ITP001 Axioms: ITP038_7.ax
%------------------------------------------------------------------------------
% File : ITP038_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 : state_transformer.ax [Gau19]
% : HL4038_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 316 ( 175 unt; 112 typ; 0 def)
% Number of atoms : 266 ( 219 equ)
% Maximal formula atoms : 11 ( 0 avg)
% Number of connectives : 67 ( 5 ~; 3 |; 7 &)
% ( 17 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 89 ( 55 >; 34 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 108 ( 108 usr; 13 con; 0-6 aty)
% Number of variables : 1069 ( 893 !; 1 ?;1069 :)
% ( 175 !>; 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_2Eone_2Eone,type,
tyop_2Eone_2Eone: $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_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_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_2Estate__transformer_2EBIND_2E0,type,
c_2Estate__transformer_2EBIND_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))) ).
tff(c_2Estate__transformer_2EBIND_2E2,type,
c_2Estate__transformer_2EBIND_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)) ) ).
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_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epair_2ECURRY_2E0,type,
c_2Epair_2ECURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))) ).
tff(c_2Epair_2ECURRY_2E1,type,
c_2Epair_2ECURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) ) ).
tff(c_2Estate__transformer_2EEXT_2E0,type,
c_2Estate__transformer_2EEXT_2E0:
!>[A_27b: $tType,A_27c: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))) ).
tff(c_2Estate__transformer_2EEXT_2E1,type,
c_2Estate__transformer_2EEXT_2E1:
!>[A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))) ) ).
tff(c_2Estate__transformer_2EEXT_2E2,type,
c_2Estate__transformer_2EEXT_2E2:
!>[A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))) * tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)) ) > tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)) ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
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_2Estate__transformer_2EFOR_2E0,type,
c_2Estate__transformer_2EFOR_2E0:
!>[A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))) ).
tff(c_2Estate__transformer_2EFOR_2E1,type,
c_2Estate__transformer_2EFOR_2E1:
!>[A_27state: $tType] : ( tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))) > tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)) ) ).
tff(c_2Estate__transformer_2EFOREACH_2E0,type,
c_2Estate__transformer_2EFOREACH_2E0:
!>[A_27a: $tType,A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))) ).
tff(c_2Estate__transformer_2EFOREACH_2E1,type,
c_2Estate__transformer_2EFOREACH_2E1:
!>[A_27a: $tType,A_27state: $tType] : ( tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))) > tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)) ) ).
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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_2Estate__transformer_2EIGNORE__BIND_2E0,type,
c_2Estate__transformer_2EIGNORE__BIND_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) ).
tff(c_2Estate__transformer_2EIGNORE__BIND_2E2,type,
c_2Estate__transformer_2EIGNORE__BIND_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)) * tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) ).
tff(c_2Estate__transformer_2EJOIN_2E0,type,
c_2Estate__transformer_2EJOIN_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ).
tff(c_2Estate__transformer_2EJOIN_2E1,type,
c_2Estate__transformer_2EJOIN_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) ).
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_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Elist_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_2Estate__transformer_2EMCOMP_2E0,type,
c_2Estate__transformer_2EMCOMP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))))) ).
tff(c_2Estate__transformer_2EMCOMP_2E2,type,
c_2Estate__transformer_2EMCOMP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))) ) ).
tff(c_2Estate__transformer_2EMMAP_2E0,type,
c_2Estate__transformer_2EMMAP_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,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) ).
tff(c_2Estate__transformer_2EMMAP_2E1,type,
c_2Estate__transformer_2EMMAP_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27c,A_27b) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2Estate__transformer_2EMMAP_2E2,type,
c_2Estate__transformer_2EMMAP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) ).
tff(c_2Estate__transformer_2EMWHILE_2E0,type,
c_2Estate__transformer_2EMWHILE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))) ).
tff(c_2Estate__transformer_2EMWHILE_2E2,type,
c_2Estate__transformer_2EMWHILE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)) * tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)) ) ).
tff(c_2Estate__transformer_2ENARROW_2E0,type,
c_2Estate__transformer_2ENARROW_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)))) ).
tff(c_2Estate__transformer_2ENARROW_2E3,type,
c_2Estate__transformer_2ENARROW_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : ( ( A_27b * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))) * A_27state ) > tyop_2Epair_2Eprod(A_27a,A_27state) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Estate__transformer_2EREAD_2E0,type,
c_2Estate__transformer_2EREAD_2E0:
!>[A_27a: $tType,A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))) ).
tff(c_2Estate__transformer_2EREAD_2E2,type,
c_2Estate__transformer_2EREAD_2E2:
!>[A_27a: $tType,A_27state: $tType] : ( ( tyop_2Emin_2Efun(A_27state,A_27a) * A_27state ) > tyop_2Epair_2Eprod(A_27a,A_27state) ) ).
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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Epair_2EUNCURRY_2E2,type,
c_2Epair_2EUNCURRY_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > A_27c ) ).
tff(c_2Estate__transformer_2EUNIT_2E0,type,
c_2Estate__transformer_2EUNIT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ).
tff(c_2Estate__transformer_2EUNIT_2E1,type,
c_2Estate__transformer_2EUNIT_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)) ) ).
tff(c_2Estate__transformer_2EUNIT_2E2,type,
c_2Estate__transformer_2EUNIT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b * A_27a ) > tyop_2Epair_2Eprod(A_27b,A_27a) ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Estate__transformer_2EWIDEN_2E0,type,
c_2Estate__transformer_2EWIDEN_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))) ).
tff(c_2Estate__transformer_2EWIDEN_2E1,type,
c_2Estate__transformer_2EWIDEN_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : ( tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))) ) ).
tff(c_2Estate__transformer_2EWRITE_2E0,type,
c_2Estate__transformer_2EWRITE_2E0:
!>[A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))) ).
tff(c_2Estate__transformer_2EWRITE_2E2,type,
c_2Estate__transformer_2EWRITE_2E2:
!>[A_27state: $tType] : ( ( tyop_2Emin_2Efun(A_27state,A_27state) * A_27state ) > tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
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_2Elist_2Elist__CASE_2E0,type,
c_2Elist_2Elist__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).
tff(c_2Elist_2Elist__CASE_2E3,type,
c_2Elist_2Elist__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).
tff(c_2Estate__transformer_2EmapM_2E0,type,
c_2Estate__transformer_2EmapM_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))) ).
tff(c_2Estate__transformer_2EmapM_2E1,type,
c_2Estate__transformer_2EmapM_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))) ) ).
tff(c_2Estate__transformer_2EmapM_2E2,type,
c_2Estate__transformer_2EmapM_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)) ) ).
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_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).
tff(c_2Epair_2Epair__CASE_2E0,type,
c_2Epair_2Epair__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)) ).
tff(c_2Epair_2Epair__CASE_2E2,type,
c_2Epair_2Epair__CASE_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) ) > A_27a ) ).
tff(c_2Estate__transformer_2Esequence_2E0,type,
c_2Estate__transformer_2Esequence_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))) ).
tff(c_2Estate__transformer_2Esequence_2E1,type,
c_2Estate__transformer_2Esequence_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) > tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: A_27a,X1_2E0: A_27state] : ( c_2Epair_2E_2C_2E2(A_27a,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2E_2C_2E0(A_27a,A_27state),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Epair_2Eprod(A_27b,A_27state)] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2E_2C_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27b: $tType,A_27state: $tType,X0_2E0: A_27b,X1_2E0: A_27state] : ( c_2Epair_2E_2C_2E2(A_27b,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state),app_2E2(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E0(A_27b,A_27state),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27state,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Eone_2Eone,X1_2E0: A_27state] : ( c_2Epair_2E_2C_2E2(tyop_2Eone_2Eone,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2E_2C_2E0(tyop_2Eone_2Eone,A_27state),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_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27b,tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,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_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2EBIND_2E0(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27b,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EBIND_2E0(A_27b,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EBIND_2E0(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0_2E0),X1_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X2_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_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(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2ECURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2ECURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27a,A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EEXT_2E0(A_27a,A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E0(A_27b,A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_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_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E0(A_27b,A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27d,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EEXT_2E0(A_27b,A_27d,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27s,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EEXT_2E0(A_27b,A_27c,A_27s),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EEXT_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X1_2E0: tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))] : ( c_2Estate__transformer_2EEXT_2E2(A_27b,A_27c,A_27s,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EEXT_2E0(A_27b,A_27c,A_27s),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EEXT_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Estate__transformer_2EEXT_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27d,A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E0(A_27d,A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27b_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))] : ( c_2Elist_2EFOLDR_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Elist_2EFOLDR_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EFOR_2E1_2Emono_2EA_27state,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2Estate__transformer_2EFOR_2E1(A_27state,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOR_2E0(A_27state),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EFOREACH_2E1_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Estate__transformer_2EFOREACH_2E1(A_27a,A_27state,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOREACH_2E0(A_27a,A_27state),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))] : ( c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EIGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))] : ( c_2Estate__transformer_2EIGNORE__BIND_2E2(A_27a,tyop_2Eone_2Eone,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Estate__transformer_2EIGNORE__BIND_2E0(A_27a,tyop_2Eone_2Eone,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EIGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EIGNORE__BIND_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EIGNORE__BIND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))] : ( c_2Estate__transformer_2EJOIN_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))] : ( c_2Estate__transformer_2EJOIN_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EK_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27state)] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Elist_2EMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Elist_2EMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EMCOMP_2E0(A_27a,A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27s,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),c_2Estate__transformer_2EMCOMP_2E0(A_27a,A_27b,A_27c,A_27s),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27b,A_27d,A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EMCOMP_2E0(A_27b,A_27d,A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27d,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EMCOMP_2E0(A_27a,A_27d,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27e_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27e,A_27d,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EMCOMP_2E0(A_27e,A_27d,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27e,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EMCOMP_2E0(A_27a,A_27e,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27e,A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))),c_2Estate__transformer_2EMCOMP_2E0(A_27a,A_27e,A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27f_20mono_2EA_27f_20mono_2EA_27e,axiom,
! [A_27d: $tType,A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27d,A_27f,A_27f,A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e)))),c_2Estate__transformer_2EMCOMP_2E0(A_27d,A_27f,A_27f,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Estate__transformer_2EMMAP_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Estate__transformer_2EMMAP_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27b)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,A_27b,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27d,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,A_27d,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Estate__transformer_2EMMAP_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27d,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,A_27d,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EMWHILE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EMWHILE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Estate__transformer_2EMWHILE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Estate__transformer_2ENARROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X2_2E0: A_27state] : ( c_2Estate__transformer_2ENARROW_2E3(A_27a,A_27b,A_27state,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Estate__transformer_2ENARROW_2E0(A_27a,A_27b,A_27state),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EREAD_2E2_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,A_27a),X1_2E0: A_27state] : ( c_2Estate__transformer_2EREAD_2E2(A_27a,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Estate__transformer_2EREAD_2E0(A_27a,A_27state),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27state)] : ( c_2Epair_2ESND_2E1(A_27b,A_27state,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),A_27state,c_2Epair_2ESND_2E0(A_27b,A_27state),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EUNCURRY_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E0(A_27a,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2EUNCURRY_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2EUNCURRY_2E0(A_27b,A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27s_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27s_29,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27s,tyop_2Epair_2Eprod(A_27c,A_27s),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Epair_2EUNCURRY_2E0(A_27b,A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E0(A_27b,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(A_27d,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E0(A_27d,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Estate__transformer_2EUNIT_2E1(A_27b,A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2Estate__transformer_2EUNIT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E0(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EUNIT_2E0(A_27a,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2Estate__transformer_2EUNIT_2E1(A_27state,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EUNIT_2E0(A_27state,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EWIDEN_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))] : ( c_2Estate__transformer_2EWIDEN_2E1(A_27a,A_27b,A_27state,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Estate__transformer_2EWIDEN_2E0(A_27a,A_27b,A_27state),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EWRITE_2E2_2Emono_2EA_27state,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,A_27state),X1_2E0: A_27state] : ( c_2Estate__transformer_2EWRITE_2E2(A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),app_2E2(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EWRITE_2E0(A_27state),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Elist_2Elist__CASE_2E0(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2EmapM_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Estate__transformer_2EmapM_2E1(A_27a,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Estate__transformer_2EmapM_2E0(A_27a,A_27b,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Estate__transformer_2EmapM_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Estate__transformer_2EmapM_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2EmapM_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27d)),c_2Ecombin_2Eo_2E0(A_27b,A_27d,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E0(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27d)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27b_29_29_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27d)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)),A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)),A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27s_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27s_29_29_20mono_2Etyop_2Emin_2Efun_28A_27s_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27s_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27c_29_2CA_27b_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2Ecombin_2Eo_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2Eo_2E0(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ecombin_2Eo_2E0(A_27b,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27a,tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ecombin_2Eo_2E0(A_27c,A_27a,tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27s_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27s_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27s_29,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),X1_2E0: tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))] : ( c_2Ecombin_2Eo_2E2(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s),tyop_2Epair_2Eprod(A_27b,A_27s),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Ecombin_2Eo_2E0(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s),tyop_2Epair_2Eprod(A_27b,A_27s)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b))] : ( c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Estate__transformer_2Esequence_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2Esequence_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2Esequence_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Estate__transformer_2EUNIT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1x_27_2E0: A_27a] : ( c_2Estate__transformer_2EUNIT_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = c_2Epair_2E_2C_2E2(A_27b,A_27a,V0x_2E0,V1x_27_2E0) ) ).
tff(thm_2Estate__transformer_2EBIND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27c,V0g_2E0,V1f_2E0) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2EUNCURRY_2E1(A_27b,A_27a,tyop_2Epair_2Eprod(A_27c,A_27a),V1f_2E0),V0g_2E0) ) ).
tff(thm_2Estate__transformer_2EIGNORE__BIND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))))] :
( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V2x_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),F0_2E0,V1g_2E0),V2x_2E0) = V1g_2E0 )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EIGNORE__BIND_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27b,V0f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),F0_2E0,V1g_2E0)) ) ) ).
tff(thm_2Estate__transformer_2EMMAP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V1m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))] : ( c_2Estate__transformer_2EMMAP_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1m_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27b,V1m_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b),V0f_2E0)) ) ).
tff(thm_2Estate__transformer_2EJOIN__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))] : ( c_2Estate__transformer_2EJOIN_2E1(A_27a,A_27b,V0z_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,V0z_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2Estate__transformer_2EEXT__DEF,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V1m_2E0: tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))] : ( c_2Estate__transformer_2EEXT_2E2(A_27b,A_27c,A_27s,V0f_2E0,V1m_2E0) = c_2Ecombin_2Eo_2E2(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s),tyop_2Epair_2Eprod(A_27b,A_27s),c_2Epair_2EUNCURRY_2E1(A_27b,A_27s,tyop_2Epair_2Eprod(A_27c,A_27s),V0f_2E0),V1m_2E0) ) ).
tff(thm_2Estate__transformer_2EMCOMP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27s,V0g_2E0,V1f_2E0) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27s,V0g_2E0),V1f_2E0) ) ).
tff(thm_2Estate__transformer_2EFOR__primitive__def,axiom,
! [A_27state: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V0R_2E0))
& ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2j_2E0: tyop_2Enum_2Enum,V3i_2E0: tyop_2Enum_2Enum] :
( ( V3i_2E0 != V2j_2E0 )
=> p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0R_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V3i_2E0,V2j_2E0),c_2Earithmetic_2E_2B_2E2(V3i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(V3i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2j_2E0,V1a_2E0))),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3i_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2j_2E0,V1a_2E0)))) ) ) )
=> ( ! [V6i_2E0: tyop_2Enum_2Enum,V8j_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0,V6i_2E0),V8j_2E0))
<=> ( V6i_2E0 = V8j_2E0 ) )
=> ( ! [V4FOR_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6i_2E0: tyop_2Enum_2Enum,V8j_2E0: tyop_2Enum_2Enum,V9a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V10u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F5_2E0,V4FOR_2E0),V6i_2E0),V8j_2E0),V9a_2E0),V10u_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V4FOR_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V6i_2E0,V8j_2E0),c_2Earithmetic_2E_2B_2E2(V6i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(V6i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V8j_2E0,V9a_2E0))) )
=> ( ! [V6i_2E0: tyop_2Enum_2Enum,V4FOR_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V8j_2E0: tyop_2Enum_2Enum,V9a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F3_2E0,V6i_2E0),V4FOR_2E0),V8j_2E0),V9a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0,V6i_2E0),V8j_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V9a_2E0,V6i_2E0),c_2Estate__transformer_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V9a_2E0,V6i_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F5_2E0,V4FOR_2E0),V6i_2E0),V8j_2E0),V9a_2E0)))) )
=> ( ! [V4FOR_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6i_2E0: tyop_2Enum_2Enum,V7v1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F2_2E0,V4FOR_2E0),V6i_2E0),V7v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F3_2E0,V6i_2E0),V4FOR_2E0)) )
=> ( ! [V4FOR_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V5a_27_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),F1_2E0,V4FOR_2E0),V5a_27_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V5a_27_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F2_2E0,V4FOR_2E0)) )
=> ( c_2Estate__transformer_2EFOR_2E0(A_27state) = c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ) ).
tff(thm_2Estate__transformer_2EFOREACH__primitive__def,axiom,
! [A_27a: $tType,A_27state: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V0R_2E0))
& ! [V1h_2E0: A_27a,V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3t_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),V0R_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3t_2E0,V2a_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2ECONS_2E2(A_27a,V1h_2E0,V3t_2E0),V2a_2E0))) ) )
=> ( ! [V4FOREACH_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9t_2E0: tyop_2Elist_2Elist(A_27a),V7a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V10u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F4_2E0,V4FOREACH_2E0),V9t_2E0),V7a_2E0),V10u_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V4FOREACH_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9t_2E0,V7a_2E0)) )
=> ( ! [V7a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V8h_2E0: A_27a,V9t_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F3_2E0,V7a_2E0),V4FOREACH_2E0),V8h_2E0),V9t_2E0) = c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V7a_2E0,V8h_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F4_2E0,V4FOREACH_2E0),V9t_2E0),V7a_2E0))) )
=> ( ! [V4FOREACH_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6v_2E0: tyop_2Elist_2Elist(A_27a),V7a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F2_2E0,V4FOREACH_2E0),V6v_2E0),V7a_2E0) = c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V6v_2E0,c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EUNIT_2E1(A_27state,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F3_2E0,V7a_2E0),V4FOREACH_2E0)) )
=> ( ! [V4FOREACH_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V5a_27_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),F1_2E0,V4FOREACH_2E0),V5a_27_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V5a_27_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F2_2E0,V4FOREACH_2E0)) )
=> ( c_2Estate__transformer_2EFOREACH_2E0(A_27a,A_27state) = c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ).
tff(thm_2Estate__transformer_2EREAD__def,axiom,
! [A_27a: $tType,A_27state: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27state,A_27a),V1x_2E0: A_27state] : ( c_2Estate__transformer_2EREAD_2E2(A_27a,A_27state,V0f_2E0,V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27state,app_2E2(A_27state,A_27a,V0f_2E0,V1x_2E0),V1x_2E0) ) ).
tff(thm_2Estate__transformer_2EWRITE__def,axiom,
! [A_27state: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27state,A_27state),V1x_2E0: A_27state] : ( c_2Estate__transformer_2EWRITE_2E2(A_27state,V0f_2E0,V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eone_2Eone,A_27state,c_2Eone_2Eone_2E0,app_2E2(A_27state,A_27state,V0f_2E0,V1x_2E0)) ) ).
tff(thm_2Estate__transformer_2ENARROW__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state)))] :
( ! [V3r_2E0: A_27a,V4s1_2E0: tyop_2Epair_2Eprod(A_27b,A_27state)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state)),F0_2E0,V3r_2E0),V4s1_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27state,V3r_2E0,c_2Epair_2ESND_2E1(A_27b,A_27state,V4s1_2E0)) )
=> ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),V2x_2E0: A_27state] : ( c_2Estate__transformer_2ENARROW_2E3(A_27a,A_27b,A_27state,V0v_2E0,V1f_2E0,V2x_2E0) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state),F0_2E0),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),V1f_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27state,V0v_2E0,V2x_2E0))) ) ) ).
tff(thm_2Estate__transformer_2EWIDEN__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))] :
( ! [V1s1_2E0: A_27b,V3r_2E0: A_27a,V4s3_2E0: A_27state] : ( app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F1_2E0,V1s1_2E0),V3r_2E0),V4s3_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),V3r_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27state,V1s1_2E0,V4s3_2E0)) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V1s1_2E0: A_27b,V2s2_2E0: A_27state] : ( app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F0_2E0,V0f_2E0),V1s1_2E0),V2s2_2E0) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2EUNCURRY_2E1(A_27a,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F1_2E0,V1s1_2E0)),app_2E2(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state),V0f_2E0,V2s2_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))] : ( c_2Estate__transformer_2EWIDEN_2E1(A_27a,A_27b,A_27state,V0f_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F0_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Estate__transformer_2Esequence__def,axiom,
! [A_27a: $tType,A_27b: $tType,F2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))] :
( ! [V2x_2E0: A_27b,V3xs_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F2_2E0,V2x_2E0),V3xs_2E0) = c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27b,V2x_2E0,V3xs_2E0)) )
=> ( ! [V1ms_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V2x_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F1_2E0,V1ms_2E0),V2x_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),V1ms_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F2_2E0,V2x_2E0)) )
=> ( ! [V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1ms_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F0_2E0,V0m_2E0),V1ms_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,tyop_2Elist_2Elist(A_27b),V0m_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F1_2E0,V1ms_2E0)) )
=> ( c_2Estate__transformer_2Esequence_2E0(A_27a,A_27b) = c_2Elist_2EFOLDR_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),F0_2E0,c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b))) ) ) ) ) ).
tff(thm_2Estate__transformer_2EmapM__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Estate__transformer_2EmapM_2E1(A_27a,A_27b,A_27c,V0f_2E0) = c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2Esequence_2E0(A_27b,A_27c),c_2Elist_2EMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),V0f_2E0)) ) ).
tff(thm_2Estate__transformer_2EMWHILE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))))] :
( ! [V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V2gv_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),F0_2E0,V1b_2E0),V0g_2E0),V2gv_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),V2gv_2E0,c_2Estate__transformer_2EIGNORE__BIND_2E2(A_27a,tyop_2Eone_2Eone,A_27b,V1b_2E0,c_2Estate__transformer_2EMWHILE_2E2(A_27a,A_27b,V0g_2E0,V1b_2E0)),c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EMWHILE_2E2(A_27a,A_27b,V0g_2E0,V1b_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Eone_2Eone,V0g_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),F0_2E0,V1b_2E0),V0g_2E0)) ) ) ).
tff(thm_2Estate__transformer_2EFOR__ind,axiom,
! [A_27state: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)] :
( ! [V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum,V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] :
( ( ( V1i_2E0 != V2j_2E0 )
=> p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V1i_2E0,V2j_2E0),c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2j_2E0,V3a_2E0)))) )
=> p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V1i_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2j_2E0,V3a_2E0)))) )
=> ! [V4v_2E0: tyop_2Enum_2Enum,V5v1_2E0: tyop_2Enum_2Enum,V6v2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4v_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V5v1_2E0,V6v2_2E0)))) ) ).
tff(thm_2Estate__transformer_2EFOR__def,axiom,
! [A_27state: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))] :
( ! [V1i_2E0: tyop_2Enum_2Enum,V0j_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1i_2E0),V0j_2E0))
<=> ( V1i_2E0 = V0j_2E0 ) )
=> ( ! [V1i_2E0: tyop_2Enum_2Enum,V0j_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F1_2E0,V1i_2E0),V0j_2E0),V2a_2E0),V3u_2E0) = c_2Estate__transformer_2EFOR_2E1(A_27state,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V1i_2E0,V0j_2E0),c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2D_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V0j_2E0,V2a_2E0))) )
=> ! [V0j_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Estate__transformer_2EFOR_2E1(A_27state,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V1i_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V0j_2E0,V2a_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1i_2E0),V0j_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V2a_2E0,V1i_2E0),c_2Estate__transformer_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V2a_2E0,V1i_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F1_2E0,V1i_2E0),V0j_2E0),V2a_2E0))) ) ) ) ).
tff(thm_2Estate__transformer_2EFOREACH__ind,axiom,
! [A_27a: $tType,A_27state: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)] :
( ( ! [V1a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2ENIL_2E0(A_27a),V1a_2E0)))
& ! [V2h_2E0: A_27a,V3t_2E0: tyop_2Elist_2Elist(A_27a),V4a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] :
( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3t_2E0,V4a_2E0)))
=> p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V3t_2E0),V4a_2E0))) ) )
=> ! [V5v_2E0: tyop_2Elist_2Elist(A_27a),V6v1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool,V0P_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V5v_2E0,V6v1_2E0))) ) ).
tff(thm_2Estate__transformer_2EFOREACH__def,axiom,
! [A_27a: $tType,A_27state: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] :
( ! [V1t_2E0: tyop_2Elist_2Elist(A_27a),V3a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F0_2E0,V1t_2E0),V3a_2E0),V4u_2E0) = c_2Estate__transformer_2EFOREACH_2E1(A_27a,A_27state,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V1t_2E0,V3a_2E0)) )
=> ( ! [V0a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Estate__transformer_2EFOREACH_2E1(A_27a,A_27state,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2ENIL_2E0(A_27a),V0a_2E0)) = c_2Estate__transformer_2EUNIT_2E1(A_27state,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) )
& ! [V1t_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a,V3a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Estate__transformer_2EFOREACH_2E1(A_27a,A_27state,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0),V3a_2E0)) = c_2Estate__transformer_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),V3a_2E0,V2h_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F0_2E0,V1t_2E0),V3a_2E0)) ) ) ) ).
tff(thm_2Estate__transformer_2EUNIT__CURRY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27a) = c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Ecombin_2EI_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) ) ).
tff(thm_2Estate__transformer_2EMCOMP__ALT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27d,A_27c,A_27b,V0g_2E0,V1f_2E0) = c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),c_2Ecombin_2Eo_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b),c_2Epair_2EUNCURRY_2E1(A_27d,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),V0g_2E0),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27b),V1f_2E0))) ) ).
tff(thm_2Estate__transformer_2EMCOMP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V1f_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e)))] :
( ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27a,A_27c,A_27b,V0g_2E0,c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27a)) = V0g_2E0 )
& ( c_2Estate__transformer_2EMCOMP_2E2(A_27d,A_27f,A_27f,A_27e,c_2Estate__transformer_2EUNIT_2E0(A_27e,A_27f),V1f_2E0) = V1f_2E0 ) ) ).
tff(thm_2Estate__transformer_2EMCOMP__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0h_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),V1g_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),V2f_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27d,A_27c,A_27b,V2f_2E0,c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27e,A_27d,A_27b,V1g_2E0,V0h_2E0)) = c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27e,A_27c,A_27b,c_2Estate__transformer_2EMCOMP_2E2(A_27e,A_27d,A_27c,A_27b,V2f_2E0,V1g_2E0),V0h_2E0) ) ).
tff(thm_2Estate__transformer_2EEXT__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27b,A_27a,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(thm_2Estate__transformer_2EEXT__MCOMP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,c_2Estate__transformer_2EMCOMP_2E2(A_27b,A_27d,A_27c,A_27a,V0g_2E0,V1f_2E0)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EEXT_2E1(A_27d,A_27c,A_27a,V0g_2E0),c_2Estate__transformer_2EEXT_2E1(A_27b,A_27d,A_27a,V1f_2E0)) ) ).
tff(thm_2Estate__transformer_2EEXT__o__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EEXT_2E1(A_27a,A_27c,A_27b,V0f_2E0),c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27a)) = V0f_2E0 ) ).
tff(thm_2Estate__transformer_2EUNIT__o__MCOMP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27d)] : ( c_2Estate__transformer_2EMCOMP_2E2(A_27a,A_27d,A_27c,A_27b,c_2Ecombin_2Eo_2E2(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c,c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27c),V0g_2E0),c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)),A_27d,c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27d),V1f_2E0)) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),A_27c,c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27c),c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27d,V0g_2E0,V1f_2E0)) ) ).
tff(thm_2Estate__transformer_2EBIND__EXT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27b,V0m_2E0,V1f_2E0) = c_2Estate__transformer_2EEXT_2E2(A_27c,A_27b,A_27a,V1f_2E0,V0m_2E0) ) ).
tff(thm_2Estate__transformer_2EMMAP__EXT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,V0f_2E0) = c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27c,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27c),V0f_2E0)) ) ).
tff(thm_2Estate__transformer_2EJOIN__EXT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b) = c_2Estate__transformer_2EEXT_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,A_27a,c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2Estate__transformer_2EEXT__JM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,V0f_2E0) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27c),c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,V0f_2E0)) ) ).
tff(thm_2Estate__transformer_2EBIND__LEFT__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V1x_2E0: A_27a] : ( c_2Estate__transformer_2EBIND_2E2(A_27b,A_27a,A_27c,c_2Estate__transformer_2EUNIT_2E1(A_27b,A_27a,V1x_2E0),V0k_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),V0k_2E0,V1x_2E0) ) ).
tff(thm_2Estate__transformer_2EUNIT__UNCURRY,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EUNCURRY_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Estate__transformer_2EUNIT_2E0(A_27b,A_27a),V0s_2E0) = V0s_2E0 ) ).
tff(thm_2Estate__transformer_2EBIND__RIGHT__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27b,V0k_2E0,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b)) = V0k_2E0 ) ).
tff(thm_2Estate__transformer_2EBIND__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))))] :
( ! [V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V2n_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V3a_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),F0_2E0,V1m_2E0),V2n_2E0),V3a_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27d,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V1m_2E0,V3a_2E0),V2n_2E0) )
=> ! [V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V2n_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27d,V0k_2E0,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),F0_2E0,V1m_2E0),V2n_2E0)) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27c,A_27d,c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27c,V0k_2E0,V1m_2E0),V2n_2E0) ) ) ).
tff(thm_2Estate__transformer_2EMMAP__ID,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27b,A_27b,c_2Ecombin_2EI_2E0(A_27b)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(thm_2Estate__transformer_2EMMAP__COMP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27d,A_27b,c_2Ecombin_2Eo_2E2(A_27b,A_27d,A_27c,V0f_2E0,V1g_2E0)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27d,A_27c,V0f_2E0),c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,V1g_2E0)) ) ).
tff(thm_2Estate__transformer_2EMMAP__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,V0f_2E0),c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b)) = c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27c,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27c),V0f_2E0) ) ).
tff(thm_2Estate__transformer_2EEXT__o__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,V0f_2E0),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b)) = c_2Estate__transformer_2EEXT_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,A_27a,c_2Estate__transformer_2EEXT_2E1(A_27b,A_27c,A_27a,V0f_2E0)) ) ).
tff(thm_2Estate__transformer_2EMMAP__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,V0f_2E0),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27c),c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EMMAP_2E1(A_27a,A_27c,A_27b,V0f_2E0))) ) ).
tff(thm_2Estate__transformer_2EJOIN__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b),c_2Estate__transformer_2EUNIT_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(thm_2Estate__transformer_2EJOIN__MMAP__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b),c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27b,c_2Estate__transformer_2EUNIT_2E0(A_27a,A_27b))) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(thm_2Estate__transformer_2EJOIN__MAP__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b),c_2Estate__transformer_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b))) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),c_2Estate__transformer_2EJOIN_2E0(A_27a,A_27b),c_2Estate__transformer_2EJOIN_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2Estate__transformer_2EJOIN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,A_27c,V0k_2E0,V1m_2E0) = c_2Estate__transformer_2EJOIN_2E1(A_27a,A_27c,c_2Estate__transformer_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,V1m_2E0,V0k_2E0)) ) ).
tff(thm_2Estate__transformer_2EFST__o__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EFST_2E0(A_27a,A_27b),c_2Estate__transformer_2EUNIT_2E1(A_27b,A_27a,V0x_2E0)) = c_2Ecombin_2EK_2E1(A_27a,A_27b,V0x_2E0) ) ).
tff(thm_2Estate__transformer_2ESND__o__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESND_2E0(A_27a,A_27b),c_2Estate__transformer_2EUNIT_2E1(A_27b,A_27a,V0x_2E0)) = c_2Ecombin_2EI_2E0(A_27b) ) ).
tff(thm_2Estate__transformer_2EFST__o__MMAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2EFST_2E0(A_27b,A_27c),c_2Estate__transformer_2EMMAP_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0)) = c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,c_2Ecombin_2Eo_2E2(A_27c,A_27a,tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2EFST_2E0(A_27a,A_27c),V1g_2E0)) ) ).
tff(thm_2Estate__transformer_2Esequence__nil,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Estate__transformer_2Esequence_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))) = c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b)) ) ).
tff(thm_2Estate__transformer_2EmapM__nil,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EmapM_2E2(A_27c,A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27c)) = c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b)) ) ).
tff(thm_2Estate__transformer_2EmapM__cons,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))))] :
( ! [V3y_2E0: A_27b,V4ys_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F1_2E0,V3y_2E0),V4ys_2E0) = c_2Estate__transformer_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(A_27b,V3y_2E0,V4ys_2E0)) )
=> ( ! [V2f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V0xs_2E0: tyop_2Elist_2Elist(A_27c),V3y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0,V2f_2E0),V0xs_2E0),V3y_2E0) = c_2Estate__transformer_2EBIND_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Estate__transformer_2EmapM_2E2(A_27c,A_27a,A_27b,V2f_2E0,V0xs_2E0),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F1_2E0,V3y_2E0)) )
=> ! [V0xs_2E0: tyop_2Elist_2Elist(A_27c),V1x_2E0: A_27c,V2f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Estate__transformer_2EmapM_2E2(A_27c,A_27a,A_27b,V2f_2E0,c_2Elist_2ECONS_2E2(A_27c,V1x_2E0,V0xs_2E0)) = c_2Estate__transformer_2EBIND_2E2(A_27a,A_27b,tyop_2Elist_2Elist(A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V2f_2E0,V1x_2E0),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0,V2f_2E0),V0xs_2E0)) ) ) ) ).
%------------------------------------------------------------------------------