ITP001 Axioms: ITP051_7.ax
%------------------------------------------------------------------------------
% File : ITP051_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 : readerMonad.ax [Gau19]
% : HL4051_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 105 ( 48 unt; 41 typ; 0 def)
% Number of atoms : 88 ( 56 equ)
% Maximal formula atoms : 3 ( 0 avg)
% Number of connectives : 27 ( 3 ~; 3 |; 3 &)
% ( 13 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 21 >; 16 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 39 ( 39 usr; 6 con; 0-7 aty)
% Number of variables : 318 ( 254 !; 1 ?; 318 :)
% ( 63 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $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_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_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_2EreaderMonad_2EBIND_2E0,type,
c_2EreaderMonad_2EBIND_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(A_27s,A_27b))) ).
tff(c_2EreaderMonad_2EBIND_2E2,type,
c_2EreaderMonad_2EBIND_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27s,A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)) ) > tyop_2Emin_2Efun(A_27s,A_27b) ) ).
tff(c_2EreaderMonad_2EBIND_2E3,type,
c_2EreaderMonad_2EBIND_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27s,A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)) * A_27s ) > A_27b ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2EreaderMonad_2EFMAP_2E0,type,
c_2EreaderMonad_2EFMAP_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b))) ).
tff(c_2EreaderMonad_2EFMAP_2E1,type,
c_2EreaderMonad_2EFMAP_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b)) ) ).
tff(c_2EreaderMonad_2EFMAP_2E2,type,
c_2EreaderMonad_2EFMAP_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27s,A_27a) ) > tyop_2Emin_2Efun(A_27s,A_27b) ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2EreaderMonad_2EJOIN_2E0,type,
c_2EreaderMonad_2EJOIN_2E0:
!>[A_27a: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),tyop_2Emin_2Efun(A_27s,A_27a)) ).
tff(c_2EreaderMonad_2EJOIN_2E1,type,
c_2EreaderMonad_2EJOIN_2E1:
!>[A_27a: $tType,A_27s: $tType] : ( tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)) > tyop_2Emin_2Efun(A_27s,A_27a) ) ).
tff(c_2EreaderMonad_2EJOIN_2E2,type,
c_2EreaderMonad_2EJOIN_2E2:
!>[A_27a: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)) * A_27s ) > A_27a ) ).
tff(c_2EreaderMonad_2EMCOMPOSE_2E0,type,
c_2EreaderMonad_2EMCOMPOSE_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c)))) ).
tff(c_2EreaderMonad_2EMCOMPOSE_2E2,type,
c_2EreaderMonad_2EMCOMPOSE_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c)) ) ).
tff(c_2EreaderMonad_2EMCOMPOSE_2E3,type,
c_2EreaderMonad_2EMCOMPOSE_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)) * A_27a ) > tyop_2Emin_2Efun(A_27s,A_27c) ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2EreaderMonad_2EUNIT_2E0,type,
c_2EreaderMonad_2EUNIT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2EreaderMonad_2EUNIT_2E1,type,
c_2EreaderMonad_2EUNIT_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2EreaderMonad_2EUNIT_2E2,type,
c_2EreaderMonad_2EUNIT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
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_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_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_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(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EBIND_2E2(A_27b,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EBIND_2E0(A_27b,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EBIND_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_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EBIND_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EBIND_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EBIND_2E2(tyop_2Emin_2Efun(A_27a,A_27b),A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),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)),c_2EreaderMonad_2EBIND_2E0(tyop_2Emin_2Efun(A_27a,A_27b),A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EreaderMonad_2EBIND_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27s,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27s,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X2_2E0: A_27s] : ( c_2EreaderMonad_2EBIND_2E3(A_27a,A_27b,A_27s,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27s,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(A_27s,A_27b)),c_2EreaderMonad_2EBIND_2E0(A_27a,A_27b,A_27s),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27s,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c))] : ( c_2EreaderMonad_2EBIND_2E2(A_27b,A_27c,A_27s,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27s,A_27c),app_2E2(tyop_2Emin_2Efun(A_27s,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27s,A_27c)),c_2EreaderMonad_2EBIND_2E0(A_27b,A_27c,A_27s),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27s,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27s,A_27a)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27a,A_27b,A_27s,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b)),c_2EreaderMonad_2EFMAP_2E0(A_27a,A_27b,A_27s),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27b,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EFMAP_2E0(A_27b,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E1(A_27b,A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E0(A_27b,A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] : ( c_2EreaderMonad_2EFMAP_2E1(A_27b,A_27d,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),c_2EreaderMonad_2EFMAP_2E0(A_27b,A_27d,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EFMAP_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EFMAP_2E0(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E1(A_27d,A_27c,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E0(A_27d,A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2EreaderMonad_2EJOIN_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EJOIN_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EJOIN_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EJOIN_2E2_2Emono_2EA_27a_20mono_2EA_27s,axiom,
! [A_27a: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),X1_2E0: A_27s] : ( c_2EreaderMonad_2EJOIN_2E2(A_27a,A_27s,X0_2E0,X1_2E0) = app_2E2(A_27s,A_27a,app_2E2(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),tyop_2Emin_2Efun(A_27s,A_27a),c_2EreaderMonad_2EJOIN_2E0(A_27a,A_27s),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27c,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27c,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27d,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27d,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27e_20mono_2EA_27b,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,A_27d)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27d,A_27e,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27d,A_27e,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27e,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27e,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EreaderMonad_2EMCOMPOSE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),X2_2E0: A_27a] : ( c_2EreaderMonad_2EMCOMPOSE_2E3(A_27a,A_27b,A_27c,A_27s,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27s,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27a,A_27b,A_27c,A_27s),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27d_20mono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27d,A_27e,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2EreaderMonad_2EMCOMPOSE_2E0(A_27d,A_27e,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EreaderMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2EreaderMonad_2EUNIT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2EreaderMonad_2EUNIT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EreaderMonad_2EUNIT_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2EreaderMonad_2EUNIT_2E1(A_27c,A_27a,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27c),c_2EreaderMonad_2EUNIT_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27s_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27s,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27s,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b)),c_2Ecombin_2Eo_2E0(A_27s,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_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,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),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,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_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,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E0(A_27b,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d))] : ( c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27d)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2EreaderMonad_2EBIND__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,V0M_2E0: tyop_2Emin_2Efun(A_27s,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V2s_2E0: A_27s] : ( c_2EreaderMonad_2EBIND_2E3(A_27a,A_27b,A_27s,V0M_2E0,V1f_2E0,V2s_2E0) = app_2E2(A_27s,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27s,A_27b),V1f_2E0,app_2E2(A_27s,A_27a,V0M_2E0,V2s_2E0)),V2s_2E0) ) ).
tff(thm_2EreaderMonad_2EUNIT__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1s_2E0: A_27b] : ( c_2EreaderMonad_2EUNIT_2E2(A_27a,A_27b,V0x_2E0,V1s_2E0) = V0x_2E0 ) ).
tff(thm_2EreaderMonad_2EMCOMPOSE__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V1f2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),V2a_2E0: A_27a] : ( c_2EreaderMonad_2EMCOMPOSE_2E3(A_27a,A_27b,A_27c,A_27s,V0f1_2E0,V1f2_2E0,V2a_2E0) = c_2EreaderMonad_2EBIND_2E2(A_27b,A_27c,A_27s,app_2E2(A_27a,tyop_2Emin_2Efun(A_27s,A_27b),V0f1_2E0,V2a_2E0),V1f2_2E0) ) ).
tff(thm_2EreaderMonad_2EFMAP__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1M1_2E0: tyop_2Emin_2Efun(A_27s,A_27a)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27a,A_27b,A_27s,V0f_2E0,V1M1_2E0) = c_2Ecombin_2Eo_2E2(A_27s,A_27b,A_27a,V0f_2E0,V1M1_2E0) ) ).
tff(thm_2EreaderMonad_2EJOIN__def,axiom,
! [A_27a: $tType,A_27s: $tType,V0MM_2E0: tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),V1s_2E0: A_27s] : ( c_2EreaderMonad_2EJOIN_2E2(A_27a,A_27s,V0MM_2E0,V1s_2E0) = app_2E2(A_27s,A_27a,app_2E2(A_27s,tyop_2Emin_2Efun(A_27s,A_27a),V0MM_2E0,V1s_2E0),V1s_2E0) ) ).
tff(thm_2EreaderMonad_2EBIND__UNITR,axiom,
! [A_27a: $tType,A_27b: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2EreaderMonad_2EBIND_2E2(A_27b,A_27b,A_27a,V0m_2E0,c_2EreaderMonad_2EUNIT_2E0(A_27b,A_27a)) = V0m_2E0 ) ).
tff(thm_2EreaderMonad_2EBIND__UNITL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EBIND_2E2(A_27c,A_27b,A_27a,c_2EreaderMonad_2EUNIT_2E1(A_27c,A_27a,V0x_2E0),V1f_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,V0x_2E0) ) ).
tff(thm_2EreaderMonad_2EMCOMPOSE__LEFT__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27a,A_27c,A_27b,c_2EreaderMonad_2EUNIT_2E0(A_27a,A_27b),V0g_2E0) = V0g_2E0 ) ).
tff(thm_2EreaderMonad_2EMCOMPOSE__RIGHT__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27c,A_27c,A_27b,V0f_2E0,c_2EreaderMonad_2EUNIT_2E0(A_27c,A_27b)) = V0f_2E0 ) ).
tff(thm_2EreaderMonad_2EMCOMPOSE__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0h_2E0: tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d))] : ( c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27d,A_27c,A_27b,V2f_2E0,c_2EreaderMonad_2EMCOMPOSE_2E2(A_27d,A_27e,A_27c,A_27b,V1g_2E0,V0h_2E0)) = c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27e,A_27c,A_27b,c_2EreaderMonad_2EMCOMPOSE_2E2(A_27a,A_27d,A_27e,A_27b,V2f_2E0,V1g_2E0),V0h_2E0) ) ).
tff(thm_2EreaderMonad_2EFMAP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,A_27b)] :
( ! [V1x_2E0: A_27b] : ( app_2E2(A_27b,A_27b,F0_2E0,V1x_2E0) = V1x_2E0 )
=> ! [V0M_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2EreaderMonad_2EFMAP_2E2(A_27b,A_27b,A_27a,F0_2E0,V0M_2E0) = V0M_2E0 )
& ( c_2EreaderMonad_2EFMAP_2E2(A_27b,A_27b,A_27a,c_2Ecombin_2EI_2E0(A_27b),V0M_2E0) = V0M_2E0 ) ) ) ).
tff(thm_2EreaderMonad_2EFMAP__o,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V1f_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E1(A_27b,A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27b,A_27c,A_27d,V1f_2E0,V0g_2E0)) = c_2Ecombin_2Eo_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27d),c_2EreaderMonad_2EFMAP_2E1(A_27d,A_27c,A_27a,V1f_2E0),c_2EreaderMonad_2EFMAP_2E1(A_27b,A_27d,A_27a,V0g_2E0)) ) ).
tff(thm_2EreaderMonad_2EFMAP__BIND,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,A_27c)] : ( c_2EreaderMonad_2EFMAP_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1M_2E0) = c_2EreaderMonad_2EBIND_2E2(A_27c,A_27b,A_27a,V1M_2E0,c_2Ecombin_2Eo_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),A_27b,c_2EreaderMonad_2EUNIT_2E0(A_27b,A_27a),V0f_2E0)) ) ).
tff(thm_2EreaderMonad_2EBIND__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : ( c_2EreaderMonad_2EBIND_2E2(A_27c,A_27b,A_27a,V1M_2E0,V0f_2E0) = c_2EreaderMonad_2EJOIN_2E1(A_27b,A_27a,c_2EreaderMonad_2EFMAP_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),A_27a,V0f_2E0,V1M_2E0)) ) ).
tff(thm_2EreaderMonad_2EJOIN__BIND,axiom,
! [A_27a: $tType,A_27b: $tType,V0M_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2EreaderMonad_2EJOIN_2E1(A_27b,A_27a,V0M_2E0) = c_2EreaderMonad_2EBIND_2E2(tyop_2Emin_2Efun(A_27a,A_27b),A_27b,A_27a,V0M_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,A_27b))) ) ).
%------------------------------------------------------------------------------