ITP001 Axioms: ITP034_7.ax
%------------------------------------------------------------------------------
% File : ITP034_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 : errorStateMonad.ax [Gau19]
% : HL4034_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 322 ( 164 unt; 124 typ; 0 def)
% Number of atoms : 269 ( 222 equ)
% Maximal formula atoms : 11 ( 0 avg)
% Number of connectives : 76 ( 5 ~; 3 |; 10 &)
% ( 17 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 104 ( 62 >; 42 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 120 ( 120 usr; 13 con; 0-7 aty)
% Number of variables : 1102 ( 899 !; 1 ?;1102 :)
% ( 202 !>; 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_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_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_2EerrorStateMonad_2EBIND_2E0,type,
c_2EerrorStateMonad_2EBIND_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))) ).
tff(c_2EerrorStateMonad_2EBIND_2E2,type,
c_2EerrorStateMonad_2EBIND_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))) ) ).
tff(c_2EerrorStateMonad_2EBIND_2E3,type,
c_2EerrorStateMonad_2EBIND_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))) * A_27a ) > tyop_2Eoption_2Eoption(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_2EerrorStateMonad_2EES__APPLY_2E0,type,
c_2EerrorStateMonad_2EES__APPLY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) ).
tff(c_2EerrorStateMonad_2EES__APPLY_2E2,type,
c_2EerrorStateMonad_2EES__APPLY_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2EerrorStateMonad_2EES__CHOICE_2E0,type,
c_2EerrorStateMonad_2EES__CHOICE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))) ).
tff(c_2EerrorStateMonad_2EES__CHOICE_2E2,type,
c_2EerrorStateMonad_2EES__CHOICE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) * tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ) > tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2EerrorStateMonad_2EES__CHOICE_2E3,type,
c_2EerrorStateMonad_2EES__CHOICE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) * tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) * A_27b ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2EerrorStateMonad_2EES__FAIL_2E0,type,
c_2EerrorStateMonad_2EES__FAIL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2EerrorStateMonad_2EES__FAIL_2E1,type,
c_2EerrorStateMonad_2EES__FAIL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2EerrorStateMonad_2EES__GUARD_2E0,type,
c_2EerrorStateMonad_2EES__GUARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))) ).
tff(c_2EerrorStateMonad_2EES__GUARD_2E1,type,
c_2EerrorStateMonad_2EES__GUARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Ebool > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))) ) ).
tff(c_2EerrorStateMonad_2EES__LIFT2_2E0,type,
c_2EerrorStateMonad_2EES__LIFT2_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))) ).
tff(c_2EerrorStateMonad_2EES__LIFT2_2E3,type,
c_2EerrorStateMonad_2EES__LIFT2_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2EerrorStateMonad_2EEXT_2E0,type,
c_2EerrorStateMonad_2EEXT_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) ).
tff(c_2EerrorStateMonad_2EEXT_2E1,type,
c_2EerrorStateMonad_2EEXT_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(c_2EerrorStateMonad_2EEXT_2E2,type,
c_2EerrorStateMonad_2EEXT_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
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_2EerrorStateMonad_2EFOR_2E0,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))) ).
tff(c_2EerrorStateMonad_2EFOR_2E1,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))) > tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))) ) ).
tff(c_2EerrorStateMonad_2EFOREACH_2E0,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))) ).
tff(c_2EerrorStateMonad_2EFOREACH_2E1,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))) > tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))) ) ).
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_2EerrorStateMonad_2EIGNORE__BIND_2E0,type,
c_2EerrorStateMonad_2EIGNORE__BIND_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))) ).
tff(c_2EerrorStateMonad_2EIGNORE__BIND_2E2,type,
c_2EerrorStateMonad_2EIGNORE__BIND_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))) * tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))) ) > tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))) ) ).
tff(c_2EerrorStateMonad_2EJOIN_2E0,type,
c_2EerrorStateMonad_2EJOIN_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ).
tff(c_2EerrorStateMonad_2EJOIN_2E1,type,
c_2EerrorStateMonad_2EJOIN_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E1,type,
c_2Elist_2EMAP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) ) ).
tff(c_2EerrorStateMonad_2EMCOMP_2E0,type,
c_2EerrorStateMonad_2EMCOMP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))) ).
tff(c_2EerrorStateMonad_2EMCOMP_2E2,type,
c_2EerrorStateMonad_2EMCOMP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : ( ( tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))) ) ).
tff(c_2EerrorStateMonad_2EMMAP_2E0,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) ).
tff(c_2EerrorStateMonad_2EMMAP_2E1,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(c_2EerrorStateMonad_2EMMAP_2E2,type,
c_2EerrorStateMonad_2EMMAP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))) ) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2EerrorStateMonad_2ENARROW_2E0,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))) ).
tff(c_2EerrorStateMonad_2ENARROW_2E3,type,
c_2EerrorStateMonad_2ENARROW_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : ( ( A_27b * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))) * A_27state ) > tyop_2Eoption_2Eoption(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_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eoption_2EOPTION__MCOMP_2E0,type,
c_2Eoption_2EOPTION__MCOMP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))) ).
tff(c_2Eoption_2EOPTION__MCOMP_2E2,type,
c_2Eoption_2EOPTION__MCOMP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)) * tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)) ) > tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2EerrorStateMonad_2EREAD_2E0,type,
c_2EerrorStateMonad_2EREAD_2E0:
!>[A_27a: $tType,A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))) ).
tff(c_2EerrorStateMonad_2EREAD_2E2,type,
c_2EerrorStateMonad_2EREAD_2E2:
!>[A_27a: $tType,A_27state: $tType] : ( ( tyop_2Emin_2Efun(A_27state,A_27a) * A_27state ) > tyop_2Eoption_2Eoption(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_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_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_2EerrorStateMonad_2EUNIT_2E0,type,
c_2EerrorStateMonad_2EUNIT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ).
tff(c_2EerrorStateMonad_2EUNIT_2E1,type,
c_2EerrorStateMonad_2EUNIT_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).
tff(c_2EerrorStateMonad_2EUNIT_2E2,type,
c_2EerrorStateMonad_2EUNIT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b * A_27a ) > tyop_2Eoption_2Eoption(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_2EerrorStateMonad_2EWIDEN_2E0,type,
c_2EerrorStateMonad_2EWIDEN_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))) ).
tff(c_2EerrorStateMonad_2EWIDEN_2E1,type,
c_2EerrorStateMonad_2EWIDEN_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27state: $tType] : ( tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))) ) ).
tff(c_2EerrorStateMonad_2EWRITE_2E0,type,
c_2EerrorStateMonad_2EWRITE_2E0:
!>[A_27state: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))) ).
tff(c_2EerrorStateMonad_2EWRITE_2E2,type,
c_2EerrorStateMonad_2EWRITE_2E2:
!>[A_27state: $tType] : ( ( tyop_2Emin_2Efun(A_27state,A_27state) * A_27state ) > tyop_2Eoption_2Eoption(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_2EerrorStateMonad_2EmapM_2E0,type,
c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))))) ).
tff(c_2EerrorStateMonad_2EmapM_2E1,type,
c_2EerrorStateMonad_2EmapM_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))) ) ).
tff(c_2EerrorStateMonad_2EmapM_2E2,type,
c_2EerrorStateMonad_2EmapM_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_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_2EerrorStateMonad_2Esequence_2E0,type,
c_2EerrorStateMonad_2Esequence_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))) ).
tff(c_2EerrorStateMonad_2Esequence_2E1,type,
c_2EerrorStateMonad_2Esequence_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) > tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EerrorStateMonad_2EBIND_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X2_2E0: A_27a] : ( c_2EerrorStateMonad_2EBIND_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27b,tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EBIND_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Eone_2Eone,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EBIND_2E0(A_27a,tyop_2Eone_2Eone,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EBIND_2E0(A_27b,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X2_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28A_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c))] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Epair_2ECURRY_2E0(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2ECURRY_2E0(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EES__APPLY_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EES__APPLY_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EES__APPLY_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EES__APPLY_2E0(A_27a,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EES__CHOICE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2EerrorStateMonad_2EES__CHOICE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EerrorStateMonad_2EES__CHOICE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X2_2E0: A_27b] : ( c_2EerrorStateMonad_2EES__CHOICE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2EerrorStateMonad_2EES__CHOICE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EES__FAIL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2EerrorStateMonad_2EES__FAIL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),c_2EerrorStateMonad_2EES__FAIL_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EES__GUARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool] : ( c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2EerrorStateMonad_2EES__LIFT2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2EerrorStateMonad_2EES__LIFT2_2E3(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EES__LIFT2_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EEXT_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,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EEXT_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EEXT_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2EerrorStateMonad_2EEXT_2E1(A_27b,A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EEXT_2E0(A_27b,A_27c,A_27d),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27b_29_2CA_27a_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))] : ( c_2Elist_2EFOLDR_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2Elist_2EFOLDR_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOR_2E0(A_27state),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOREACH_2E0(A_27a,A_27state),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))] : ( c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27b,A_27a,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0(A_27b,A_27a,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(tyop_2Eone_2Eone,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0(tyop_2Eone_2Eone,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))] : ( c_2EerrorStateMonad_2EJOIN_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a)))] : ( c_2EerrorStateMonad_2EJOIN_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2Elist_2EMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Elist_2EMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27a,A_27b,A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27d_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27d,A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27a,A_27b,A_27c,A_27d,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27f_20mono_2EA_27g_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X1_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27f,A_27g,A_27c,A_27d,A_27e,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c)))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27f,A_27g,A_27c,A_27d,A_27e),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27f_20mono_2EA_27g,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27f: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27f,A_27g,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27a,A_27b,A_27c,A_27f,A_27g),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27e_29_20mono_2EA_27f_20mono_2EA_27g,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27e),A_27f,A_27g,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27e),A_27f,A_27g),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27e_20mono_2Etyop_2Epair_2Eprod_28A_27f_2CA_27g_29_20mono_2EA_27f_20mono_2EA_27g,axiom,
! [A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27d,A_27e,tyop_2Epair_2Eprod(A_27f,A_27g),A_27f,A_27g,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),app_2E2(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))),c_2EerrorStateMonad_2EMCOMP_2E0(A_27d,A_27e,tyop_2Epair_2Eprod(A_27f,A_27g),A_27f,A_27g),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_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)] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27c,A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27c,A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27d,A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,A_27b,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2EerrorStateMonad_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27d,A_27a,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EMMAP_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27d,A_27b,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27b_29_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27d,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27d,A_27b),A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),c_2EerrorStateMonad_2EMMAP_2E0(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X0_2E0) ) ).
tff(arityeq3_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X2_2E0: A_27state] : ( c_2EerrorStateMonad_2ENARROW_2E3(A_27a,A_27b,A_27state,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2EerrorStateMonad_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_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27e_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))] : ( c_2Eoption_2EOPTION__MCOMP_2E2(A_27c,tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__MCOMP_2E0(A_27c,tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2EerrorStateMonad_2EREAD_2E2(A_27a,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),c_2EerrorStateMonad_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(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,
! [A_27a: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27state)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_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_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27d_2CA_27e_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27state_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E0(A_27b,A_27state,tyop_2Eoption_2Eoption(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_27e_20mono_2Etyop_2Eoption_2Eoption_28A_27c_29,axiom,
! [A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c)))] : ( c_2Epair_2EUNCURRY_2E1(A_27d,A_27e,tyop_2Eoption_2Eoption(A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),c_2Epair_2EUNCURRY_2E0(A_27d,A_27e,tyop_2Eoption_2Eoption(A_27c)),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27b,A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2EerrorStateMonad_2EUNIT_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2EerrorStateMonad_2EUNIT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27a,A_27c,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2EerrorStateMonad_2EUNIT_2E1(A_27state,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))] : ( c_2EerrorStateMonad_2EWIDEN_2E1(A_27a,A_27b,A_27state,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2EerrorStateMonad_2EWIDEN_2E0(A_27a,A_27b,A_27state),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_2EWRITE_2E2_2Emono_2EA_27state,axiom,
! [A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(A_27state,A_27state),X1_2E0: A_27state] : ( c_2EerrorStateMonad_2EWRITE_2E2(A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_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_2Eoption_2Eoption_28tyop_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_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2Elist_2Elist__CASE_2E3(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Elist_2Elist__CASE_2E0(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2EerrorStateMonad_2EmapM_2E1(A_27a,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2EerrorStateMonad_2EmapM_2E0(A_27a,A_27b,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_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_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27d_2CA_27b_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_2CA_27c_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27d_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27d_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27c_29_2CA_27b_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))] : ( c_2Ecombin_2Eo_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29_20mono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),A_27a,A_27state,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),A_27a,A_27state),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2Esequence_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_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_2EerrorStateMonad_2EUNIT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1x_27_2E0: A_27a] : ( c_2EerrorStateMonad_2EUNIT_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V0x_2E0,V1x_27_2E0)) ) ).
tff(thm_2EerrorStateMonad_2EBIND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V4b_2E0: A_27b,V5s_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),F1_2E0,V1f_2E0),V4b_2E0),V5s_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1f_2E0,V4b_2E0),V5s_2E0) )
=> ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V3v_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),F0_2E0,V1f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),A_27b,A_27a,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),F1_2E0,V1f_2E0)) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V2s0_2E0: A_27a] : ( c_2EerrorStateMonad_2EBIND_2E3(A_27a,A_27b,A_27c,V0g_2E0,V1f_2E0,V2s0_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V0g_2E0,V2s0_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),F0_2E0,V1f_2E0)) ) ) ) ).
tff(thm_2EerrorStateMonad_2EIGNORE__BIND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))] :
( ! [V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),F0_2E0,V1g_2E0),V2x_2E0) = V1g_2E0 )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))] : ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27b,A_27a,A_27c,V0f_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),F0_2E0,V1g_2E0)) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EMMAP_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1m_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27b,V1m_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b,c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27b),V0f_2E0)) ) ).
tff(thm_2EerrorStateMonad_2EJOIN__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))] : ( c_2EerrorStateMonad_2EJOIN_2E1(A_27a,A_27b,V0z_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b,V0z_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) ) ).
tff(thm_2EerrorStateMonad_2EEXT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V1m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EEXT_2E2(A_27a,A_27b,A_27c,V0g_2E0,V1m_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27b,V1m_2E0,V0g_2E0) ) ).
tff(thm_2EerrorStateMonad_2EMCOMP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27d,A_27e,V0g_2E0,V1f_2E0) = c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MCOMP_2E2(A_27c,tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27d,A_27e,tyop_2Eoption_2Eoption(A_27c),V0g_2E0),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)),V1f_2E0))) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),V0R_2E0))
& ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V10u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0,V6i_2E0),c_2EerrorStateMonad_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0,V4FOR_2E0)) )
=> ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V10u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6v_2E0,c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0,V4FOREACH_2E0)) )
=> ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ).
tff(thm_2EerrorStateMonad_2EREAD__def,axiom,
! [A_27a: $tType,A_27state: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27state,A_27a),V1x_2E0: A_27state] : ( c_2EerrorStateMonad_2EREAD_2E2(A_27a,A_27state,V0f_2E0,V1x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(A_27a,A_27state,app_2E2(A_27state,A_27a,V0f_2E0,V1x_2E0),V1x_2E0)) ) ).
tff(thm_2EerrorStateMonad_2EWRITE__def,axiom,
! [A_27state: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27state,A_27state),V1x_2E0: A_27state] : ( c_2EerrorStateMonad_2EWRITE_2E2(A_27state,V0f_2E0,V1x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),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_2EerrorStateMonad_2ENARROW__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))] :
( ! [V4r_2E0: A_27a,V5s1_2E0: tyop_2Epair_2Eprod(A_27b,A_27state)] : ( app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),F1_2E0,V4r_2E0),V5s1_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(A_27a,A_27state,V4r_2E0,c_2Epair_2ESND_2E1(A_27b,A_27state,V5s1_2E0))) )
=> ( ! [V3v_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),F0_2E0,V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),V3v_2E0,F1_2E0) )
=> ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),V2x_2E0: A_27state] : ( c_2EerrorStateMonad_2ENARROW_2E3(A_27a,A_27b,A_27state,V0v_2E0,V1f_2E0,V2x_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(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)),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,A_27state)),F0_2E0) ) ) ) ).
tff(thm_2EerrorStateMonad_2EWIDEN__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27state: $tType,F2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))))] :
( ! [V1s1_2E0: A_27b,V4r_2E0: A_27a,V5s3_2E0: A_27state] : ( app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F2_2E0,V1s1_2E0),V4r_2E0),V5s3_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state),V4r_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27state,V1s1_2E0,V5s3_2E0))) )
=> ( ! [V1s1_2E0: A_27b,V3v_2E0: tyop_2Epair_2Eprod(A_27a,A_27state)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F1_2E0,V1s1_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),A_27a,A_27state,V3v_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F2_2E0,V1s1_2E0)) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),V1s1_2E0: A_27b,V2s2_2E0: A_27state] : ( app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0,V0f_2E0),V1s1_2E0),V2s2_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0,V2s2_2E0),c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),F1_2E0,V1s1_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))] : ( c_2EerrorStateMonad_2EWIDEN_2E1(A_27a,A_27b,A_27state,V0f_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0,V0f_2E0)) ) ) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0,V2x_2E0),V3xs_2E0) = c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),V2x_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0,V1ms_2E0),V2x_2E0) = c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0,V2x_2E0)) )
=> ( ! [V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1ms_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0,V0m_2E0),V1ms_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,tyop_2Elist_2Elist(A_27b),V0m_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0,V1ms_2E0)) )
=> ( c_2EerrorStateMonad_2Esequence_2E0(A_27a,A_27b) = c_2Elist_2EFOLDR_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),F0_2E0,c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b))) ) ) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2Esequence_2E0(A_27b,A_27c),c_2Elist_2EMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V0f_2E0)) ) ).
tff(thm_2EerrorStateMonad_2EES__FAIL__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: A_27b] : ( c_2EerrorStateMonad_2EES__FAIL_2E1(A_27a,A_27b,V0s_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) ).
tff(thm_2EerrorStateMonad_2EES__CHOICE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] :
( ! [V3v1_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),F0_2E0,V3v1_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3v1_2E0) )
=> ! [V0xM_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1yM_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2s_2E0: A_27b] : ( c_2EerrorStateMonad_2EES__CHOICE_2E3(A_27a,A_27b,V0xM_2E0,V1yM_2E0,V2s_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),V0xM_2E0,V2s_2E0),app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),V1yM_2E0,V2s_2E0),F0_2E0) ) ) ).
tff(thm_2EerrorStateMonad_2EES__GUARD__DEF,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Ebool] : ( c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,V0b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),V0b_2E0,c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a),A_27a)) ) ).
tff(thm_2EerrorStateMonad_2EES__APPLY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))] :
( ! [V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V3x_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0,V2f_2E0),V3x_2E0) = c_2EerrorStateMonad_2EUNIT_2E1(A_27a,A_27b,app_2E2(A_27c,A_27b,V2f_2E0,V3x_2E0)) )
=> ( ! [V1xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F0_2E0,V1xM_2E0),V2f_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27b,V1xM_2E0,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0,V2f_2E0)) )
=> ! [V0fM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),V1xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))] : ( c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27c,V0fM_2E0,V1xM_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),A_27b,V0fM_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F0_2E0,V1xM_2E0)) ) ) ) ).
tff(thm_2EerrorStateMonad_2EES__LIFT2__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),V1xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V2yM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))] : ( c_2EerrorStateMonad_2EES__LIFT2_2E3(A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1xM_2E0,V2yM_2E0) = c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27d,c_2EerrorStateMonad_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27d,A_27b),A_27c,V0f_2E0,V1xM_2E0),V2yM_2E0) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V5v1_2E0,V6v2_2E0)))) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F1_2E0,V1i_2E0),V0j_2E0),V2a_2E0),V3u_2E0) = c_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V0j_2E0,V2a_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0,V1i_2E0),c_2EerrorStateMonad_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F1_2E0,V1i_2E0),V0j_2E0),V2a_2E0))) ) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)] :
( ( ! [V1a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V5v_2E0,V6v1_2E0))) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4u_2E0: tyop_2Eone_2Eone] : ( app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F0_2E0,V1t_2E0),V3a_2E0),V4u_2E0) = c_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Elist_2ENIL_2E0(A_27a),V0a_2E0)) = c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))] : ( c_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1t_2E0),V3a_2E0)) = c_2EerrorStateMonad_2EBIND_2E2(A_27state,tyop_2Eone_2Eone,tyop_2Eone_2Eone,app_2E2(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F0_2E0,V1t_2E0),V3a_2E0)) ) ) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V1x_2E0: A_27a] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27b,A_27a,A_27c,c_2EerrorStateMonad_2EUNIT_2E1(A_27b,A_27a,V1x_2E0),V0k_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V0k_2E0,V1x_2E0) ) ).
tff(thm_2EerrorStateMonad_2EMCOMP__THM,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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,A_27b),A_27d,A_27b,V0g_2E0,V1f_2E0) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),c_2EerrorStateMonad_2EEXT_2E1(A_27b,A_27c,A_27d,V0g_2E0),V1f_2E0) ) ).
tff(thm_2EerrorStateMonad_2EMCOMP__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,V0h_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V1g_2E0: tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V2f_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c)))] : ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27d,A_27e,V2f_2E0,c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27d,A_27e),A_27f,A_27g,V1g_2E0,V0h_2E0)) = c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27f,A_27g,c_2EerrorStateMonad_2EMCOMP_2E2(A_27f,A_27g,A_27c,A_27d,A_27e,V2f_2E0,V1g_2E0),V0h_2E0) ) ).
tff(thm_2EerrorStateMonad_2EUNIT__CURRY,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2EerrorStateMonad_2EUNIT_2E0(A_27b,A_27a) = c_2Epair_2ECURRY_2E1(A_27a,A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) ) ).
tff(thm_2EerrorStateMonad_2EMCOMP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V1f_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))] :
( ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27a,A_27b,A_27c,A_27a,A_27b,V0g_2E0,c_2EerrorStateMonad_2EUNIT_2E0(A_27b,A_27a)) = V0g_2E0 )
& ( c_2EerrorStateMonad_2EMCOMP_2E2(A_27d,A_27e,tyop_2Epair_2Eprod(A_27f,A_27g),A_27f,A_27g,c_2EerrorStateMonad_2EUNIT_2E0(A_27g,A_27f),V1f_2E0) = V1f_2E0 ) ) ).
tff(thm_2EerrorStateMonad_2EBIND__RIGHT__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,A_27b,V0k_2E0,c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27b)) = V0k_2E0 ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))))] :
( ! [V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V2n_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),V3a_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),F0_2E0,V1m_2E0),V2n_2E0),V3a_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27d,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0,V3a_2E0),V2n_2E0) )
=> ! [V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V2n_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,A_27d,V0k_2E0,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),F0_2E0,V1m_2E0),V2n_2E0)) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27d,c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,A_27c,V0k_2E0,V1m_2E0),V2n_2E0) ) ) ).
tff(thm_2EerrorStateMonad_2EMMAP__ID,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27a,A_27b,A_27b,c_2Ecombin_2EI_2E0(A_27b)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2EerrorStateMonad_2EMMAP__COMP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27b,A_27c,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27b,A_27a,V0f_2E0),c_2EerrorStateMonad_2EMMAP_2E1(A_27d,A_27a,A_27c,V1g_2E0)) ) ).
tff(thm_2EerrorStateMonad_2EMMAP__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2EerrorStateMonad_2EMMAP_2E1(A_27c,A_27b,A_27a,V0f_2E0),c_2EerrorStateMonad_2EUNIT_2E0(A_27c,A_27a)) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27b,c_2EerrorStateMonad_2EUNIT_2E0(A_27c,A_27b),V0f_2E0) ) ).
tff(thm_2EerrorStateMonad_2EMMAP__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2EerrorStateMonad_2EMMAP_2E1(A_27c,A_27b,A_27a,V0f_2E0),c_2EerrorStateMonad_2EJOIN_2E0(A_27c,A_27a)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),c_2EerrorStateMonad_2EJOIN_2E0(A_27c,A_27b),c_2EerrorStateMonad_2EMMAP_2E1(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2EerrorStateMonad_2EMMAP_2E1(A_27c,A_27b,A_27a,V0f_2E0))) ) ).
tff(thm_2EerrorStateMonad_2EJOIN__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b),c_2EerrorStateMonad_2EUNIT_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2EerrorStateMonad_2EJOIN__MMAP__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b),c_2EerrorStateMonad_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27b,c_2EerrorStateMonad_2EUNIT_2E0(A_27a,A_27b))) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).
tff(thm_2EerrorStateMonad_2EJOIN__MAP__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b),c_2EerrorStateMonad_2EMMAP_2E1(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b))) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,A_27b),c_2EerrorStateMonad_2EJOIN_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) ) ).
tff(thm_2EerrorStateMonad_2EJOIN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,A_27c,V0k_2E0,V1m_2E0) = c_2EerrorStateMonad_2EJOIN_2E1(A_27a,A_27c,c_2EerrorStateMonad_2EMMAP_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27b,V1m_2E0,V0k_2E0)) ) ).
tff(thm_2EerrorStateMonad_2Esequence__nil,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2EerrorStateMonad_2Esequence_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))) = c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b)) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EmapM_2E2(A_27c,A_27a,A_27b,V0f_2E0,c_2Elist_2ENIL_2E0(A_27c)) = c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0(A_27b)) ) ).
tff(thm_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0,V3y_2E0),V4ys_2E0) = c_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F0_2E0,V2f_2E0),V0xs_2E0),V3y_2E0) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2EerrorStateMonad_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_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EmapM_2E2(A_27c,A_27a,A_27b,V2f_2E0,c_2Elist_2ECONS_2E2(A_27c,V1x_2E0,V0xs_2E0)) = c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27b,tyop_2Elist_2Elist(A_27b),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F0_2E0,V2f_2E0),V0xs_2E0)) ) ) ) ).
tff(thm_2EerrorStateMonad_2EES__CHOICE__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0zM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1yM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,V2xM_2E0,c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,V1yM_2E0,V0zM_2E0)) = c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,V2xM_2E0,V1yM_2E0),V0zM_2E0) ) ).
tff(thm_2EerrorStateMonad_2EES__CHOICE__FAIL__LID,axiom,
! [A_27a: $tType,A_27b: $tType,V0xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,c_2EerrorStateMonad_2EES__FAIL_2E0(A_27b,A_27a),V0xM_2E0) = V0xM_2E0 ) ).
tff(thm_2EerrorStateMonad_2EES__CHOICE__FAIL__RID,axiom,
! [A_27a: $tType,A_27b: $tType,V0xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2EerrorStateMonad_2EES__CHOICE_2E2(A_27b,A_27a,V0xM_2E0,c_2EerrorStateMonad_2EES__FAIL_2E0(A_27b,A_27a)) = V0xM_2E0 ) ).
tff(thm_2EerrorStateMonad_2EBIND__FAIL__L,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0fM_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,A_27c,A_27b,c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a),V0fM_2E0) = c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a) ) ).
tff(thm_2EerrorStateMonad_2EBIND__ESGUARD,axiom,
! [A_27a: $tType,A_27b: $tType,V0fM_2E0: tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))] :
( ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Eone_2Eone,A_27b,c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,c_2Ebool_2EF_2E0),V0fM_2E0) = c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a) )
& ( c_2EerrorStateMonad_2EBIND_2E2(A_27a,tyop_2Eone_2Eone,A_27b,c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,c_2Ebool_2ET_2E0),V0fM_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0fM_2E0,c_2Eone_2Eone_2E0) ) ) ).
tff(thm_2EerrorStateMonad_2EIGNORE__BIND__ESGUARD,axiom,
! [A_27a: $tType,A_27b: $tType,V0xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
( ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(tyop_2Eone_2Eone,A_27a,A_27b,c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,c_2Ebool_2EF_2E0),V0xM_2E0) = c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a) )
& ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(tyop_2Eone_2Eone,A_27a,A_27b,c_2EerrorStateMonad_2EES__GUARD_2E1(A_27a,c_2Ebool_2ET_2E0),V0xM_2E0) = V0xM_2E0 ) ) ).
tff(thm_2EerrorStateMonad_2EIGNORE__BIND__FAIL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
( ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27c,A_27a,A_27b,c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),A_27a),V0xM_2E0) = c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a) )
& ( c_2EerrorStateMonad_2EIGNORE__BIND_2E2(A_27b,A_27a,A_27d,V0xM_2E0,c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27d,A_27a),A_27a)) = c_2EerrorStateMonad_2EES__FAIL_2E0(tyop_2Epair_2Eprod(A_27d,A_27a),A_27a) ) ) ).
tff(thm_2EerrorStateMonad_2EAPPLY__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0xM_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27c,c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),V0xM_2E0) = c_2EerrorStateMonad_2EMMAP_2E2(A_27a,A_27b,A_27c,V1f_2E0,V0xM_2E0) ) ).
tff(thm_2EerrorStateMonad_2EAPPLY__UNIT__UNIT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2EerrorStateMonad_2EES__APPLY_2E2(A_27a,A_27b,A_27c,c_2EerrorStateMonad_2EUNIT_2E1(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),c_2EerrorStateMonad_2EUNIT_2E1(A_27a,A_27c,V0x_2E0)) = c_2EerrorStateMonad_2EUNIT_2E1(A_27a,A_27b,app_2E2(A_27c,A_27b,V1f_2E0,V0x_2E0)) ) ).
%------------------------------------------------------------------------------