] : ( c_2Esorting_2EPART3_2E3(A_27a,V0R_2E0,V2hd_2E0,V1tl_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2hd_2E0),V1tl_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2hd_2E0),V1tl_2E0),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2hd_2E0),V1tl_2E0))) ) ) ) ) ).
tff(thm_2Esorting_2EQSORT3__IND,axiom,
! [A_27a: $tType,V0P_2E0: 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_2Emin_2Ebool))] :
( ( ! [V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V1R_2E0),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3hd_2E0: A_27a,V4tl_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ! [V5lo_2E0: tyop_2Elist_2Elist(A_27a),V6eq_2E0: tyop_2Elist_2Elist(A_27a),V7hi_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),V5lo_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V6eq_2E0,V7hi_2E0)) = c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3hd_2E0,V4tl_2E0) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2R_2E0),V7hi_2E0)) )
& ! [V8lo_2E0: tyop_2Elist_2Elist(A_27a),V9eq_2E0: tyop_2Elist_2Elist(A_27a),V10hi_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),V8lo_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V9eq_2E0,V10hi_2E0)) = c_2Esorting_2EPART3_2E3(A_27a,V2R_2E0,V3hd_2E0,V4tl_2E0) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2R_2E0),V8lo_2E0)) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2R_2E0),c_2Elist_2ECONS_2E2(A_27a,V3hd_2E0,V4tl_2E0))) ) )
=> ! [V11v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V12v1_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V11v_2E0),V12v1_2E0)) ) ).
tff(thm_2Esorting_2EQSORT3__DEF,axiom,
! [A_27a: $tType,F1_2E0: 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_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)))))] :
( ! [V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4lo_2E0: tyop_2Elist_2Elist(A_27a),V2hd_2E0: A_27a,V5eq_2E0: tyop_2Elist_2Elist(A_27a),V6hi_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),F1_2E0,V3R_2E0),V4lo_2E0),V2hd_2E0),V5eq_2E0),V6hi_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Esorting_2EQSORT3_2E2(A_27a,V3R_2E0,V4lo_2E0),c_2Elist_2ECONS_2E2(A_27a,V2hd_2E0,V5eq_2E0)),c_2Esorting_2EQSORT3_2E2(A_27a,V3R_2E0,V6hi_2E0)) )
=> ( ! [V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2hd_2E0: A_27a,V4lo_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)))),F0_2E0,V3R_2E0),V2hd_2E0),V4lo_2E0) = c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),F1_2E0,V3R_2E0),V4lo_2E0),V2hd_2E0)) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1tl_2E0: tyop_2Elist_2Elist(A_27a),V2hd_2E0: A_27a,V3R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Esorting_2EQSORT3_2E2(A_27a,V3R_2E0,c_2Elist_2ECONS_2E2(A_27a,V2hd_2E0,V1tl_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)))),F0_2E0,V3R_2E0),V2hd_2E0)),c_2Esorting_2EPART3_2E3(A_27a,V3R_2E0,V2hd_2E0,V1tl_2E0)) ) ) ) ) ).
tff(thm_2Esorting_2EPERM3,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1a_2E0: tyop_2Elist_2Elist(A_27a),V2a_27_2E0: tyop_2Elist_2Elist(A_27a),V3b_2E0: tyop_2Elist_2Elist(A_27a),V4b_27_2E0: tyop_2Elist_2Elist(A_27a),V5c_2E0: tyop_2Elist_2Elist(A_27a),V6c_27_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2EPERM_2E2(A_27a,V1a_2E0,V2a_27_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V3b_2E0,V4b_27_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V5c_2E0,V6c_27_2E0))
& p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V1a_2E0,V3b_2E0),V5c_2E0))) )
=> p(c_2Esorting_2EPERM_2E2(A_27a,V0x_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2a_27_2E0,V4b_27_2E0),V6c_27_2E0))) ) ).
tff(thm_2Esorting_2EPERM3__FILTER,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2h_2E0: A_27a,V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2h_2E0),V4x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V2h_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2h_2E0),V4x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2h_2E0: A_27a,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2h_2E0),V3x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V2h_2E0))
& ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2h_2E0),V3x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2h_2E0: A_27a,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2h_2E0),V5x_2E0))
<=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V2h_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a] : p(c_2Esorting_2EPERM_2E2(A_27a,V1l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2h_2E0),V1l_2E0),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2h_2E0),V1l_2E0)),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2h_2E0),V1l_2E0)))) ) ) ) ).
tff(thm_2Esorting_2EPERM__QSORT3,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Esorting_2EPERM_2E2(A_27a,V0l_2E0,c_2Esorting_2EQSORT3_2E2(A_27a,V1R_2E0,V0l_2E0))) ).
tff(thm_2Esorting_2ESORTED__EQ__PART,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0hd_2E0: A_27a,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2R_2E0),V0hd_2E0),V3x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3x_2E0),V0hd_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V0hd_2E0),V3x_2E0)) ) )
=> ! [V0hd_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V2R_2E0))
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V2R_2E0,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2R_2E0),V0hd_2E0),V1l_2E0))) ) ) ).
tff(thm_2Esorting_2EQSORT3__SORTS,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> p(c_2Esorting_2ESORTS_2E2(A_27a,c_2Esorting_2EQSORT3_2E0(A_27a),V0R_2E0)) ) ).
tff(thm_2Esorting_2EQSORT3__SPLIT,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2e_2E0: A_27a,V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2e_2E0),V4x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4x_2E0),V2e_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2e_2E0),V4x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2e_2E0: A_27a,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2e_2E0),V3x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V2e_2E0))
& ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2e_2E0),V3x_2E0)) ) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2e_2E0: A_27a,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2e_2E0),V5x_2E0))
<=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V2e_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V2e_2E0: A_27a] : ( c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,V1l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V2e_2E0),V1l_2E0)),c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0R_2E0),V2e_2E0),V1l_2E0)),c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V0R_2E0),V2e_2E0),V1l_2E0))) ) ) ) ) ) ).
tff(thm_2Esorting_2EQSORT3__STABLE,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> p(c_2Esorting_2ESTABLE_2E2(A_27a,c_2Esorting_2EQSORT3_2E0(A_27a),V0R_2E0)) ) ).
tff(thm_2Esorting_2EQSORT3__MEM,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,V1L_2E0))) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1L_2E0)) ) ).
tff(thm_2Esorting_2EQSORT3__SORTED,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etotal_2E1(A_27a,V0R_2E0)) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Esorting_2EQSORT3_2E2(A_27a,V0R_2E0,V1L_2E0))) ) ).
tff(thm_2Esorting_2Esorted__count__list,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Esorting_2ESORTED_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_3C_3D_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0))) ).
tff(thm_2Esorting_2Esorted__map,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27b)] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0))
=> ( c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f_2E0,V2l_2E0)) = c_2Esorting_2ESORTED_2E2(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,A_27a,V0R_2E0,V1f_2E0),V2l_2E0) ) ) ).
tff(thm_2Esorting_2Esorted__perm__count__list,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2l_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Esorting_2ESORTED_2E2(A_27b,c_2Erelation_2Einv__image_2E2(A_27b,tyop_2Enum_2Enum,c_2Earithmetic_2E_3C_3D_2E0,V1f_2E0),V2l_2E0))
& p(c_2Esorting_2EPERM_2E2(tyop_2Enum_2Enum,c_2Elist_2EMAP_2E2(A_27b,tyop_2Enum_2Enum,V1f_2E0,V2l_2E0),c_2Erich__list_2ECOUNT__LIST_2E1(V3n_2E0))) )
=> ( c_2Elist_2EMAP_2E2(A_27b,tyop_2Enum_2Enum,V1f_2E0,V2l_2E0) = c_2Erich__list_2ECOUNT__LIST_2E1(V3n_2E0) ) ) ).
tff(thm_2Esorting_2ESORTED__weaken,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V2ls_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_27_2E0,V3x_2E0),V4y_2E0)) ) )
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V1R_27_2E0,V2ls_2E0)) ) ).
tff(thm_2Esorting_2Eless__sorted__eq,axiom,
! [V0L_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1x_2E0: tyop_2Enum_2Enum] :
( p(c_2Esorting_2ESORTED_2E2(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0,c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V1x_2E0,V0L_2E0)))
<=> ( p(c_2Esorting_2ESORTED_2E2(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0,V0L_2E0))
& ! [V2y_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2y_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V0L_2E0)))
=> p(c_2Eprim__rec_2E_3C_2E2(V1x_2E0,V2y_2E0)) ) ) ) ).
tff(thm_2Esorting_2ESORTED__GENLIST__PLUS,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum] : p(c_2Esorting_2ESORTED_2E2(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E0,c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V1k_2E0),V0n_2E0))) ).
tff(thm_2Esorting_2ESORTED__ALL__DISTINCT,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( p(c_2Erelation_2Eirreflexive_2E1(A_27a,V0R_2E0))
& p(c_2Erelation_2Etransitive_2E1(A_27a,V0R_2E0)) )
=> ! [V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esorting_2ESORTED_2E2(A_27a,V0R_2E0,V1ls_2E0))
=> p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V1ls_2E0)) ) ) ).
tff(thm_2Esorting_2Esorted__filter,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erelation_2Etransitive_2E1(A_27a,V1R_2E0))
=> ( p(c_2Esorting_2ESORTED_2E2(A_27a,V1R_2E0,V2ls_2E0))
=> p(c_2Esorting_2ESORTED_2E2(A_27a,V1R_2E0,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2ls_2E0))) ) ) ).
%------------------------------------------------------------------------------