ITP001 Axioms: ITP037_7.ax
%------------------------------------------------------------------------------
% File : ITP037_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : rich_list.ax [Gau19]
% : HL4037_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 827 ( 338 unt; 221 typ; 0 def)
% Number of atoms : 1014 ( 653 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 439 ( 31 ~; 15 |; 85 &)
% ( 52 <=>; 256 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 184 ( 112 >; 72 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 218 ( 218 usr; 24 con; 0-5 aty)
% Number of variables : 2480 (2243 !; 5 ?;2480 :)
% ( 232 !>; 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_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_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_2Earithmetic_2E_3E_2E0,type,
c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_2E2,type,
c_2Earithmetic_2E_3E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
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_2Erich__list_2EAND__EL_2E0,type,
c_2Erich__list_2EAND__EL_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Erich__list_2EAND__EL_2E1,type,
c_2Erich__list_2EAND__EL_2E1: tyop_2Elist_2Elist(tyop_2Emin_2Ebool) > 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_2Epred__set_2EBIGINTER_2E0,type,
c_2Epred__set_2EBIGINTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EBIGINTER_2E1,type,
c_2Epred__set_2EBIGINTER_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Erich__list_2EBUTLASTN_2E0,type,
c_2Erich__list_2EBUTLASTN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Erich__list_2EBUTLASTN_2E2,type,
c_2Erich__list_2EBUTLASTN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Erich__list_2ECOUNT__LIST__AUX_2E0,type,
c_2Erich__list_2ECOUNT__LIST__AUX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))) ).
tff(c_2Erich__list_2ECOUNT__LIST__AUX_2E2,type,
c_2Erich__list_2ECOUNT__LIST__AUX_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Enum_2Enum) ) > tyop_2Elist_2Elist(tyop_2Enum_2Enum) ).
tff(c_2Elist_2EDROP_2E0,type,
c_2Elist_2EDROP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EDROP_2E2,type,
c_2Elist_2EDROP_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).
tff(c_2Erich__list_2EELL_2E0,type,
c_2Erich__list_2EELL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Erich__list_2EELL_2E2,type,
c_2Erich__list_2EELL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E1,type,
c_2Elist_2EEVERY_2E1:
!>[A_27a: $tType] : ( 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_2Elist_2EEXISTS_2E0,type,
c_2Elist_2EEXISTS_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_2EEXISTS_2E1,type,
c_2Elist_2EEXISTS_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2EEXISTS_2E2,type,
c_2Elist_2EEXISTS_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_2Ecombin_2EFAIL_2E0,type,
c_2Ecombin_2EFAIL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EFAIL_2E2,type,
c_2Ecombin_2EFAIL_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
tff(c_2Ecombin_2EFCOMM_2E0,type,
c_2Ecombin_2EFCOMM_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2EFCOMM_2E2,type,
c_2Ecombin_2EFCOMM_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)) ) > 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_2E1,type,
c_2Elist_2EFILTER_2E1:
!>[A_27a: $tType] : ( 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_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EFLAT_2E0,type,
c_2Elist_2EFLAT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EFLAT_2E1,type,
c_2Elist_2EFLAT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E2,type,
c_2Elist_2EFOLDL_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b ) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b) ) ).
tff(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Elist_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_2E2,type,
c_2Elist_2EFOLDR_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * 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_2EFRONT_2E0,type,
c_2Elist_2EFRONT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EFRONT_2E1,type,
c_2Elist_2EFRONT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Earithmetic_2EFUNPOW_2E0,type,
c_2Earithmetic_2EFUNPOW_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Earithmetic_2EFUNPOW_2E3,type,
c_2Earithmetic_2EFUNPOW_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Enum_2Enum * A_27a ) > A_27a ) ).
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_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_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_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Erich__list_2EIS__SUBLIST_2E0,type,
c_2Erich__list_2EIS__SUBLIST_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_2Erich__list_2EIS__SUBLIST_2E2,type,
c_2Erich__list_2EIS__SUBLIST_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erich__list_2EIS__SUFFIX_2E0,type,
c_2Erich__list_2EIS__SUFFIX_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_2Erich__list_2EIS__SUFFIX_2E2,type,
c_2Erich__list_2EIS__SUFFIX_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Elist_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_2Erich__list_2ELASTN_2E0,type,
c_2Erich__list_2ELASTN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Erich__list_2ELASTN_2E2,type,
c_2Erich__list_2ELASTN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ecombin_2ELEFT__ID_2E0,type,
c_2Ecombin_2ELEFT__ID_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_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2ELEFT__ID_2E2,type,
c_2Ecombin_2ELEFT__ID_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27a ) > tyop_2Emin_2Ebool ) ).
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_2Erich__list_2ELIST__ELEM__COUNT_2E0,type,
c_2Erich__list_2ELIST__ELEM__COUNT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Erich__list_2ELIST__ELEM__COUNT_2E2,type,
c_2Erich__list_2ELIST__ELEM__COUNT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ELIST__REL_2E0,type,
c_2Elist_2ELIST__REL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Elist_2ELIST__REL_2E3,type,
c_2Elist_2ELIST__REL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ELUPDATE_2E0,type,
c_2Elist_2ELUPDATE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Elist_2ELUPDATE_2E3,type,
c_2Elist_2ELUPDATE_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
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_2E1,type,
c_2Elist_2EMAP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( 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_2Ecombin_2EMONOID_2E0,type,
c_2Ecombin_2EMONOID_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2EMONOID_2E2,type,
c_2Ecombin_2EMONOID_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Elist_2ENULL_2E0,type,
c_2Elist_2ENULL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2ENULL_2E1,type,
c_2Elist_2ENULL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Erich__list_2EOR__EL_2E0,type,
c_2Erich__list_2EOR__EL_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Erich__list_2EOR__EL_2E1,type,
c_2Erich__list_2EOR__EL_2E1: tyop_2Elist_2Elist(tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ).
tff(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Erich__list_2EPREFIX_2E0,type,
c_2Erich__list_2EPREFIX_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_2Erich__list_2EPREFIX_2E2,type,
c_2Erich__list_2EPREFIX_2E2:
!>[A_27a: $tType] : ( ( 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_2Ecombin_2ERIGHT__ID_2E0,type,
c_2Ecombin_2ERIGHT__ID_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2ERIGHT__ID_2E2,type,
c_2Ecombin_2ERIGHT__ID_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erich__list_2ESCANL_2E0,type,
c_2Erich__list_2ESCANL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))) ).
tff(c_2Erich__list_2ESCANL_2E3,type,
c_2Erich__list_2ESCANL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Erich__list_2ESCANR_2E0,type,
c_2Erich__list_2ESCANR_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),tyop_2Elist_2Elist(A_27b)))) ).
tff(c_2Erich__list_2ESCANR_2E3,type,
c_2Erich__list_2ESCANR_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) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Erich__list_2ESEG_2E0,type,
c_2Erich__list_2ESEG_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Erich__list_2ESEG_2E3,type,
c_2Erich__list_2ESEG_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Elist_2ESNOC_2E0,type,
c_2Elist_2ESNOC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ESNOC_2E2,type,
c_2Elist_2ESNOC_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Erich__list_2ESPLITL_2E0,type,
c_2Erich__list_2ESPLITL_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_2Erich__list_2ESPLITL_2E1,type,
c_2Erich__list_2ESPLITL_2E1:
!>[A_27a: $tType] : ( 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_2Erich__list_2ESPLITP_2E0,type,
c_2Erich__list_2ESPLITP_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_2Erich__list_2ESPLITP_2E1,type,
c_2Erich__list_2ESPLITP_2E1:
!>[A_27a: $tType] : ( 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_2Erich__list_2ESPLITP_2E2,type,
c_2Erich__list_2ESPLITP_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_2Erich__list_2ESPLITP__AUX_2E0,type,
c_2Erich__list_2ESPLITP__AUX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Erich__list_2ESPLITP__AUX_2E1,type,
c_2Erich__list_2ESPLITP__AUX_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > 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_2Erich__list_2ESPLITP__AUX_2E3,type,
c_2Erich__list_2ESPLITP__AUX_2E3:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * 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_2Erich__list_2ESPLITR_2E0,type,
c_2Erich__list_2ESPLITR_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_2Erich__list_2ESPLITR_2E2,type,
c_2Erich__list_2ESPLITR_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_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_2Erich__list_2ESUFFIX_2E0,type,
c_2Erich__list_2ESUFFIX_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_2Erich__list_2ESUFFIX_2E2,type,
c_2Erich__list_2ESUFFIX_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_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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Elist_2ETAKE_2E0,type,
c_2Elist_2ETAKE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ETAKE_2E2,type,
c_2Elist_2ETAKE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Erich__list_2ETL__T_2E0,type,
c_2Erich__list_2ETL__T_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Erich__list_2ETL__T_2E1,type,
c_2Erich__list_2ETL__T_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Elist_2EUNIQUE_2E0,type,
c_2Elist_2EUNIQUE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EUNIQUE_2E2,type,
c_2Elist_2EUNIQUE_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EUNZIP_2E0,type,
c_2Elist_2EUNZIP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EUNZIP_2E1,type,
c_2Elist_2EUNZIP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) ) ).
tff(c_2Erich__list_2EUNZIP__FST_2E0,type,
c_2Erich__list_2EUNZIP__FST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Erich__list_2EUNZIP__FST_2E1,type,
c_2Erich__list_2EUNZIP__FST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Erich__list_2EUNZIP__SND_2E0,type,
c_2Erich__list_2EUNZIP__SND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Erich__list_2EUNZIP__SND_2E1,type,
c_2Erich__list_2EUNZIP__SND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Elist_2EZIP_2E0,type,
c_2Elist_2EZIP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Elist_2EZIP_2E1,type,
c_2Elist_2EZIP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Erich__list_2Ecommon__prefixes_2E0,type,
c_2Erich__list_2Ecommon__prefixes_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Erich__list_2Ecommon__prefixes_2E1,type,
c_2Erich__list_2Ecommon__prefixes_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Elist_2EisPREFIX_2E0,type,
c_2Elist_2EisPREFIX_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_2Elist_2EisPREFIX_2E2,type,
c_2Elist_2EisPREFIX_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Eis__measure__maximal_2E0,type,
c_2Epred__set_2Eis__measure__maximal_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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2Eis__measure__maximal_2E3,type,
c_2Epred__set_2Eis__measure__maximal_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erich__list_2Elongest__prefix_2E0,type,
c_2Erich__list_2Elongest__prefix_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Erich__list_2Elongest__prefix_2E1,type,
c_2Erich__list_2Elongest__prefix_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_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_2D_2E0,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(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_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_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_2Emin_2E_40_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),c_2Emin_2E_40_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EALL__DISTINCT_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2EAND__EL_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EAND__EL_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Erich__list_2EAND__EL_2E0,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(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EAPPEND_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_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EAPPEND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EAPPEND_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_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_2EASSOC_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_2Elist_2Elist(A_27a)))] : ( c_2Ecombin_2EASSOC_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_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EBUTLASTN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Erich__list_2EBUTLASTN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EBUTLASTN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Erich__list_2EBUTLASTN_2E0(A_27b),X0_2E0),X1_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_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0),X2_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(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(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Elist_2ECONS_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ECONS_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27d,axiom,
! [A_27d: $tType,X0_2E0: A_27d,X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2ECONS_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d)),c_2Elist_2ECONS_2E0(A_27d),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_2Erich__list_2ECOUNT__LIST__AUX_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(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_2Erich__list_2ECOUNT__LIST__AUX_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EDROP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EDROP_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EDROP_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EEL_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Elist_2EEL_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EELL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_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_2Erich__list_2EELL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EELL_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2EELL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Erich__list_2EELL_2E0(A_27b),X0_2E0),X1_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_2EEVERY_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEVERY_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_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EEVERY_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EEVERY_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_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEXISTS_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_2EEXISTS_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_2EEXISTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EEXISTS_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEXISTS_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EFAIL_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFILTER_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Elist_2EFILTER_2E1(A_27a,X0_2E0) = 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) ) ).
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(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFILTER_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EFILTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EFILTER_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2EFILTER_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFLAT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))] : ( c_2Elist_2EFLAT_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFLAT_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum))] : ( c_2Elist_2EFLAT_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EFLAT_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDL_2E2_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] : ( c_2Elist_2EFOLDL_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = 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_2EFOLDL_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_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_2EFOLDL_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_2EFOLDL_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDL_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_27b,A_27a)),X1_2E0: A_27a] : ( c_2Elist_2EFOLDL_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EFOLDL_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EFOLDL_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDL_2E3(A_27c,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)),c_2Elist_2EFOLDL_2E0(A_27c,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Elist_2EFOLDL_2E0(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_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))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFOLDL_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFOLDL_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EFOLDL_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Elist_2EFOLDL_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDR_2E2_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] : ( c_2Elist_2EFOLDR_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = 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) ) ).
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(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(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)),c_2Elist_2EFOLDR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2EFOLDR_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Elist_2EFOLDR_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EFOLDR_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDR_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EFOLDR_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDR_2E3(A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b)),c_2Elist_2EFOLDR_2E0(A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Elist_2EFOLDR_2E0(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_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))),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFOLDR_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFOLDR_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EFOLDR_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Elist_2EFOLDR_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFRONT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EFST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_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_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Earithmetic_2EFUNPOW_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),c_2Elist_2EGENLIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),c_2Elist_2EGENLIST_2E0(A_27b),X0_2E0),X1_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(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum))),c_2Elist_2EGENLIST_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_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_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_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(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EHD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2EHD_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Elist_2Elist(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(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EIS__SUBLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUBLIST_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_2Erich__list_2EIS__SUBLIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EIS__SUFFIX_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUFFIX_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_2Erich__list_2EIS__SUFFIX_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EK_2E1(A_27a,tyop_2Enum_2Enum,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E0(A_27a,tyop_2Enum_2Enum),X0_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(arityeq2_2Ec_2Erich__list_2ELASTN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Erich__list_2ELASTN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ELASTN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2ELASTN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Erich__list_2ELASTN_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_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] : ( c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ELEFT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,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_2Elist_2Elist_28A_27a_29_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_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))),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_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_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_2Elist_2Elist(A_27a)),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ELIST__ELEM__COUNT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Erich__list_2ELIST__ELEM__COUNT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ELIST__ELEM__COUNT_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum),c_2Erich__list_2ELIST__ELEM__COUNT_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ELIST__ELEM__COUNT_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Erich__list_2ELIST__ELEM__COUNT_2E0(A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ELIST__ELEM__COUNT_2E2_2Emono_2EA_27d,axiom,
! [A_27d: $tType,X0_2E0: A_27d,X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Enum_2Enum,app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Enum_2Enum),c_2Erich__list_2ELIST__ELEM__COUNT_2E0(A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_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(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELUPDATE_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELUPDATE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,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,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27b,X0_2E0) = 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) ) ).
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_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E0(A_27a,tyop_2Emin_2Ebool),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_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_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_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27b),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_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(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2EMONOID_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_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_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ecombin_2EMONOID_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(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_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2EOR__EL_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EOR__EL_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Erich__list_2EOR__EL_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EPREFIX_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_2Erich__list_2EPREFIX_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_2Erich__list_2EPREFIX_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2EPREFIX_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2EPREFIX_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Erich__list_2EPREFIX_2E0(A_27b),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(arityeq2_2Ec_2Erich__list_2EREPLICATE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27b] : ( c_2Erich__list_2EREPLICATE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27b)),c_2Erich__list_2EREPLICATE_2E0(A_27b),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_2Elist_2EREVERSE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EREVERSE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EREVERSE_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EREVERSE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EREVERSE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_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] : ( c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ERIGHT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Erich__list_2ESCANL_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2ESCANL_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Erich__list_2ESCANL_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Erich__list_2ESCANL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESCANL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Erich__list_2ESCANL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Erich__list_2ESCANR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(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),tyop_2Elist_2Elist(A_27b))),c_2Erich__list_2ESCANR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Erich__list_2ESEG_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Erich__list_2ESEG_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ESND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))] : ( c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Epair_2ESND_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))] : ( c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Epair_2ESND_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_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_2ESNOC_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ESNOC_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ESNOC_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ESNOC_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2ESNOC_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESNOC_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_2ESNOC_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ESNOC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2ESPLITL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2ESPLITL_2E1(A_27a,X0_2E0) = 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_2Erich__list_2ESPLITL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2ESPLITP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2ESPLITP_2E1(A_27a,X0_2E0) = 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_2Erich__list_2ESPLITP_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ESPLITP_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_2Erich__list_2ESPLITP_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_2Erich__list_2ESPLITP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2ESPLITP__AUX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESPLITP__AUX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),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)))),c_2Erich__list_2ESPLITP__AUX_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Erich__list_2ESPLITP__AUX_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESPLITP__AUX_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_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))),app_2E2(tyop_2Elist_2Elist(A_27a),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)))),c_2Erich__list_2ESPLITP__AUX_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Erich__list_2ESPLITR_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_2Erich__list_2ESPLITR_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_2Erich__list_2ESPLITR_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(arityeq2_2Ec_2Erich__list_2ESUFFIX_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_2Erich__list_2ESUFFIX_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_2Erich__list_2ESUFFIX_2E0(A_27a),X0_2E0),X1_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_2Elist_2ETAKE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETAKE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ETAKE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ETAKE_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ETAKE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ETAKE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2ETL__T_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ETL__T_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2ETL__T_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27a))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a),c_2Epair_2EUNCURRY_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27b,A_27a,tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27a),c_2Epair_2EUNCURRY_2E0(A_27b,A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_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_2Epair_2EUNCURRY_2E0(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) ) ).
tff(arityeq2_2Ec_2Elist_2EUNIQUE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EUNIQUE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EUNIQUE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EUNZIP_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EUNZIP_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2EUNZIP__FST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Erich__list_2EUNZIP__FST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2EUNZIP__FST_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2EUNZIP__SND_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Erich__list_2EUNZIP__SND_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b),c_2Erich__list_2EUNZIP__SND_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2EUNZIP__SND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Erich__list_2EUNZIP__SND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2EUNZIP__SND_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum))] : ( c_2Elist_2EZIP_2E1(A_27a,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),c_2Elist_2EZIP_2E0(A_27a,tyop_2Enum_2Enum),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_2Erich__list_2Ecommon__prefixes_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Erich__list_2Ecommon__prefixes_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2Ecommon__prefixes_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Erich__list_2Ecommon__prefixes_2E0(A_27b),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(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_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_2Elist_2EisPREFIX_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2Eis__measure__maximal_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epred__set_2Eis__measure__maximal_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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2Eis__measure__maximal_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erich__list_2Elongest__prefix_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2Elongest__prefix_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(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_2Ebool)),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_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_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_2Erich__list_2Elongest__prefix__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0),V1x_2E0) = c_2Epred__set_2Eis__measure__maximal_2E3(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELENGTH_2E0(A_27a),c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0),V1x_2E0) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,V0s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Emin_2E_40_2E1(tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0))) ) ) ) ).
tff(thm_2Erich__list_2Ecommon__prefixes__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1p_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0),V1p_2E0))
<=> ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V2m_2E0,V0s_2E0))
=> p(c_2Elist_2EisPREFIX_2E2(A_27a,V1p_2E0,V2m_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1p_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0),V1p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V1p_2E0,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0),V1p_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EELL,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ELAST_2E1(A_27a,V0l_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),V2l_2E0) = c_2Erich__list_2EELL_2E2(A_27a,V1n_2E0,c_2Elist_2EFRONT_2E1(A_27a,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EREPLICATE,axiom,
! [A_27a: $tType] :
( ! [V0x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Enum_2E0_2E0,V0x_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),V2x_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V1n_2E0,V2x_2E0)) ) ) ).
tff(thm_2Erich__list_2ESCANL,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V1e_2E0: A_27b] : ( c_2Erich__list_2ESCANL_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(A_27b,V1e_2E0,c_2Elist_2ENIL_2E0(A_27b)) )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V3e_2E0: A_27b,V4x_2E0: A_27a,V5l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESCANL_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V5l_2E0)) = c_2Elist_2ECONS_2E2(A_27b,V3e_2E0,c_2Erich__list_2ESCANL_2E3(A_27a,A_27b,V2f_2E0,app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,V3e_2E0),V4x_2E0),V5l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESCANR,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b] : ( c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(A_27b,V1e_2E0,c_2Elist_2ENIL_2E0(A_27b)) )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3e_2E0: A_27b,V4x_2E0: A_27a,V5l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,V5l_2E0)) = c_2Elist_2ECONS_2E2(A_27b,app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V2f_2E0,V4x_2E0),c_2Elist_2EHD_2E1(A_27b,c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,V5l_2E0))),c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,V2f_2E0,V3e_2E0,V5l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESPLITP,axiom,
! [A_27a: $tType] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2ESPLITP_2E2(A_27a,V0P_2E0,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)) )
& ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESPLITP_2E2(A_27a,V1P_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_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,V1P_2E0,V2x_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2ESPLITP_2E2(A_27a,V1P_2E0,V3l_2E0))),c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2ESPLITP_2E2(A_27a,V1P_2E0,V3l_2E0)))) ) ) ).
tff(thm_2Erich__list_2ESPLITP__AUX__def,axiom,
! [A_27a: $tType] :
( ! [V0acc_2E0: tyop_2Elist_2Elist(A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2ESPLITP__AUX_2E3(A_27a,V0acc_2E0,V1P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V0acc_2E0,c_2Elist_2ENIL_2E0(A_27a)) )
& ! [V2acc_2E0: tyop_2Elist_2Elist(A_27a),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4h_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESPLITP__AUX_2E3(A_27a,V2acc_2E0,V3P_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_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_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V2acc_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_2E0)),c_2Erich__list_2ESPLITP__AUX_2E3(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2acc_2E0,c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3P_2E0,V5t_2E0)) ) ) ).
tff(thm_2Erich__list_2ESPLITL__def,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2ESPLITL_2E1(A_27a,V0P_2E0) = c_2Erich__list_2ESPLITP_2E1(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0)) ) ).
tff(thm_2Erich__list_2ESPLITR__def,axiom,
! [A_27a: $tType,F0_2E0: 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))))] :
( ! [V2a_2E0: tyop_2Elist_2Elist(A_27a),V3b_2E0: tyop_2Elist_2Elist(A_27a)] : ( 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))),F0_2E0,V2a_2E0),V3b_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(A_27a,V3b_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V2a_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESPLITR_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Ebool_2ELET_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)),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),F0_2E0),c_2Erich__list_2ESPLITP_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EPREFIX__DEF,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EPREFIX_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Erich__list_2ESPLITP_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_2Erich__list_2ESUFFIX__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_27_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(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(A_27a,tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),V2l_27_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0),c_2Elist_2ESNOC_2E2(A_27a,V3x_2E0,V2l_27_2E0),c_2Elist_2ENIL_2E0(A_27a)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESUFFIX_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(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(A_27a,tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),c_2Elist_2ENIL_2E0(A_27a),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EAND__EL__DEF,axiom,
c_2Erich__list_2EAND__EL_2E0 = c_2Elist_2EEVERY_2E1(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E0(tyop_2Emin_2Ebool)) ).
tff(thm_2Erich__list_2EOR__EL__DEF,axiom,
c_2Erich__list_2EOR__EL_2E0 = c_2Elist_2EEXISTS_2E1(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E0(tyop_2Emin_2Ebool)) ).
tff(thm_2Erich__list_2EUNZIP__FST__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Erich__list_2EUNZIP__FST_2E1(A_27a,A_27b,V0l_2E0) = c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V0l_2E0)) ) ).
tff(thm_2Erich__list_2EUNZIP__SND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Erich__list_2EUNZIP__SND_2E1(A_27a,A_27b,V0l_2E0) = c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),c_2Elist_2EUNZIP_2E1(A_27b,A_27a,V0l_2E0)) ) ).
tff(thm_2Erich__list_2ELIST__ELEM__COUNT__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0e_2E0: A_27a,V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0e_2E0),V2x_2E0))
<=> ( V2x_2E0 = V0e_2E0 ) )
=> ! [V0e_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27a,V0e_2E0,V1l_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0e_2E0),V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__def,axiom,
( ( c_2Erich__list_2ECOUNT__LIST_2E1(c_2Enum_2E0_2E0) = c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum) )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0))) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__AUX__def,axiom,
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V2l_2E0) = c_2Erich__list_2ECOUNT__LIST__AUX_2E2(V1n_2E0,c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V1n_2E0,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ETL__T__def,axiom,
! [A_27a: $tType] :
( ( c_2Erich__list_2ETL__T_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V0h_2E0: A_27a,V1t_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ETL__T_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0h_2E0,V1t_2E0)) = V1t_2E0 ) ) ).
tff(thm_2Erich__list_2ELASTN__def,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1xs_2E0) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1xs_2E0))) ) ).
tff(thm_2Erich__list_2EBUTLASTN__def,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1xs_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1xs_2E0) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1xs_2E0))) ) ).
tff(thm_2Erich__list_2EIS__SUBLIST,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Ebool_2EF_2E0 )
& ! [V3x1_2E0: A_27a,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5x2_2E0: A_27a,V6l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V3x1_2E0,V4l1_2E0),c_2Elist_2ECONS_2E2(A_27a,V5x2_2E0,V6l2_2E0)))
<=> ( ( ( V3x1_2E0 = V5x2_2E0 )
& p(c_2Elist_2EisPREFIX_2E2(A_27a,V6l2_2E0,V4l1_2E0)) )
| p(c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V4l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V5x2_2E0,V6l2_2E0))) ) ) ) ).
tff(thm_2Erich__list_2ESEG,axiom,
! [A_27a: $tType] :
( ! [V0k_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2E0_2E0,V0k_2E0,V1l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V2m_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2ESUC_2E1(V2m_2E0),c_2Enum_2E0_2E0,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Erich__list_2ESEG_2E3(A_27a,V2m_2E0,c_2Enum_2E0_2E0,V4l_2E0)) )
& ! [V5m_2E0: tyop_2Enum_2Enum,V6k_2E0: tyop_2Enum_2Enum,V7x_2E0: A_27a,V8l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2ESUC_2E1(V5m_2E0),c_2Enum_2ESUC_2E1(V6k_2E0),c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,V8l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2ESUC_2E1(V5m_2E0),V6k_2E0,V8l_2E0) ) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Ebool_2EF_2E0 )
& ! [V3x1_2E0: A_27a,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5x2_2E0: A_27a,V6l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V3x1_2E0,V4l1_2E0),c_2Elist_2ESNOC_2E2(A_27a,V5x2_2E0,V6l2_2E0)))
<=> ( ( V3x1_2E0 = V5x2_2E0 )
& p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V4l1_2E0,V6l2_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EEL__REPLICATE,axiom,
! [A_27a: $tType,V0n1_2E0: tyop_2Enum_2Enum,V1n2_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n1_2E0,V1n2_2E0))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n1_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V1n2_2E0,V2x_2E0)) = V2x_2E0 ) ) ).
tff(thm_2Erich__list_2EREPLICATE__GENLIST,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,V0n_2E0,V1x_2E0) = c_2Elist_2EGENLIST_2E2(A_27a,c_2Ecombin_2EK_2E1(A_27a,tyop_2Enum_2Enum,V1x_2E0),V0n_2E0) ) ).
tff(thm_2Erich__list_2ELIST__TO__SET__EQ__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1ls_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) )
<=> ( ( V1ls_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
& p(c_2Elist_2EEVERY_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1ls_2E0)) ) ) ).
tff(thm_2Erich__list_2ELIST__ELEM__COUNT__MEM,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Earithmetic_2E_3E_2E2(c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27a,V0e_2E0,V1l_2E0),c_2Enum_2E0_2E0) = c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) ) ).
tff(thm_2Erich__list_2ELIST__ELEM__COUNT__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0e_2E0: A_27a] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27a,V0e_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1e_2E0: A_27b,V2l1_2E0: tyop_2Elist_2Elist(A_27b),V3l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27b,V1e_2E0,c_2Elist_2EAPPEND_2E2(A_27b,V2l1_2E0,V3l2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27b,V1e_2E0,V2l1_2E0),c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27b,V1e_2E0,V3l2_2E0)) )
& ! [V4e_2E0: A_27c,V5h_2E0: A_27c,V6l_2E0: tyop_2Elist_2Elist(A_27c)] :
( ( V5h_2E0 = V4e_2E0 )
=> ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27c,V4e_2E0,c_2Elist_2ECONS_2E2(A_27c,V5h_2E0,V6l_2E0)) = c_2Enum_2ESUC_2E1(c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27c,V4e_2E0,V6l_2E0)) ) )
& ! [V7e_2E0: A_27d,V8h_2E0: A_27d,V9l_2E0: tyop_2Elist_2Elist(A_27d)] :
( ( V8h_2E0 != V7e_2E0 )
=> ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27d,V7e_2E0,c_2Elist_2ECONS_2E2(A_27d,V8h_2E0,V9l_2E0)) = c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27d,V7e_2E0,V9l_2E0) ) ) ) ).
tff(thm_2Erich__list_2EMEM__LAST__FRONT,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
& ( V0e_2E0 != c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1l_2E0)) ) )
=> p(c_2Ebool_2EIN_2E2(A_27a,V0e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1l_2E0))))) ) ).
tff(thm_2Erich__list_2EDROP__CONS__EL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EMEM__LAST,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Ebool_2EIN_2E2(A_27a,c_2Elist_2ELAST_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0e_2E0,V1l_2E0)),c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0e_2E0,V1l_2E0)))) ).
tff(thm_2Erich__list_2EEL__FRONT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0))))
& ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0)) )
=> ( c_2Elist_2EEL_2E2(A_27a,V1n_2E0,c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0)) = c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EFRONT__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2e_2E0: A_27a] : ( c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,V1l2_2E0))) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V2e_2E0,V1l2_2E0))) ) ).
tff(thm_2Erich__list_2EMEM__FRONT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1e_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,V0l_2E0)))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1e_2E0,V0l_2E0)))) ) ).
tff(thm_2Erich__list_2ESPLITP__EVERY,axiom,
! [A_27a: $tType,F0_2E0: 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),V2x_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),F0_2E0,V0P_2E0),V2x_2E0))
<=> ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_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),F0_2E0,V0P_2E0),V1l_2E0))
=> ( c_2Erich__list_2ESPLITP_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),V1l_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ) ).
tff(thm_2Erich__list_2EFOLDL__MAP2,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V4x_2E0: A_27a,V5y_2E0: A_27c] : ( app_2E2(A_27c,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))),F0_2E0,V0f_2E0),V2g_2E0),V4x_2E0),V5y_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V4x_2E0),app_2E2(A_27c,A_27b,V2g_2E0,V5y_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V3l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27b,V2g_2E0,V3l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))),F0_2E0,V0f_2E0),V2g_2E0),V1e_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EAPPEND__SNOC1,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V0l1_2E0),V2l2_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l2_2E0)) ) ).
tff(thm_2Erich__list_2EAPPEND__ASSOC__CONS,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1h_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27a),V3l3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2l2_2E0)),V3l3_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l2_2E0,V3l3_2E0))) ) ).
tff(thm_2Erich__list_2EZIP__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Elist_2Elist(A_27a),V1b_2E0: tyop_2Elist_2Elist(A_27b),V2c_2E0: tyop_2Elist_2Elist(A_27a),V3d_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( ( c_2Elist_2ELENGTH_2E1(A_27a,V0a_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1b_2E0) )
& ( c_2Elist_2ELENGTH_2E1(A_27a,V2c_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V3d_2E0) ) )
=> ( c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0a_2E0,V1b_2E0)),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V2c_2E0,V3d_2E0))) = c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V2c_2E0),c_2Elist_2EAPPEND_2E2(A_27b,V1b_2E0,V3d_2E0))) ) ) ).
tff(thm_2Erich__list_2EEL__TAKE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V1x_2E0,V0n_2E0))
=> ( c_2Elist_2EEL_2E2(A_27a,V1x_2E0,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V2l_2E0)) = c_2Elist_2EEL_2E2(A_27a,V1x_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EZIP__TAKE,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Elist_2Elist(A_27a),V2b_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1a_2E0)))
& ( c_2Elist_2ELENGTH_2E1(A_27a,V1a_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2b_2E0) ) )
=> ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1a_2E0),c_2Elist_2ETAKE_2E2(A_27b,V0n_2E0,V2b_2E0))) = c_2Elist_2ETAKE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0n_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1a_2E0,V2b_2E0))) ) ) ).
tff(thm_2Erich__list_2EZIP__TAKE__LEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Elist_2Elist(A_27a),V2b_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1a_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1a_2E0),c_2Elist_2ELENGTH_2E1(A_27b,V2b_2E0))) )
=> ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1a_2E0),c_2Elist_2ETAKE_2E2(A_27b,V0n_2E0,V2b_2E0))) = c_2Elist_2ETAKE_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0n_2E0,c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V1a_2E0,c_2Elist_2ETAKE_2E2(A_27b,c_2Elist_2ELENGTH_2E1(A_27a,V1a_2E0),V2b_2E0)))) ) ) ).
tff(thm_2Erich__list_2ESNOC__EL__TAKE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ESNOC_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__DROP,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,V0m_2E0,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V2l_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0),V2l_2E0) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__ADD,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V2n_27_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),F0_2E0,V0n_2E0),V2n_27_2E0) = c_2Earithmetic_2E_2B_2E2(V2n_27_2E0,V0n_2E0) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0)) = c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0),c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0n_2E0),c_2Erich__list_2ECOUNT__LIST_2E1(V1m_2E0))) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__COUNT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0)) = c_2Epred__set_2Ecount_2E1(V0n_2E0) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__SNOC,axiom,
( ( c_2Erich__list_2ECOUNT__LIST_2E1(c_2Enum_2E0_2E0) = c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum) )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Elist_2ESNOC_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0)) ) ) ).
tff(thm_2Erich__list_2EMEM__COUNT__LIST,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0m_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Erich__list_2ECOUNT__LIST_2E1(V1n_2E0))) = c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) ) ).
tff(thm_2Erich__list_2EEL__COUNT__LIST,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
=> ( c_2Elist_2EEL_2E2(tyop_2Enum_2Enum,V0m_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V1n_2E0)) = V0m_2E0 ) ) ).
tff(thm_2Erich__list_2ELENGTH__COUNT__LIST,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2ELENGTH_2E1(tyop_2Enum_2Enum,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0)) = V0n_2E0 ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__GENLIST,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0) = c_2Elist_2EGENLIST_2E2(tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum),V0n_2E0) ) ).
tff(thm_2Erich__list_2Elongest__prefix__PAIR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V3x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1y_2E0))
<=> ( V3x_2E0 = V1y_2E0 ) )
=> ! [V0ys_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: A_27a,V2xs_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] :
( ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V0ys_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))))) = c_2Elist_2ENIL_2E0(A_27a) )
& ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V2xs_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))))) = c_2Elist_2ENIL_2E0(A_27a) )
& ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V2xs_2E0),c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(A_27a,V1y_2E0,V0ys_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))))) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V3x_2E0),V1y_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V2xs_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V0ys_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)))))),c_2Elist_2ENIL_2E0(A_27a)) ) ) ) ).
tff(thm_2Erich__list_2Ecommon__prefixes__PAIR,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V4a_2E0: A_27b,V3b_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0,V4a_2E0),V3b_2E0))
<=> ( V4a_2E0 = V3b_2E0 ) )
=> ! [V0ys_2E0: tyop_2Elist_2Elist(A_27b),V1xs_2E0: tyop_2Elist_2Elist(A_27b),V2x_2E0: tyop_2Elist_2Elist(A_27a),V3b_2E0: A_27b,V4a_2E0: A_27b] :
( ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V2x_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))))) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) )
& ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V2x_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))))) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) )
& ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27b,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27b,V4a_2E0,V1xs_2E0),c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27b,V3b_2E0,V0ys_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27b))))) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b),c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0,V4a_2E0),V3b_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E1(A_27b,V4a_2E0),c_2Erich__list_2Ecommon__prefixes_2E1(A_27b,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),V1xs_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27b),V0ys_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27b)))))),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27b)))) ) ) ) ).
tff(thm_2Erich__list_2Elongest__prefix__SING,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),V0s_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)))) = V0s_2E0 ) ).
tff(thm_2Erich__list_2Elongest__prefix__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2Erich__list_2ENIL__IN__common__prefixes,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0))) ).
tff(thm_2Erich__list_2Elongest__prefix__NIL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0s_2E0))
=> ( c_2Erich__list_2Elongest__prefix_2E1(A_27a,V0s_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ) ).
tff(thm_2Erich__list_2Ecommon__prefixes__NIL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0s_2E0))
=> ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) ) ) ).
tff(thm_2Erich__list_2Elongest__prefix__UNIQUE,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: tyop_2Elist_2Elist(A_27a),V2s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( ( ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)) )
& p(c_2Epred__set_2Eis__measure__maximal_2E3(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELENGTH_2E0(A_27a),c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V2s_2E0),V1x_2E0))
& p(c_2Epred__set_2Eis__measure__maximal_2E3(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELENGTH_2E0(A_27a),c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V2s_2E0),V0y_2E0)) )
=> ( V1x_2E0 = V0y_2E0 ) ) ).
tff(thm_2Erich__list_2Etwo__common__prefixes,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1p2_2E0: tyop_2Elist_2Elist(A_27a),V2p1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)) )
& p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V2p1_2E0,c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Elist_2Elist(A_27a),V1p2_2E0,c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0))) )
=> ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V2p1_2E0,V1p2_2E0))
| p(c_2Elist_2EisPREFIX_2E2(A_27a,V1p2_2E0,V2p1_2E0)) ) ) ).
tff(thm_2Erich__list_2Ecommon__prefixes__NONEMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0) != c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)) ) ).
tff(thm_2Erich__list_2EFINITE__common__prefixes,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a)) )
=> p(c_2Epred__set_2EFINITE_2E1(tyop_2Elist_2Elist(A_27a),c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Erich__list_2EFINITE__prefix,axiom,
! [A_27a: $tType,F0_2E0: 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_2Emin_2Ebool)))] :
( ! [V0b_2E0: tyop_2Elist_2Elist(A_27a),V1a_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0b_2E0),V1a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V1a_2E0,c_2Elist_2EisPREFIX_2E2(A_27a,V1a_2E0,V0b_2E0)) )
=> ! [V0b_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Elist_2Elist(A_27a),c_2Epred__set_2EGSPEC_2E1(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_2Emin_2Ebool)),F0_2E0,V0b_2E0)))) ) ).
tff(thm_2Erich__list_2Ecommon__prefixes__BIGINTER,axiom,
! [A_27a: $tType,F1_2E0: 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_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] :
( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V2p_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0,V1l_2E0),V2p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V2p_2E0,c_2Elist_2EisPREFIX_2E2(A_27a,V2p_2E0,V1l_2E0)) )
=> ( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V1l_2E0) = c_2Epred__set_2EGSPEC_2E1(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_2Emin_2Ebool)),F1_2E0,V1l_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Erich__list_2Ecommon__prefixes_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EBIGINTER_2E1(tyop_2Elist_2Elist(A_27a),c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0s_2E0)) ) ) ) ).
tff(thm_2Erich__list_2Eprefixes__is__prefix__total,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)] :
( ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1l1_2E0,V0l_2E0))
& p(c_2Elist_2EisPREFIX_2E2(A_27a,V2l2_2E0,V0l_2E0)) )
=> ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1l1_2E0,V2l2_2E0))
| p(c_2Elist_2EisPREFIX_2E2(A_27a,V2l2_2E0,V1l1_2E0)) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__APPEND3,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Elist_2Elist(A_27a),V1a_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2EisPREFIX_2E2(A_27a,V1a_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1a_2E0,V0c_2E0))) ).
tff(thm_2Erich__list_2EIS__PREFIX__APPENDS,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)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V1b_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V2c_2E0)) = c_2Elist_2EisPREFIX_2E2(A_27a,V1b_2E0,V2c_2E0) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__APPEND2,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_2Elist_2EisPREFIX_2E2(A_27a,V0a_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1b_2E0,V2c_2E0)))
=> ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0a_2E0,V1b_2E0))
| p(c_2Elist_2EisPREFIX_2E2(A_27a,V1b_2E0,V0a_2E0)) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__APPEND1,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_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V0a_2E0,V1b_2E0),V2c_2E0))
=> p(c_2Elist_2EisPREFIX_2E2(A_27a,V0a_2E0,V2c_2E0)) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__SNOC,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: tyop_2Elist_2Elist(A_27a),V2z_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,V2z_2E0,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1y_2E0)))
<=> ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V2z_2E0,V1y_2E0))
| ( V2z_2E0 = c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1y_2E0) ) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__LENGTH__ANTI,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,V1y_2E0))
& ( c_2Elist_2ELENGTH_2E1(A_27a,V0x_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V1y_2E0) ) )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__LENGTH,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,V1y_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0x_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1y_2E0))) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__BUTLAST,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2EFRONT_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1y_2E0)),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1y_2E0))) ).
tff(thm_2Erich__list_2EIS__PREFIX__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_2Elist_2EisPREFIX_2E2(A_27a,V1y_2E0,V0x_2E0))
& p(c_2Elist_2EisPREFIX_2E2(A_27a,V2z_2E0,V1y_2E0)) )
=> p(c_2Elist_2EisPREFIX_2E2(A_27a,V2z_2E0,V0x_2E0)) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__ANTISYM,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1y_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,V1y_2E0))
& p(c_2Elist_2EisPREFIX_2E2(A_27a,V1y_2E0,V0x_2E0)) )
=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__REFL,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,V0x_2E0)) ).
tff(thm_2Erich__list_2EIS__PREFIX__NIL,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0x_2E0))
& ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)))
<=> ( V0x_2E0 = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).
tff(thm_2Erich__list_2EOR__EL__FOLDR,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EOR__EL_2E1(V0l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2EOR__EL__FOLDL,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EOR__EL_2E1(V0l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2EAND__EL__FOLDR,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EAND__EL_2E1(V0l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2EAND__EL__FOLDL,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EAND__EL_2E1(V0l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2EDROP__LENGTH__NIL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2Erich__list_2ETAKE__TAKE,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,V0m_2E0))
=> ( c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,c_2Elist_2ETAKE_2E2(A_27a,V0m_2E0,V1l_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,V1l_2E0) ) ) ) ).
tff(thm_2Erich__list_2ETAKE__TAKE__T,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,V0m_2E0))
=> ( c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,c_2Elist_2ETAKE_2E2(A_27a,V0m_2E0,V1l_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,V2n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEVERY__BUTLASTN,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V2m_2E0,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EEVERY__LASTN,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V2m_2E0,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27b,V0n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0)) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Erich__list_2ELASTN_2E2(A_27b,V0n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0)) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__APPEND1,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0),V1n_2E0))
=> ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V0l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)),V2l1_2E0),V0l2_2E0) ) ) ).
tff(thm_2Erich__list_2ELASTN__APPEND2,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0)))
=> ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__APPEND1,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0),V1n_2E0))
=> ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V0l2_2E0)) = c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)),V2l1_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__1,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0l_2E0) = c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2ELASTN__1,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0l_2E0) = c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2ELAST_2E1(A_27a,V0l_2E0),c_2Elist_2ENIL_2E0(A_27a)) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__LASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0))) )
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V1n_2E0,V2l_2E0)) = c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,V0m_2E0),c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V1m_2E0,V2l_2E0)) = c_2Erich__list_2EBUTLASTN_2E2(A_27a,V1m_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__LASTN__NIL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) = c_2Elist_2ENIL_2E0(A_27a) ) ) ).
tff(thm_2Erich__list_2ELAST__LASTN__LAST,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ( c_2Elist_2ELAST_2E1(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) = c_2Elist_2ELAST_2E1(A_27a,V1l_2E0) ) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__LENGTH__CONS,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).
tff(thm_2Erich__list_2EBUTLASTN__CONS,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = V0l2_2E0 ) ).
tff(thm_2Erich__list_2EBUTLASTN__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = V1l1_2E0 ) ).
tff(thm_2Erich__list_2EBUTLASTN__APPEND2,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V2l2_2E0)) ) ) ).
tff(thm_2Erich__list_2EAPPEND__TAKE__LASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) )
=> ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V2l_2E0),c_2Erich__list_2ELASTN_2E2(A_27a,V0m_2E0,V2l_2E0)) = V2l_2E0 ) ) ).
tff(thm_2Erich__list_2EAPPEND__BUTLASTN__LASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) = V1l_2E0 ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V1n_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,V2l_2E0)) = c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0m_2E0),V2l_2E0) ) ) ).
tff(thm_2Erich__list_2ELENGTH__BUTLASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__FRONT,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EFRONT_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFRONT_2E1(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__SUC__FRONT,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1l_2E0) = c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EFRONT_2E1(A_27a,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EELL__compute,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ELAST_2E1(A_27a,V0l_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2l_2E0) = c_2Erich__list_2EELL_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2EFRONT_2E1(A_27a,V2l_2E0)) )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4l_2E0) = c_2Erich__list_2EELL_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Elist_2EFRONT_2E1(A_27a,V4l_2E0)) ) ) ).
tff(thm_2Erich__list_2EREPLICATE__compute,axiom,
! [A_27a: $tType] :
( ! [V0x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Enum_2E0_2E0,V0x_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2x_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2x_2E0)) )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4x_2E0: A_27a] : ( c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4x_2E0) = c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),V4x_2E0)) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__AUX__def__compute,axiom,
( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2l_2E0) = c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2l_2E0)) )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4l_2E0) = c_2Erich__list_2ECOUNT__LIST__AUX_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),V4l_2E0)) ) ) ).
tff(thm_2Erich__list_2ETAKE,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V3l_2E0)) ) ) ).
tff(thm_2Erich__list_2EDROP,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_2E0)) = c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__FUNPOW__TL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Earithmetic_2EFUNPOW_2E3(tyop_2Elist_2Elist(A_27a),c_2Erich__list_2ETL__T_2E0(A_27a),V0n_2E0,V1l_2E0) ) ).
tff(thm_2Erich__list_2ENOT__NULL__SNOC,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ~ p(c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0))) ).
tff(thm_2Erich__list_2ELASTN,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27b,V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2ELASTN_2E2(A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ESNOC_2E2(A_27b,V2x_2E0,V3l_2E0)) = c_2Elist_2ESNOC_2E2(A_27b,V2x_2E0,c_2Erich__list_2ELASTN_2E2(A_27b,V1n_2E0,V3l_2E0)) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27b,V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ESNOC_2E2(A_27b,V2x_2E0,V3l_2E0)) = c_2Erich__list_2EBUTLASTN_2E2(A_27b,V1n_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2ELENGTH__NOT__NULL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
<=> ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0)) ) ).
tff(thm_2Erich__list_2ENOT__NIL__SNOC,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENIL_2E0(A_27a) != c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0) ) ).
tff(thm_2Erich__list_2ENOT__SNOC__NIL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0) != c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2Erich__list_2ESNOC__EQ__LENGTH__EQ,axiom,
! [A_27a: $tType,V0x1_2E0: A_27a,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2x2_2E0: A_27a,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Elist_2ESNOC_2E2(A_27a,V0x1_2E0,V1l1_2E0) = c_2Elist_2ESNOC_2E2(A_27a,V2x2_2E0,V3l2_2E0) )
=> ( c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0) ) ) ).
tff(thm_2Erich__list_2ESNOC__REVERSE__CONS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0))) ) ).
tff(thm_2Erich__list_2EFOLDR__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V3l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),V1e_2E0),V3l_2E0) ) ).
tff(thm_2Erich__list_2EFOLDR__FOLDL,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1e_2E0: A_27a] :
( p(c_2Ecombin_2EMONOID_2E2(A_27a,V0f_2E0,V1e_2E0))
=> ! [V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,V2l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2ELENGTH__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V1x_2E0: A_27a,V2l_27_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V1x_2E0),V2l_27_2E0) = c_2Enum_2ESUC_2E1(V2l_27_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Enum_2Enum,F0_2E0,c_2Enum_2E0_2E0,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2ELENGTH__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))] :
( ! [V1l_27_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),F0_2E0,V1l_27_2E0),V2x_2E0) = c_2Enum_2ESUC_2E1(V1l_27_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Enum_2Enum,F0_2E0,c_2Enum_2E0_2E0,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EMAP__FOLDR,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a,V3l_27_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),V2x_2E0),V3l_27_2E0) = c_2Elist_2ECONS_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),V3l_27_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),c_2Elist_2ENIL_2E0(A_27b),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EMAP__FOLDL,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_27_2E0: tyop_2Elist_2Elist(A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),V2l_27_2E0),V3x_2E0) = c_2Elist_2ESNOC_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2l_27_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),F0_2E0,V0f_2E0),c_2Elist_2ENIL_2E0(A_27b),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EFILTER__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3l_27_2E0: tyop_2Elist_2Elist(A_27a)] : ( 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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),V2x_2E0),V3l_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_27_2E0),V3l_27_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),c_2Elist_2ENIL_2E0(A_27a),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EFILTER__SNOC,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2l_2E0)),c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V2l_2E0)) ) ).
tff(thm_2Erich__list_2EFILTER__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_27_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(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(A_27a,tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),V2l_27_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0),c_2Elist_2ESNOC_2E2(A_27a,V3x_2E0,V2l_27_2E0),V2l_27_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(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(A_27a,tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),c_2Elist_2ENIL_2E0(A_27a),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EFILTER__COMM,axiom,
! [A_27a: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0f1_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1f2_2E0,V2l_2E0)) = c_2Elist_2EFILTER_2E2(A_27a,V1f2_2E0,c_2Elist_2EFILTER_2E2(A_27a,V0f1_2E0,V2l_2E0)) ) ).
tff(thm_2Erich__list_2EFILTER__IDEM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0f_2E0,c_2Elist_2EFILTER_2E2(A_27a,V0f_2E0,V1l_2E0)) = c_2Elist_2EFILTER_2E2(A_27a,V0f_2E0,V1l_2E0) ) ).
tff(thm_2Erich__list_2EFILTER__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f2_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0f1_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f2_2E0,V2l_2E0)) = c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f2_2E0,c_2Elist_2EFILTER_2E2(A_27b,c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Ebool,A_27a,V0f1_2E0,V1f2_2E0),V2l_2E0)) ) ).
tff(thm_2Erich__list_2ELENGTH__FILTER__LEQ,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1l_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0))) ).
tff(thm_2Erich__list_2EFILTER__EQ,axiom,
! [A_27a: $tType,V0P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Elist_2EFILTER_2E2(A_27a,V0P1_2E0,V2l_2E0) = c_2Elist_2EFILTER_2E2(A_27a,V1P2_2E0,V2l_2E0) )
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0)))
=> ( app_2E2(A_27a,tyop_2Emin_2Ebool,V0P1_2E0,V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P2_2E0,V3x_2E0) ) ) ) ).
tff(thm_2Erich__list_2ELENGTH__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1k_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1k_2E0,V2l_2E0)) = V0n_2E0 ) ) ).
tff(thm_2Erich__list_2EAPPEND__NIL,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V0l_2E0 )
& ! [V1l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,c_2Elist_2ENIL_2E0(A_27b),V1l_2E0) = V1l_2E0 ) ) ).
tff(thm_2Erich__list_2EAPPEND__FOLDR,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E0(A_27a),V1l2_2E0,V0l1_2E0) ) ).
tff(thm_2Erich__list_2EAPPEND__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))] :
( ! [V2l_27_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0,V2l_27_2E0),V3x_2E0) = c_2Elist_2ESNOC_2E2(A_27a,V3x_2E0,V2l_27_2E0) )
=> ! [V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27a),F0_2E0,V0l1_2E0,V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2EFOLDR__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2l1_2E0: tyop_2Elist_2Elist(A_27a),V3l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,V3l2_2E0),V2l1_2E0) ) ).
tff(thm_2Erich__list_2EFOLDL__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2l1_2E0: tyop_2Elist_2Elist(A_27b),V3l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EAPPEND_2E2(A_27b,V2l1_2E0,V3l2_2E0)) = c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,V2l1_2E0),V3l2_2E0) ) ).
tff(thm_2Erich__list_2ECONS__APPEND,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,V1l_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)),V1l_2E0) ) ).
tff(thm_2Erich__list_2EASSOC__APPEND,axiom,
! [A_27a: $tType] : p(c_2Ecombin_2EASSOC_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E0(A_27a))) ).
tff(thm_2Erich__list_2EMONOID__APPEND__NIL,axiom,
! [A_27a: $tType] : p(c_2Ecombin_2EMONOID_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a))) ).
tff(thm_2Erich__list_2EFLAT__SNOC,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Elist_2Elist(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2ESNOC_2E2(tyop_2Elist_2Elist(A_27a),V0x_2E0,V1l_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V1l_2E0),V0x_2E0) ) ).
tff(thm_2Erich__list_2EFLAT__FOLDR,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) ) ).
tff(thm_2Erich__list_2EFLAT__FOLDL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) ) ).
tff(thm_2Erich__list_2ELENGTH__FLAT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0)) = c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),V0l_2E0)) ) ).
tff(thm_2Erich__list_2EREVERSE__FOLDR,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) ) ).
tff(thm_2Erich__list_2EREVERSE__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))] :
( ! [V1l_27_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0,V1l_27_2E0),V2x_2E0) = c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1l_27_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27a),F0_2E0,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EALL__EL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27a,V1f_2E0,V2l_2E0)) = c_2Elist_2EEVERY_2E2(A_27b,c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Ebool,A_27a,V0P_2E0,V1f_2E0),V2l_2E0) ) ).
tff(thm_2Erich__list_2EMEM__EXISTS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) = c_2Elist_2EEXISTS_2E2(A_27a,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l_2E0) ) ).
tff(thm_2Erich__list_2ESUM__FOLDR,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(V0l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E0,c_2Enum_2E0_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2ESUM__FOLDL,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(V0l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E0,c_2Enum_2E0_2E0,V0l_2E0) ) ).
tff(thm_2Erich__list_2EIS__PREFIX,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) = c_2Ebool_2ET_2E0 )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2EF_2E0 )
& ! [V3x1_2E0: A_27a,V4l1_2E0: tyop_2Elist_2Elist(A_27a),V5x2_2E0: A_27a,V6l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V5x2_2E0,V6l2_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x1_2E0,V4l1_2E0)))
<=> ( ( V3x1_2E0 = V5x2_2E0 )
& p(c_2Elist_2EisPREFIX_2E2(A_27a,V6l2_2E0,V4l1_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1l2_2E0,V0l1_2E0))
<=> ? [V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l1_2E0,V1l2_2E0))
<=> ? [V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V2l_2E0,V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2EIS__SUBLIST__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V0l1_2E0,V1l2_2E0))
<=> ? [V2l_2E0: tyop_2Elist_2Elist(A_27a),V3l_27_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0l1_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V2l_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l2_2E0,V3l_27_2E0)) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__IS__SUBLIST,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1l2_2E0,V0l1_2E0))
=> p(c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V0l1_2E0,V1l2_2E0)) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__IS__SUBLIST,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l1_2E0,V1l2_2E0))
=> p(c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V0l1_2E0,V1l2_2E0)) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__REVERSE,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0)) = c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l1_2E0,V1l2_2E0) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__REVERSE,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1l1_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V0l2_2E0)) = c_2Elist_2EisPREFIX_2E2(A_27a,V0l2_2E0,V1l1_2E0) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__CONS2__E,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Elist_2Elist(A_27a),V1h_2E0: A_27a,V2t_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0s_2E0,c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V2t_2E0)))
=> p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0s_2E0,V2t_2E0)) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__REFL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l_2E0,V0l_2E0)) ).
tff(thm_2Erich__list_2EIS__SUBLIST__REVERSE,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0)) = c_2Erich__list_2EIS__SUBLIST_2E2(A_27a,V0l1_2E0,V1l2_2E0) ) ).
tff(thm_2Erich__list_2EPREFIX__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3l_27_2E0: tyop_2Elist_2Elist(A_27a)] : ( 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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),V2x_2E0),V3l_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0),c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_27_2E0),c_2Elist_2ENIL_2E0(A_27a)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EPREFIX_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),F0_2E0,V0P_2E0),c_2Elist_2ENIL_2E0(A_27a),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EPREFIX,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Erich__list_2EPREFIX_2E2(A_27a,V0P_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27b,V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Erich__list_2EPREFIX_2E2(A_27b,V1P_2E0,c_2Elist_2ECONS_2E2(A_27b,V2x_2E0,V3l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0),c_2Elist_2ECONS_2E2(A_27b,V2x_2E0,c_2Erich__list_2EPREFIX_2E2(A_27b,V1P_2E0,V3l_2E0)),c_2Elist_2ENIL_2E0(A_27b)) ) ) ).
tff(thm_2Erich__list_2EIS__PREFIX__PREFIX,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2EisPREFIX_2E2(A_27a,c_2Erich__list_2EPREFIX_2E2(A_27a,V0P_2E0,V1l_2E0),V1l_2E0)) ).
tff(thm_2Erich__list_2ELENGTH__SCANL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2ESCANL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,V2l_2E0)) = c_2Enum_2ESUC_2E1(c_2Elist_2ELENGTH_2E1(A_27b,V2l_2E0)) ) ).
tff(thm_2Erich__list_2ELENGTH__SCANR,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27b,c_2Erich__list_2ESCANR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,V2l_2E0)) = c_2Enum_2ESUC_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)) ) ).
tff(thm_2Erich__list_2ECOMM__MONOID__FOLDL,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0))
=> ! [V1e_27_2E0: A_27a] :
( p(c_2Ecombin_2EMONOID_2E2(A_27a,V0f_2E0,V1e_27_2E0))
=> ! [V2e_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V2e_2E0,V3l_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2e_2E0),c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_27_2E0,V3l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2ECOMM__MONOID__FOLDR,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0))
=> ! [V1e_27_2E0: A_27a] :
( p(c_2Ecombin_2EMONOID_2E2(A_27a,V0f_2E0,V1e_27_2E0))
=> ! [V2e_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V2e_2E0,V3l_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2e_2E0),c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_27_2E0,V3l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EFCOMM__FOLDR__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27b,V0g_2E0,V1f_2E0))
=> ! [V2e_2E0: A_27a] :
( p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,V0g_2E0,V2e_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27b),V4l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDR_2E3(A_27b,A_27a,V1f_2E0,V2e_2E0,c_2Elist_2EAPPEND_2E2(A_27b,V3l1_2E0,V4l2_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0,c_2Elist_2EFOLDR_2E3(A_27b,A_27a,V1f_2E0,V2e_2E0,V3l1_2E0)),c_2Elist_2EFOLDR_2E3(A_27b,A_27a,V1f_2E0,V2e_2E0,V4l2_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EFCOMM__FOLDL__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27a,V0f_2E0,V1g_2E0))
=> ! [V2e_2E0: A_27a] :
( p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,V1g_2E0,V2e_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27b),V4l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V2e_2E0,c_2Elist_2EAPPEND_2E2(A_27b,V3l1_2E0,V4l2_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0,c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V2e_2E0,V3l1_2E0)),c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V2e_2E0,V4l2_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EFOLDL__SINGLE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2x_2E0: A_27b] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2ECONS_2E2(A_27b,V2x_2E0,c_2Elist_2ENIL_2E0(A_27b))) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V1e_2E0),V2x_2E0) ) ).
tff(thm_2Erich__list_2EFOLDR__SINGLE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2x_2E0: A_27a] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ENIL_2E0(A_27a))) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),V1e_2E0) ) ).
tff(thm_2Erich__list_2EFOLDR__CONS__NIL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) = V0l_2E0 ) ).
tff(thm_2Erich__list_2EFOLDL__SNOC__NIL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))] :
( ! [V1xs_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0,V1xs_2E0),V2x_2E0) = c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1xs_2E0) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Elist_2Elist(A_27a),F0_2E0,c_2Elist_2ENIL_2E0(A_27a),V0l_2E0) = V0l_2E0 ) ) ).
tff(thm_2Erich__list_2EFOLDR__FOLDL__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3x_2E0: A_27b,V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V3x_2E0),V4y_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4y_2E0),V3x_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,V2l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EFOLDL__FOLDR__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V3x_2E0: A_27b,V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),F0_2E0,V0f_2E0),V3x_2E0),V4y_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V4y_2E0),V3x_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,V2l_2E0) = c_2Elist_2EFOLDR_2E3(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),F0_2E0,V0f_2E0),V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27b,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EFOLDR__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3x_2E0: A_27b,V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V3x_2E0),V4y_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4y_2E0),V3x_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V2l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0,V0f_2E0),V1e_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EFOLDL__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V3x_2E0: A_27b,V4y_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),F0_2E0,V0f_2E0),V3x_2E0),V4y_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V4y_2E0),V3x_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27b,V2l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),F0_2E0,V0f_2E0),V1e_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EFOLDR__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V4x_2E0: A_27c,V5y_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),F0_2E0,V0f_2E0),V2g_2E0),V4x_2E0),V5y_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,app_2E2(A_27c,A_27a,V2g_2E0,V4x_2E0)),V5y_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V3l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27a,V2g_2E0,V3l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),F0_2E0,V0f_2E0),V2g_2E0),V1e_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EFOLDL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V4x_2E0: A_27a,V5y_2E0: A_27c] : ( app_2E2(A_27c,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))),F0_2E0,V0f_2E0),V2g_2E0),V4x_2E0),V5y_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V4x_2E0),app_2E2(A_27c,A_27b,V2g_2E0,V5y_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2g_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V3l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EMAP_2E2(A_27c,A_27b,V2g_2E0,V3l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27a))),F0_2E0,V0f_2E0),V2g_2E0),V1e_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EEVERY__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3l_27_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2x_2E0),V3l_27_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& p(V3l_27_2E0) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Ebool_2ET_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEVERY__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_27_2E0: tyop_2Emin_2Ebool,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(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_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2l_27_2E0),V3x_2E0))
<=> ( p(V2l_27_2E0)
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Ebool_2ET_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEXISTS__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3l_27_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2x_2E0),V3l_27_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
| p(V3l_27_2E0) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Ebool_2EF_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEXISTS__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_27_2E0: tyop_2Emin_2Ebool,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(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_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2l_27_2E0),V3x_2E0))
<=> ( p(V2l_27_2E0)
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Ebool_2EF_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEVERY__FOLDR__MAP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0)) ) ).
tff(thm_2Erich__list_2EEVERY__FOLDL__MAP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0)) ) ).
tff(thm_2Erich__list_2EEXISTS__FOLDR__MAP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0)) ) ).
tff(thm_2Erich__list_2EEXISTS__FOLDL__MAP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0) = c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0)) ) ).
tff(thm_2Erich__list_2EFOLDR__FILTER,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))))] :
( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4x_2E0: A_27a,V5y_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),F0_2E0,V2P_2E0),V0f_2E0),V4x_2E0),V5y_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V4x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4x_2E0),V5y_2E0),V5y_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27b,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V0f_2E0,V1e_2E0,c_2Elist_2EFILTER_2E2(A_27a,V2P_2E0,V3l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),F0_2E0,V2P_2E0),V0f_2E0),V1e_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EFOLDL__FILTER,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a))))] :
( ! [V2P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V4x_2E0: A_27a,V5y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a))),F0_2E0,V2P_2E0),V0f_2E0),V4x_2E0),V5y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,app_2E2(A_27b,tyop_2Emin_2Ebool,V2P_2E0,V5y_2E0),app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V4x_2E0),V5y_2E0),V4x_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EFILTER_2E2(A_27b,V2P_2E0,V3l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a))),F0_2E0,V2P_2E0),V0f_2E0),V1e_2E0,V3l_2E0) ) ) ).
tff(thm_2Erich__list_2EASSOC__FOLDR__FLAT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
=> ! [V1e_2E0: A_27a] :
( p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0))
=> ! [V2l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EFLAT_2E1(A_27a,V2l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EFOLDR_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0),V2l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EASSOC__FOLDL__FLAT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
=> ! [V1e_2E0: A_27a] :
( p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0))
=> ! [V2l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EFLAT_2E1(A_27a,V2l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2EFOLDL_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0),V2l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EMAP__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EFLAT_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFLAT_2E1(A_27b,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E1(A_27a,A_27b,V0f_2E0),V1l_2E0)) ) ).
tff(thm_2Erich__list_2EFILTER__FLAT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,c_2Elist_2EFLAT_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E1(A_27a,V0P_2E0),V1l_2E0)) ) ).
tff(thm_2Erich__list_2EEXISTS__DISJ,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_2EEXISTS_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_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V2l_2E0))
| p(c_2Elist_2EEXISTS_2E2(A_27a,V1Q_2E0,V2l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EMEM__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))] :
( ! [V0y_2E0: A_27a,V2x_2E0: A_27a,V3l_27_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),V2x_2E0),V3l_27_2E0))
<=> ( ( V0y_2E0 = V2x_2E0 )
| p(V3l_27_2E0) ) )
=> ! [V0y_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),c_2Ebool_2EF_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EMEM__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0y_2E0: A_27a,V2l_27_2E0: tyop_2Emin_2Ebool,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),V2l_27_2E0),V3x_2E0))
<=> ( p(V2l_27_2E0)
| ( V0y_2E0 = V3x_2E0 ) ) )
=> ! [V0y_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),c_2Ebool_2EF_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ENULL__FOLDR,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2l_27_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V1x_2E0),V2l_27_2E0) = c_2Ebool_2EF_2E0 )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Emin_2Ebool,F0_2E0,c_2Ebool_2ET_2E0,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2ENULL__FOLDL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: tyop_2Emin_2Ebool,V2l_27_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1x_2E0),V2l_27_2E0) = c_2Ebool_2EF_2E0 )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,V0l_2E0) = c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Emin_2Ebool,F0_2E0,c_2Ebool_2ET_2E0,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EMAP__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27b,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l_2E0)) ) ).
tff(thm_2Erich__list_2ESEG__LENGTH__ID,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Enum_2E0_2E0,V0l_2E0) = V0l_2E0 ) ).
tff(thm_2Erich__list_2ESEG__SUC__CONS,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a),V3x_2E0: A_27a] : ( c_2Erich__list_2ESEG_2E3(A_27a,V0m_2E0,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V2l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V0m_2E0,V1n_2E0,V2l_2E0) ) ).
tff(thm_2Erich__list_2ESEG__0__SNOC,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2x_2E0: A_27a] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V0m_2E0,c_2Enum_2E0_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V0m_2E0,c_2Enum_2E0_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),c_2Enum_2E0_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ELASTN__CONS,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] : ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ELENGTH__LASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) = V0n_2E0 ) ) ).
tff(thm_2Erich__list_2ELASTN__LENGTH__ID,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V0l_2E0) = V0l_2E0 ) ).
tff(thm_2Erich__list_2ELASTN__LASTN,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)))
=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V2m_2E0))
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,V1n_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V2m_2E0,V0l_2E0)) = c_2Erich__list_2ELASTN_2E2(A_27a,V1n_2E0,V0l_2E0) ) ) ) ).
tff(thm_2Erich__list_2ETAKE__SNOC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__LENGTH__NIL,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ).
tff(thm_2Erich__list_2EDROP__APPEND,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l1_2E0),c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)),V2l2_2E0)) ) ).
tff(thm_2Erich__list_2EDROP__APPEND1,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
=> ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l1_2E0),V2l2_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__APPEND2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),V1n_2E0))
=> ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0)) = c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V2l2_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__DROP__T,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V2l_2E0)) = c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),V2l_2E0) ) ).
tff(thm_2Erich__list_2EDROP__DROP,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V2l_2E0)) = c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),V2l_2E0) ) ) ).
tff(thm_2Erich__list_2ELASTN__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ETAKE__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,c_2Enum_2E0_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__SNOC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Elist_2ESNOC_2E2(A_27a,V2x_2E0,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EAPPEND__BUTLASTN__DROP,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) )
=> ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,V2l_2E0),c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V2l_2E0)) = V2l_2E0 ) ) ).
tff(thm_2Erich__list_2ESEG__SEG,axiom,
! [A_27a: $tType,V0n1_2E0: tyop_2Enum_2Enum,V1m1_2E0: tyop_2Enum_2Enum,V2n2_2E0: tyop_2Enum_2Enum,V3m2_2E0: tyop_2Enum_2Enum,V4l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n1_2E0,V1m1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V4l_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V2n2_2E0,V3m2_2E0),V0n1_2E0)) )
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V2n2_2E0,V3m2_2E0,c_2Erich__list_2ESEG_2E3(A_27a,V0n1_2E0,V1m1_2E0,V4l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V2n2_2E0,c_2Earithmetic_2E_2B_2E2(V1m1_2E0,V3m2_2E0),V4l_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG__APPEND1,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0)))
=> ! [V3l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V3l2_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,V2l1_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG__APPEND2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),V1m_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0))) )
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V2n_2E0,V1m_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V3l2_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V2n_2E0,c_2Earithmetic_2E_2D_2E2(V1m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V3l2_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG__TAKE__DROP,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,V2l_2E0) = c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESEG__APPEND,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum,V3l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Earithmetic_2E_2B_2E2(V2n_2E0,V0m_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,V0m_2E0),c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V3l2_2E0)))) )
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V2n_2E0,V0m_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V3l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),V0m_2E0),V0m_2E0,V1l1_2E0),c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,V0m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)),c_2Enum_2E0_2E0,V3l2_2E0)) ) ) ).
tff(thm_2Erich__list_2ESEG__LENGTH__SNOC,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V0l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).
tff(thm_2Erich__list_2ESEG__SNOC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ! [V3x_2E0: A_27a] : ( c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,c_2Elist_2ESNOC_2E2(A_27a,V3x_2E0,V2l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EHD_2E1(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0)),V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESNOC__FOLDR,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V0x_2E0,c_2Elist_2ENIL_2E0(A_27a)),V1l_2E0) ) ).
tff(thm_2Erich__list_2EMEM__FOLDR__MAP,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFOLDR_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l_2E0)) ) ).
tff(thm_2Erich__list_2EMEM__FOLDL__MAP,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) = c_2Elist_2EFOLDL_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0,c_2Elist_2EMAP_2E2(A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E1(A_27a,V0x_2E0),V1l_2E0)) ) ).
tff(thm_2Erich__list_2EFILTER__FILTER,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)] : ( c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1Q_2E0,V2l_2E0)) = c_2Elist_2EFILTER_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) ) ) ).
tff(thm_2Erich__list_2EFCOMM__FOLDR__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27b,V0g_2E0,V1f_2E0))
=> ! [V2e_2E0: A_27a] :
( p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,V0g_2E0,V2e_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFOLDR_2E3(A_27b,A_27a,V1f_2E0,V2e_2E0,c_2Elist_2EFLAT_2E1(A_27b,V3l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0g_2E0,V2e_2E0,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),A_27a,c_2Elist_2EFOLDR_2E2(A_27b,A_27a,V1f_2E0,V2e_2E0),V3l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EFCOMM__FOLDL__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27a,V0f_2E0,V1g_2E0))
=> ! [V2e_2E0: A_27a] :
( p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,V1g_2E0,V2e_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V0f_2E0,V2e_2E0,c_2Elist_2EFLAT_2E1(A_27b,V3l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V1g_2E0,V2e_2E0,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),A_27a,c_2Elist_2EFOLDL_2E2(A_27b,A_27a,V0f_2E0,V2e_2E0),V3l_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EFOLDR__MAP__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( ! [V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1a_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2b_2E0),V3c_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2b_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1a_2E0),V3c_2E0)) )
=> ! [V4e_2E0: A_27a,V5g_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V6l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V4e_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27a,V5g_2E0,c_2Elist_2EREVERSE_2E1(A_27b,V6l_2E0))) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V4e_2E0,c_2Elist_2EMAP_2E2(A_27b,A_27a,V5g_2E0,V6l_2E0)) ) ) ).
tff(thm_2Erich__list_2EFOLDR__FILTER__REVERSE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( ! [V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1a_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2b_2E0),V3c_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2b_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1a_2E0),V3c_2E0)) )
=> ! [V4e_2E0: A_27a,V5P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V4e_2E0,c_2Elist_2EFILTER_2E2(A_27a,V5P_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V6l_2E0))) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V4e_2E0,c_2Elist_2EFILTER_2E2(A_27a,V5P_2E0,V6l_2E0)) ) ) ).
tff(thm_2Erich__list_2ECOMM__ASSOC__FOLDR__REVERSE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0))
=> ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
=> ! [V1e_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V2l_2E0)) = c_2Elist_2EFOLDR_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,V2l_2E0) ) ) ) ).
tff(thm_2Erich__list_2ECOMM__ASSOC__FOLDL__REVERSE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27a,V0f_2E0))
=> ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
=> ! [V1e_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V2l_2E0)) = c_2Elist_2EFOLDL_2E3(A_27a,A_27a,V0f_2E0,V1e_2E0,V2l_2E0) ) ) ) ).
tff(thm_2Erich__list_2EELL__LAST,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l_2E0))
=> ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2E0_2E0,V0l_2E0) = c_2Elist_2ELAST_2E1(A_27a,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__0__SNOC,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2E0_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V0l_2E0)) = V1x_2E0 ) ).
tff(thm_2Erich__list_2EELL__SNOC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(V0n_2E0),V2l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__SUC__SNOC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V2l_2E0) ) ).
tff(thm_2Erich__list_2EELL__CONS,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] : ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V1l_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__LENGTH__CONS,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V0l_2E0)) = V1x_2E0 ) ).
tff(thm_2Erich__list_2EELL__LENGTH__SNOC,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1x_2E0: A_27a] : ( c_2Erich__list_2EELL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0),c_2Elist_2ESNOC_2E2(A_27a,V1x_2E0,V0l_2E0)) = c_2Ebool_2ECOND_2E3(A_27a,c_2Elist_2ENULL_2E1(A_27a,V0l_2E0),V1x_2E0,c_2Elist_2EHD_2E1(A_27a,V0l_2E0)) ) ).
tff(thm_2Erich__list_2EELL__APPEND2,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0)))
=> ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__APPEND1,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0),V1n_2E0))
=> ! [V2l1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EELL_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V0l2_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l2_2E0)),V2l1_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__PRE__LENGTH,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Erich__list_2EELL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)),V0l_2E0) = c_2Elist_2EHD_2E1(A_27a,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__PRE__LENGTH,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)),V0l_2E0) = c_2Elist_2ELAST_2E1(A_27a,V0l_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__ELL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2EELL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0)),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27a),V1l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l2_2E0))
=> ( c_2Elist_2EEL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V0l2_2E0)) = c_2Elist_2EHD_2E1(A_27a,V0l2_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__EL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0)),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EELL_2E2(A_27b,V0n_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V2f_2E0,V1l_2E0)) = app_2E2(A_27a,A_27b,V2f_2E0,c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELENGTH__FRONT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0l_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFRONT_2E1(A_27a,V0l_2E0)) = c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)) ) ) ).
tff(thm_2Erich__list_2EDROP__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EDROP_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = V1l2_2E0 ) ).
tff(thm_2Erich__list_2ETAKE__APPEND,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l1_2E0),c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)),V2l2_2E0)) ) ).
tff(thm_2Erich__list_2ETAKE__APPEND1,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
=> ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l1_2E0) ) ) ).
tff(thm_2Erich__list_2ETAKE__APPEND2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),V1n_2E0))
=> ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V2l2_2E0)) ) ) ).
tff(thm_2Erich__list_2ETAKE__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETAKE_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = V0l1_2E0 ) ).
tff(thm_2Erich__list_2EREVERSE__FLAT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,V0l_2E0)) = c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EREVERSE_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),V0l_2E0))) ) ).
tff(thm_2Erich__list_2EMAP__FILTER,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,app_2E2(A_27a,A_27a,V0f_2E0,V3x_2E0)) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3x_2E0) )
=> ( c_2Elist_2EMAP_2E2(A_27a,A_27a,V0f_2E0,c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,V2l_2E0)) = c_2Elist_2EFILTER_2E2(A_27a,V1P_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27a,V0f_2E0,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EFLAT__REVERSE,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EREVERSE_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),V0l_2E0))) ) ).
tff(thm_2Erich__list_2EFLAT__FLAT,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))] : ( c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EFLAT_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0)) = c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E0(A_27a),V0l_2E0)) ) ).
tff(thm_2Erich__list_2EEVERY__REVERSE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0) ) ).
tff(thm_2Erich__list_2EEXISTS__REVERSE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EEXISTS_2E2(A_27a,V0P_2E0,V1l_2E0) ) ).
tff(thm_2Erich__list_2EEVERY__SEG,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V2m_2E0,V3k_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Erich__list_2ESEG_2E3(A_27a,V2m_2E0,V3k_2E0,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EEVERY__TAKE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2ETAKE_2E2(A_27a,V2m_2E0,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EEVERY__DROP,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Elist_2EEVERY_2E2(A_27a,V0P_2E0,c_2Elist_2EDROP_2E2(A_27a,V2m_2E0,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EEXISTS__SEG,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1k_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1k_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V3P_2E0,c_2Erich__list_2ESEG_2E3(A_27a,V0m_2E0,V1k_2E0,V2l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V3P_2E0,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EEXISTS__TAKE__IMP,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,V0l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V0l_2E0)) ) ).
tff(thm_2Erich__list_2EEXISTS__DROP__IMP,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V0l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V0l_2E0)) ) ).
tff(thm_2Erich__list_2EEXISTS__TAKE,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Elist_2ETAKE_2E2(A_27a,V0m_2E0,V1l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EEXISTS__DROP,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Elist_2EDROP_2E2(A_27a,V0m_2E0,V1l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EEXISTS__LASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V0m_2E0,V1l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EEXISTS__BUTLASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,V1l_2E0)))
=> p(c_2Elist_2EEXISTS_2E2(A_27a,V2P_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EMEM__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,V2l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0))) ) ) ).
tff(thm_2Erich__list_2EMEM__TAKE__IMP,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,V0l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ) ).
tff(thm_2Erich__list_2EMEM__DROP__IMP,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V0l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0l_2E0))) ) ).
tff(thm_2Erich__list_2EMEM__TAKE,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0m_2E0,V1l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EMEM__DROP,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0m_2E0,V1l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EMEM__BUTLASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0m_2E0,V1l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EMEM__LASTN,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,V0m_2E0,V1l_2E0))))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ) ).
tff(thm_2Erich__list_2EZIP__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
=> ! [V2x1_2E0: A_27a,V3x2_2E0: A_27b] : ( c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(A_27a,V2x1_2E0,V0l1_2E0),c_2Elist_2ESNOC_2E2(A_27b,V3x2_2E0,V1l2_2E0))) = c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x1_2E0,V3x2_2E0),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) ) ) ).
tff(thm_2Erich__list_2EUNZIP__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EUNZIP_2E1(A_27a,A_27b,c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0,V1l_2E0)) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V0x_2E0),c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V1l_2E0))),c_2Elist_2ESNOC_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V0x_2E0),c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EUNZIP_2E1(A_27a,A_27b,V1l_2E0)))) ) ).
tff(thm_2Erich__list_2ELENGTH__UNZIP__FST,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2EUNZIP__FST_2E1(A_27a,A_27b,V0l_2E0)) = c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l_2E0) ) ).
tff(thm_2Erich__list_2ELENGTH__UNZIP__SND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELENGTH_2E1(A_27b,c_2Erich__list_2EUNZIP__SND_2E1(A_27b,A_27a,V0l_2E0)) = c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l_2E0) ) ).
tff(thm_2Erich__list_2ESUM__REVERSE,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ESUM_2E1(c_2Elist_2EREVERSE_2E1(tyop_2Enum_2Enum,V0l_2E0)) = c_2Elist_2ESUM_2E1(V0l_2E0) ) ).
tff(thm_2Erich__list_2ESUM__FLAT,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Enum_2Enum))] : ( c_2Elist_2ESUM_2E1(c_2Elist_2EFLAT_2E1(tyop_2Enum_2Enum,V0l_2E0)) = c_2Elist_2ESUM_2E1(c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Elist_2ESUM_2E0,V0l_2E0)) ) ).
tff(thm_2Erich__list_2EEL__APPEND1,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1l1_2E0,V2l2_2E0)) = c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l1_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__APPEND2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),V1n_2E0))
=> ! [V2l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,V1n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V2l2_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V2l2_2E0) ) ) ).
tff(thm_2Erich__list_2ELUPDATE__APPEND2,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0),V2n_2E0))
=> ( c_2Elist_2ELUPDATE_2E3(A_27a,V3x_2E0,V2n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,c_2Elist_2ELUPDATE_2E3(A_27a,V3x_2E0,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)),V1l2_2E0)) ) ) ).
tff(thm_2Erich__list_2ELUPDATE__APPEND1,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a] :
( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0)))
=> ( c_2Elist_2ELUPDATE_2E3(A_27a,V3x_2E0,V2n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ELUPDATE_2E3(A_27a,V3x_2E0,V2n_2E0,V0l1_2E0),V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2Eis__prefix__el,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Elist_2EisPREFIX_2E2(A_27a,V1l1_2E0,V2l2_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V2l2_2E0))) )
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l1_2E0) = c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V2l2_2E0) ) ) ).
tff(thm_2Erich__list_2EEL__CONS,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0)) = c_2Elist_2EEL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(V0n_2E0),V2l_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG1,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0,V1l_2E0) = c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2ENIL_2E0(A_27a)) ) ) ).
tff(thm_2Erich__list_2EEL__SEG,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EHD_2E1(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESEG__CONS,axiom,
! [A_27a: $tType,V0j_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0j_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V1n_2E0,V0j_2E0),c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V3t_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V1n_2E0,V0j_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,V1n_2E0,c_2Earithmetic_2E_2D_2E2(V0j_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3t_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG__SUC__EL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2E_2B_2E2(V1i_2E0,V0n_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0),V1i_2E0,V2l_2E0) = c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V1i_2E0,V2l_2E0),c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ETAKE__SEG__DROP,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V1i_2E0,V0n_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V1i_2E0,V2l_2E0),c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1i_2E0,V2l_2E0)),c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V1i_2E0,V0n_2E0),V2l_2E0)) = V2l_2E0 ) ) ).
tff(thm_2Erich__list_2EEL__MEM,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Ebool_2EIN_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ).
tff(thm_2Erich__list_2ETL__SNOC,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ETL_2E1(A_27a,c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,V1l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENULL_2E1(A_27a,V1l_2E0),c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ESNOC_2E2(A_27a,V0x_2E0,c_2Elist_2ETL_2E1(A_27a,V1l_2E0))) ) ).
tff(thm_2Erich__list_2EEL__REVERSE__ELL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ~ p(c_2Elist_2ENULL_2E1(A_27a,V0l1_2E0))
=> ( c_2Erich__list_2EELL_2E2(A_27a,c_2Elist_2ELENGTH_2E1(A_27a,V1l2_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0l1_2E0,V1l2_2E0)) = c_2Elist_2ELAST_2E1(A_27a,V0l1_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__MEM,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> p(c_2Ebool_2EIN_2E2(A_27a,c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0))) ) ).
tff(thm_2Erich__list_2EELL__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Erich__list_2EELL_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0)),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EELL__REVERSE__EL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EELL_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ETAKE__BUTLASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__TAKE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ELASTN__DROP,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__LASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0) = c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0),V0n_2E0),V1l_2E0) ) ) ).
tff(thm_2Erich__list_2ESEG__LASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,V2l_2E0) = c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0),c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0)),V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2EDROP__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ETAKE__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)))
=> ( c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,V0n_2E0,V1l_2E0)) ) ) ).
tff(thm_2Erich__list_2ESEG__REVERSE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)))
=> ( c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,V1m_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V2l_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Erich__list_2ESEG_2E3(A_27a,V0n_2E0,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0),c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0)),V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELENGTH__REPLICATE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: A_27a] : ( c_2Elist_2ELENGTH_2E1(A_27a,c_2Erich__list_2EREPLICATE_2E2(A_27a,V0n_2E0,V1x_2E0)) = V0n_2E0 ) ).
tff(thm_2Erich__list_2EMEM__REPLICATE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ! [V1x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Erich__list_2EREPLICATE_2E2(A_27a,V0n_2E0,V1x_2E0)))) ) ).
tff(thm_2Erich__list_2EEVERY__REPLICATE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] :
( p(c_2Elist_2EEVERY_2E2(A_27a,V0f_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V1n_2E0,V2x_2E0)))
<=> ( ( V1n_2E0 = c_2Enum_2E0_2E0 )
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V2x_2E0)) ) ) ).
tff(thm_2Erich__list_2EALL__DISTINCT__DROP,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V0ls_2E0))
=> p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0))) ) ).
tff(thm_2Erich__list_2EMAP__SND__FILTER__NEQ,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0z_2E0: A_27a,V2x_2E0: A_27b,V3y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0z_2E0),V2x_2E0),V3y_2E0))
<=> ( V3y_2E0 != V0z_2E0 ) )
=> ( ! [V0z_2E0: A_27a,V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0z_2E0),V4y_2E0))
<=> ( V0z_2E0 != V4y_2E0 ) )
=> ! [V0z_2E0: A_27a,V1ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),c_2Elist_2EFILTER_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0z_2E0)),V1ls_2E0)) = c_2Elist_2EFILTER_2E2(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0z_2E0),c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a,c_2Epair_2ESND_2E0(A_27b,A_27a),V1ls_2E0)) ) ) ) ).
tff(thm_2Erich__list_2EMEM__SING__APPEND,axiom,
! [A_27a: $tType,V0d_2E0: tyop_2Elist_2Elist(A_27a),V1b_2E0: A_27a] :
( ! [V2a_2E0: tyop_2Elist_2Elist(A_27a),V3c_2E0: tyop_2Elist_2Elist(A_27a)] : ( V0d_2E0 != c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,V2a_2E0,c_2Elist_2ECONS_2E2(A_27a,V1b_2E0,c_2Elist_2ENIL_2E0(A_27a))),V3c_2E0) )
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V1b_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V0d_2E0))) ) ).
tff(thm_2Erich__list_2EEL__LENGTH__APPEND__rwt,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l2_2E0: tyop_2Elist_2Elist(A_27a),V2l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ~ p(c_2Elist_2ENULL_2E1(A_27a,V1l2_2E0))
& ( V0n_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V2l1_2E0) ) )
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V2l1_2E0,V1l2_2E0)) = c_2Elist_2EHD_2E1(A_27a,V1l2_2E0) ) ) ).
tff(thm_2Erich__list_2EMAP__FST__funs,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27a))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27b,V3z_2E0: A_27c] : ( app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),F1_2E0,V1x_2E0),V2y_2E0),V3z_2E0) = V1x_2E0 )
=> ( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27a),F0_2E0,V1x_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27c,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),F1_2E0,V1x_2E0)) )
=> ! [V0funs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a,c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),A_27a,F0_2E0),V0funs_2E0) = c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),A_27a,c_2Epair_2EFST_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0funs_2E0) ) ) ) ).
tff(thm_2Erich__list_2ETAKE__PRE__LENGTH,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0ls_2E0 != c_2Elist_2ENIL_2E0(A_27a) )
=> ( c_2Elist_2ETAKE_2E2(A_27a,c_2Eprim__rec_2EPRE_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)),V0ls_2E0) = c_2Elist_2EFRONT_2E1(A_27a,V0ls_2E0) ) ) ).
tff(thm_2Erich__list_2EDROP__LENGTH__NIL__rwt,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a),V1m_2E0: tyop_2Enum_2Enum] :
( ( V1m_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0) )
=> ( c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V0l_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ) ).
tff(thm_2Erich__list_2EDROP__EL__CONS,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)))
=> ( c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0) = c_2Elist_2ECONS_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0ls_2E0),c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0ls_2E0)) ) ) ).
tff(thm_2Erich__list_2ETAKE__EL__SNOC,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)))
=> ( c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0ls_2E0) = c_2Elist_2ESNOC_2E2(A_27a,c_2Elist_2EEL_2E2(A_27a,V1n_2E0,V0ls_2E0),c_2Elist_2ETAKE_2E2(A_27a,V1n_2E0,V0ls_2E0)) ) ) ).
tff(thm_2Erich__list_2EREVERSE__DROP,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0)))
=> ( c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EDROP_2E2(A_27a,V1n_2E0,V0ls_2E0)) = c_2Elist_2EREVERSE_2E1(A_27a,c_2Erich__list_2ELASTN_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0ls_2E0),V1n_2E0),V0ls_2E0)) ) ) ).
tff(thm_2Erich__list_2ELENGTH__FILTER__LESS,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EEXISTS_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1ls_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EFILTER_2E2(A_27a,V0P_2E0,V1ls_2E0)),c_2Elist_2ELENGTH_2E1(A_27a,V1ls_2E0))) ) ).
tff(thm_2Erich__list_2EEVERY2__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l4_2E0: tyop_2Elist_2Elist(A_27b),V1l3_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V3l1_2E0,V2l2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V1l3_2E0,V0l4_2E0)) )
<=> ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V1l3_2E0),c_2Elist_2EAPPEND_2E2(A_27b,V2l2_2E0,V0l4_2E0)))
& ( c_2Elist_2ELENGTH_2E1(A_27a,V3l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2l2_2E0) )
& ( c_2Elist_2ELENGTH_2E1(A_27a,V1l3_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V0l4_2E0) ) ) ) ).
tff(thm_2Erich__list_2ELIST__REL__APPEND__IMP,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1xs_2E0: tyop_2Elist_2Elist(A_27a),V2ys_2E0: tyop_2Elist_2Elist(A_27b),V3xs1_2E0: tyop_2Elist_2Elist(A_27a),V4ys1_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1xs_2E0,V3xs1_2E0),c_2Elist_2EAPPEND_2E2(A_27b,V2ys_2E0,V4ys1_2E0)))
& ( c_2Elist_2ELENGTH_2E1(A_27a,V1xs_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V2ys_2E0) ) )
=> ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V1xs_2E0,V2ys_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V3xs1_2E0,V4ys1_2E0)) ) ) ).
tff(thm_2Erich__list_2EEVERY2__APPEND__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0l4_2E0: tyop_2Elist_2Elist(A_27b),V1l3_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V3l1_2E0,V2l2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V1l3_2E0,V0l4_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V1l3_2E0),c_2Elist_2EAPPEND_2E2(A_27b,V2l2_2E0,V0l4_2E0))) ) ).
tff(thm_2Erich__list_2EEVERY2__DROP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,V2l2_2E0))
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2EDROP_2E2(A_27a,V3n_2E0,V1l1_2E0),c_2Elist_2EDROP_2E2(A_27b,V3n_2E0,V2l2_2E0))) ) ).
tff(thm_2Erich__list_2EEVERY2__TAKE,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1xs_2E0: tyop_2Elist_2Elist(A_27a),V2ys_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,V1xs_2E0,V2ys_2E0))
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0P_2E0,c_2Elist_2ETAKE_2E2(A_27a,V3n_2E0,V1xs_2E0),c_2Elist_2ETAKE_2E2(A_27b,V3n_2E0,V2ys_2E0))) ) ).
tff(thm_2Erich__list_2ELIST__REL__APPEND__SING,axiom,
! [A_27a: $tType,A_27b: $tType,V0x2_2E0: A_27b,V1x1_2E0: A_27a,V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x1_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Elist_2EAPPEND_2E2(A_27b,V2l2_2E0,c_2Elist_2ECONS_2E2(A_27b,V0x2_2E0,c_2Elist_2ENIL_2E0(A_27b)))))
<=> ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V4R_2E0,V3l1_2E0,V2l2_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4R_2E0,V1x1_2E0),V0x2_2E0)) ) ) ).
tff(thm_2Erich__list_2ELIST__REL__GENLIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Enum_2Enum,V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3P_2E0,c_2Elist_2EGENLIST_2E2(A_27a,V2f_2E0,V0l_2E0),c_2Elist_2EGENLIST_2E2(A_27b,V1g_2E0,V0l_2E0)))
<=> ! [V4i_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4i_2E0,V0l_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V4i_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V1g_2E0,V4i_2E0))) ) ) ).
tff(thm_2Erich__list_2EALL__DISTINCT__MEM__ZIP__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V2ls_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,V2ls_2E0))
=> ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V2ls_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2ls_2E0))))))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V1x_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2ls_2E0)))
& ( c_2Epair_2ESND_2E1(A_27a,A_27b,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,c_2Epair_2EFST_2E1(A_27a,A_27b,V1x_2E0)) ) ) ) ) ).
tff(thm_2Erich__list_2EREVERSE__ZIP,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27b)] :
( ( c_2Elist_2ELENGTH_2E1(A_27a,V0l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27b,V1l2_2E0) )
=> ( c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),V0l1_2E0,V1l2_2E0))) = c_2Elist_2EZIP_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0),c_2Elist_2EREVERSE_2E1(A_27b,V1l2_2E0))) ) ) ).
tff(thm_2Erich__list_2EEVERY2__REVERSE1,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,V1l1_2E0,c_2Elist_2EREVERSE_2E1(A_27b,V2l2_2E0)) = c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0R_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l1_2E0),V2l2_2E0) ) ).
tff(thm_2Erich__list_2ELIST__REL__REVERSE__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2_2E0: tyop_2Elist_2Elist(A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V1l1_2E0),c_2Elist_2EREVERSE_2E1(A_27b,V0l2_2E0)) = c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V2R_2E0,V1l1_2E0,V0l2_2E0) ) ).
tff(thm_2Erich__list_2Eevery__count__list,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Elist_2EEVERY_2E2(tyop_2Enum_2Enum,V0P_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V1n_2E0)))
<=> ! [V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V1n_2E0))
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2m_2E0)) ) ) ).
tff(thm_2Erich__list_2Ecount__list__sub1,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( V0n_2E0 != c_2Enum_2E0_2E0 )
=> ( c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0) = c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ) ).
tff(thm_2Erich__list_2Eel__map__count,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V2m_2E0))
=> ( c_2Elist_2EEL_2E2(A_27a,V0n_2E0,c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V2m_2E0))) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V0n_2E0) ) ) ).
tff(thm_2Erich__list_2EZIP__COUNT__LIST,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)))] :
( ! [V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),F0_2E0,V1l1_2E0),V2n_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Enum_2Enum,c_2Elist_2EEL_2E2(A_27a,V2n_2E0,V1l1_2E0),V2n_2E0) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( V0n_2E0 = c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0) )
=> ( c_2Elist_2EZIP_2E1(A_27a,tyop_2Enum_2Enum,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0))) = c_2Elist_2EGENLIST_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Enum_2Enum)),F0_2E0,V1l1_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)) ) ) ) ).
tff(thm_2Erich__list_2Emap__replicate,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V1n_2E0,V2x_2E0)) = c_2Erich__list_2EREPLICATE_2E2(A_27b,V1n_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0)) ) ).
tff(thm_2Erich__list_2EREPLICATE__NIL,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2EREPLICATE_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
<=> ( V1x_2E0 = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Erich__list_2EREPLICATE__APPEND,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] : ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Erich__list_2EREPLICATE_2E2(A_27a,V0n_2E0,V2a_2E0),c_2Erich__list_2EREPLICATE_2E2(A_27a,V1m_2E0,V2a_2E0)) = c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0),V2a_2E0) ) ).
tff(thm_2Erich__list_2EDROP__REPLICATE,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] : ( c_2Elist_2EDROP_2E2(A_27a,V0n_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V1m_2E0,V2a_2E0)) = c_2Erich__list_2EREPLICATE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V1m_2E0,V0n_2E0),V2a_2E0) ) ).
tff(thm_2Erich__list_2ELIST__REL__REPLICATE__same,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum,V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V3P_2E0,c_2Erich__list_2EREPLICATE_2E2(A_27a,V2n_2E0,V1x_2E0),c_2Erich__list_2EREPLICATE_2E2(A_27b,V2n_2E0,V0y_2E0)))
<=> ( p(c_2Earithmetic_2E_3E_2E2(V2n_2E0,c_2Enum_2E0_2E0))
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0,V1x_2E0),V0y_2E0)) ) ) ).
tff(thm_2Erich__list_2Etake__drop__partition,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0))
=> ( c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2ETAKE_2E2(A_27a,V1m_2E0,V2l_2E0),c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V0n_2E0,V1m_2E0),c_2Elist_2EDROP_2E2(A_27a,V1m_2E0,V2l_2E0))) = c_2Elist_2ETAKE_2E2(A_27a,V0n_2E0,V2l_2E0) ) ) ).
tff(thm_2Erich__list_2Eall__distinct__count__list,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Elist_2EALL__DISTINCT_2E1(tyop_2Enum_2Enum,c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0))) ).
tff(thm_2Erich__list_2Elist__rel__lastn,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0f_2E0,V1l1_2E0,V2l2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0f_2E0,c_2Erich__list_2ELASTN_2E2(A_27a,V3n_2E0,V1l1_2E0),c_2Erich__list_2ELASTN_2E2(A_27b,V3n_2E0,V2l2_2E0))) ) ).
tff(thm_2Erich__list_2Elist__rel__butlastn,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27b),V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l1_2E0)))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0f_2E0,V1l1_2E0,V2l2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27b,V0f_2E0,c_2Erich__list_2EBUTLASTN_2E2(A_27a,V3n_2E0,V1l1_2E0),c_2Erich__list_2EBUTLASTN_2E2(A_27b,V3n_2E0,V2l2_2E0))) ) ).
tff(thm_2Erich__list_2EUNIQUE__LIST__ELEM__COUNT,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1L_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2EUNIQUE_2E2(A_27a,V0e_2E0,V1L_2E0))
<=> ( c_2Erich__list_2ELIST__ELEM__COUNT_2E2(A_27a,V0e_2E0,V1L_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Erich__list_2ECOUNT__LIST__compute,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Erich__list_2ECOUNT__LIST_2E1(V0n_2E0) = c_2Erich__list_2ECOUNT__LIST__AUX_2E2(V0n_2E0,c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum)) ) ).
tff(thm_2Erich__list_2ESPLITP__compute,axiom,
! [A_27a: $tType] : ( c_2Erich__list_2ESPLITP_2E0(A_27a) = c_2Erich__list_2ESPLITP__AUX_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) ) ).
tff(thm_2Erich__list_2EIS__SUFFIX__compute,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EIS__SUFFIX_2E2(A_27a,V0l1_2E0,V1l2_2E0) = c_2Elist_2EisPREFIX_2E2(A_27a,c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0)) ) ).
tff(thm_2Erich__list_2ESEG__compute,axiom,
! [A_27a: $tType] :
( ! [V0k_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Enum_2E0_2E0,V0k_2E0,V1l_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V2m_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2m_2E0)),c_2Enum_2E0_2E0,c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Enum_2E0_2E0,V4l_2E0)) )
& ! [V5m_2E0: tyop_2Enum_2Enum,V6x_2E0: A_27a,V7l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V5m_2E0)),c_2Enum_2E0_2E0,c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,V7l_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V5m_2E0)),c_2Enum_2E0_2E0,V7l_2E0)) )
& ! [V8m_2E0: tyop_2Enum_2Enum,V9k_2E0: tyop_2Enum_2Enum,V10x_2E0: A_27a,V11l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V8m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V9k_2E0)),c_2Elist_2ECONS_2E2(A_27a,V10x_2E0,V11l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V8m_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V9k_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V11l_2E0) )
& ! [V12m_2E0: tyop_2Enum_2Enum,V13k_2E0: tyop_2Enum_2Enum,V14x_2E0: A_27a,V15l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V12m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V13k_2E0)),c_2Elist_2ECONS_2E2(A_27a,V14x_2E0,V15l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V12m_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V13k_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V15l_2E0) )
& ! [V16m_2E0: tyop_2Enum_2Enum,V17k_2E0: tyop_2Enum_2Enum,V18x_2E0: A_27a,V19l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V16m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V17k_2E0)),c_2Elist_2ECONS_2E2(A_27a,V18x_2E0,V19l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V16m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V17k_2E0)),V19l_2E0) )
& ! [V20m_2E0: tyop_2Enum_2Enum,V21k_2E0: tyop_2Enum_2Enum,V22x_2E0: A_27a,V23l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V20m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V21k_2E0)),c_2Elist_2ECONS_2E2(A_27a,V22x_2E0,V23l_2E0)) = c_2Erich__list_2ESEG_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V20m_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V21k_2E0)),V23l_2E0) ) ) ).
tff(thm_2Erich__list_2EBUTLASTN__compute,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))))] :
( ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a),V0longer_20than_20list_2E0: tyop_2Emin_2Ebool,V3m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2l_2E0),V0longer_20than_20list_2E0),V3m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V3m_2E0),c_2Elist_2ETAKE_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V3m_2E0,V1n_2E0),V2l_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,c_2Erich__list_2EBUTLASTN_2E0(A_27a),V0longer_20than_20list_2E0),V1n_2E0),V2l_2E0)) )
=> ! [V0longer_20than_20list_2E0: tyop_2Emin_2Ebool,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2EBUTLASTN_2E2(A_27a,V1n_2E0,V2l_2E0) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2l_2E0),V0longer_20than_20list_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)) ) ) ).
tff(thm_2Erich__list_2ELASTN__compute,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))))] :
( ! [V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a),V0longer_20than_20list_2E0: tyop_2Emin_2Ebool,V3m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2l_2E0),V0longer_20than_20list_2E0),V3m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V3m_2E0),c_2Elist_2EDROP_2E2(A_27a,c_2Earithmetic_2E_2D_2E2(V3m_2E0,V1n_2E0),V2l_2E0),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EFAIL_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,c_2Erich__list_2ELASTN_2E0(A_27a),V0longer_20than_20list_2E0),V1n_2E0),V2l_2E0)) )
=> ! [V0longer_20than_20list_2E0: tyop_2Emin_2Ebool,V1n_2E0: tyop_2Enum_2Enum,V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Erich__list_2ELASTN_2E2(A_27a,V1n_2E0,V2l_2E0) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)))),F0_2E0,V1n_2E0),V2l_2E0),V0longer_20than_20list_2E0),c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0)) ) ) ).
%------------------------------------------------------------------------------