ITP001 Axioms: ITP038+5.ax
%------------------------------------------------------------------------------
% File : ITP038+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : state_transformer+2.ax [Gau20]
% : HL4038+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 105 ( 6 unt; 0 def)
% Number of atoms : 419 ( 90 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 315 ( 1 ~; 0 |; 3 &)
% ( 0 <=>; 311 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 93 ( 93 usr; 13 con; 0-6 aty)
% Number of variables : 419 ( 419 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Estate__transformer_2EBIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EEXT,axiom,
! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27s] :
( ne(A_27s)
=> mem(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),arr(arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))),arr(arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s)),arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EFOR,axiom,
! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2EFOR(A_27state),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) ) ).
fof(mem_c_2Estate__transformer_2EFOREACH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) ) ) ).
fof(mem_c_2Estate__transformer_2EIGNORE__BIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Estate__transformer_2EIGNORE__BIND(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EJOIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Estate__transformer_2EJOIN(A_27a,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ) ) ).
fof(mem_c_2Estate__transformer_2EMCOMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27s] :
( ne(A_27s)
=> mem(c_2Estate__transformer_2EMCOMP(A_27a,A_27b,A_27c,A_27s),arr(arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))),arr(arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))),arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)))))) ) ) ) ) ).
fof(mem_c_2Estate__transformer_2EMMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EMWHILE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))))) ) ) ).
fof(mem_c_2Estate__transformer_2ENARROW,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2ENARROW(A_27a,A_27b,A_27state),arr(A_27b,arr(arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EREAD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2EREAD(A_27a,A_27state),arr(arr(A_27state,A_27a),arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))) ) ) ).
fof(mem_c_2Estate__transformer_2EUNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Estate__transformer_2EUNIT(A_27a,A_27b),arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ) ) ).
fof(mem_c_2Estate__transformer_2EWIDEN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2EWIDEN(A_27a,A_27b,A_27state),arr(arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)),arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2EWRITE,axiom,
! [A_27state] :
( ne(A_27state)
=> mem(c_2Estate__transformer_2EWRITE(A_27state),arr(arr(A_27state,A_27state),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) ) ).
fof(mem_c_2Estate__transformer_2EmapM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Estate__transformer_2EmapM(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))),arr(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b))))) ) ) ) ).
fof(mem_c_2Estate__transformer_2Esequence,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Estate__transformer_2Esequence(A_27a,A_27b),arr(ty_2Elist_2Elist(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))) ) ) ).
fof(lameq_f497,axiom,
! [A_27b,A_27a,V0x] :
( mem(V0x,A_27b)
=> ! [V1s] : ap(f497(A_27b,A_27a,V0x),V1s) = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V0x),V1s) ) ).
fof(ax_thm_2Estate__transformer_2EUNIT__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27b)
=> ap(c_2Estate__transformer_2EUNIT(A_27a,A_27b),V0x) = f497(A_27b,A_27a,V0x) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EBIND__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0g] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0g),V1f) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Epair_2Eprod(A_27c,A_27a),ty_2Epair_2Eprod(A_27b,A_27a)),ap(c_2Epair_2EUNCURRY(A_27b,A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),V1f)),V0g) ) ) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EIGNORE__BIND__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ap(ap(c_2Estate__transformer_2EIGNORE__BIND(A_27a,A_27b,A_27c),V0f),V1g) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V0f),k(A_27c,V1g)) ) ) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EMMAP__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1m] :
( mem(V1m,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))
=> ap(ap(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27c),V0f),V1m) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V1m),ap(ap(c_2Ecombin_2Eo(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),c_2Estate__transformer_2EUNIT(A_27a,A_27b)),V0f)) ) ) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EJOIN__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0z] :
( mem(V0z,arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)))
=> ap(c_2Estate__transformer_2EJOIN(A_27a,A_27b),V0z) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),V0z),c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EEXT__DEF,axiom,
! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27s] :
( ne(A_27s)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))
=> ! [V1m] :
( mem(V1m,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s)))
=> ap(ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),V0f),V1m) = ap(ap(c_2Ecombin_2Eo(A_27s,ty_2Epair_2Eprod(A_27c,A_27s),ty_2Epair_2Eprod(A_27b,A_27s)),ap(c_2Epair_2EUNCURRY(A_27b,A_27s,ty_2Epair_2Eprod(A_27c,A_27s)),V0f)),V1m) ) ) ) ) ) ).
fof(ax_thm_2Estate__transformer_2EMCOMP__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27s] :
( ne(A_27s)
=> ! [V0g] :
( mem(V0g,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))))
=> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27b,A_27c,A_27s),V0g),V1f) = ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)),arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),V0g)),V1f) ) ) ) ) ) ) ).
fof(lameq_f498,axiom,
! [A_27state,V1a] :
( mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool)))
=> ! [V2j] :
( mem(V2j,ty_2Enum_2Enum)
=> ! [V3i] : ap(f498(A_27state,V1a,V0R,V2j),V3i) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3i),V2j))),ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V3i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V1a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V3i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V1a)))) ) ) ) ).
fof(lameq_f499,axiom,
! [A_27state,V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool)))
=> ! [V1a] :
( mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V2j] : ap(f499(A_27state,V0R,V1a),V2j) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f498(A_27state,V1a,V0R,V2j)) ) ) ).
fof(lameq_f500,axiom,
! [A_27state,V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool)))
=> ! [V1a] : ap(f500(A_27state,V0R),V1a) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f499(A_27state,V0R,V1a)) ) ).
fof(lameq_f501,axiom,
! [A_27state,V0R] : ap(f501(A_27state),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V0R)),ap(c_2Ebool_2E_21(arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),f500(A_27state,V0R))) ).
fof(lameq_f502,axiom,
! [A_27state,V6i] :
( mem(V6i,ty_2Enum_2Enum)
=> ! [V8j] :
( mem(V8j,ty_2Enum_2Enum)
=> ! [V4FOR] :
( mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V9a] : ap(f502(A_27state,V6i,V8j,V4FOR),V9a) = ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6i),V8j)),ap(V9a,V6i)),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V9a,V6i)),k(ty_2Eone_2Eone,ap(V4FOR,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V6i),V8j)),ap(ap(c_2Earithmetic_2E_2B,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V8j),V9a))))))) ) ) ) ).
fof(lameq_f503,axiom,
! [A_27state,V6i] :
( mem(V6i,ty_2Enum_2Enum)
=> ! [V4FOR] :
( mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V8j] : ap(f503(A_27state,V6i,V4FOR),V8j) = f502(A_27state,V6i,V8j,V4FOR) ) ) ).
fof(lameq_f504,axiom,
! [A_27state,V4FOR] :
( mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V6i] :
( mem(V6i,ty_2Enum_2Enum)
=> ! [V7v1] : ap(f504(A_27state,V4FOR,V6i),V7v1) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V7v1),f503(A_27state,V6i,V4FOR)) ) ) ).
fof(lameq_f505,axiom,
! [A_27state,V4FOR] :
( mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V6i] : ap(f505(A_27state,V4FOR),V6i) = f504(A_27state,V4FOR,V6i) ) ).
fof(lameq_f506,axiom,
! [A_27state,V4FOR] :
( mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V5a_27] : ap(f506(A_27state,V4FOR),V5a_27) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V5a_27),f505(A_27state,V4FOR)) ) ).
fof(lameq_f507,axiom,
! [A_27state,V4FOR] : ap(f507(A_27state),V4FOR) = f506(A_27state,V4FOR) ).
fof(ax_thm_2Estate__transformer_2EFOR__primitive__def,axiom,
! [A_27state] :
( ne(A_27state)
=> c_2Estate__transformer_2EFOR(A_27state) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))),f501(A_27state))),f507(A_27state)) ) ).
fof(conj_thm_2Estate__transformer_2EFOR__ind,axiom,
! [A_27state] :
( ne(A_27state)
=> ! [V0P] :
( mem(V0P,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))
=> ( ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2j] :
( mem(V2j,ty_2Enum_2Enum)
=> ! [V3a] :
( mem(V3a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ( ( V1i != V2j
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V3a)))) )
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V3a)))) ) ) ) )
=> ! [V4v] :
( mem(V4v,ty_2Enum_2Enum)
=> ! [V5v1] :
( mem(V5v1,ty_2Enum_2Enum)
=> ! [V6v2] :
( mem(V6v2,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V4v),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5v1),V6v2)))) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EFOR__def,axiom,
! [A_27state] :
( ne(A_27state)
=> ! [V0j] :
( mem(V0j,ty_2Enum_2Enum)
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ap(c_2Estate__transformer_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V0j),V2a))) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1i),V0j)),ap(V2a,V1i)),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V2a,V1i)),k(ty_2Eone_2Eone,ap(c_2Estate__transformer_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V0j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V0j),V2a)))))) ) ) ) ) ).
fof(lameq_f508,axiom,
! [A_27state,A_27a,V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool)))
=> ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2a] :
( mem(V2a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V3t] : ap(f508(A_27state,A_27a,V0R,V1h,V2a),V3t) = ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V3t),V2a)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3t)),V2a)) ) ) ) ).
fof(lameq_f509,axiom,
! [A_27state,A_27a,V1h] :
( mem(V1h,A_27a)
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool)))
=> ! [V2a] : ap(f509(A_27state,A_27a,V1h,V0R),V2a) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27a)),f508(A_27state,A_27a,V0R,V1h,V2a)) ) ) ).
fof(lameq_f510,axiom,
! [A_27state,A_27a,V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool)))
=> ! [V1h] : ap(f510(A_27state,A_27a,V0R),V1h) = ap(c_2Ebool_2E_21(arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),f509(A_27state,A_27a,V1h,V0R)) ) ).
fof(lameq_f511,axiom,
! [A_27state,A_27a,V0R] : ap(f511(A_27state,A_27a),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V0R)),ap(c_2Ebool_2E_21(A_27a),f510(A_27state,A_27a,V0R))) ).
fof(lameq_f512,axiom,
! [A_27state,A_27a,V7a] :
( mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V8h] :
( mem(V8h,A_27a)
=> ! [V4FOREACH] :
( mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V9t] : ap(f512(A_27state,A_27a,V7a,V8h,V4FOREACH),V9t) = ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V7a,V8h)),k(ty_2Eone_2Eone,ap(V4FOREACH,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V9t),V7a))))) ) ) ) ).
fof(lameq_f513,axiom,
! [A_27state,A_27a,V7a] :
( mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V4FOREACH] :
( mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V8h] : ap(f513(A_27state,A_27a,V7a,V4FOREACH),V8h) = f512(A_27state,A_27a,V7a,V8h,V4FOREACH) ) ) ).
fof(lameq_f514,axiom,
! [A_27state,A_27a,V4FOREACH] :
( mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(A_27a))
=> ! [V7a] : ap(f514(A_27state,A_27a,V4FOREACH,V6v),V7a) = ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),V6v),ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Estate__transformer_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone))),f513(A_27state,A_27a,V7a,V4FOREACH)) ) ) ).
fof(lameq_f515,axiom,
! [A_27state,A_27a,V4FOREACH] :
( mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V6v] : ap(f515(A_27state,A_27a,V4FOREACH),V6v) = f514(A_27state,A_27a,V4FOREACH,V6v) ) ).
fof(lameq_f516,axiom,
! [A_27state,A_27a,V4FOREACH] :
( mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V5a_27] : ap(f516(A_27state,A_27a,V4FOREACH),V5a_27) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5a_27),f515(A_27state,A_27a,V4FOREACH)) ) ).
fof(lameq_f517,axiom,
! [A_27state,A_27a,V4FOREACH] : ap(f517(A_27state,A_27a),V4FOREACH) = f516(A_27state,A_27a,V4FOREACH) ).
fof(ax_thm_2Estate__transformer_2EFOREACH__primitive__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> c_2Estate__transformer_2EFOREACH(A_27a,A_27state) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))),f511(A_27state,A_27a))),f517(A_27state,A_27a)) ) ) ).
fof(conj_thm_2Estate__transformer_2EFOREACH__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> ! [V0P] :
( mem(V0P,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))
=> ( ( ! [V1a] :
( mem(V1a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),c_2Elist_2ENIL(A_27a)),V1a))) )
& ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ! [V4a] :
( mem(V4a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ( p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V3t),V4a)))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)),V4a))) ) ) ) ) )
=> ! [V5v] :
( mem(V5v,ty_2Elist_2Elist(A_27a))
=> ! [V6v1] :
( mem(V6v1,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5v),V6v1))) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EFOREACH__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> ( ! [V0a] :
( mem(V0a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),c_2Elist_2ENIL(A_27a)),V0a)) = ap(c_2Estate__transformer_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone) )
& ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3a] :
( mem(V3a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t)),V3a)) = ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V3a,V2h)),k(ty_2Eone_2Eone,ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V1t),V3a)))) ) ) ) ) ) ) ).
fof(lameq_f518,axiom,
! [A_27a,A_27state,V0f] :
( mem(V0f,arr(A_27state,A_27a))
=> ! [V1s] : ap(f518(A_27a,A_27state,V0f),V1s) = ap(ap(c_2Epair_2E_2C(A_27a,A_27state),ap(V0f,V1s)),V1s) ) ).
fof(ax_thm_2Estate__transformer_2EREAD__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27state] :
( ne(A_27state)
=> ! [V0f] :
( mem(V0f,arr(A_27state,A_27a))
=> ap(c_2Estate__transformer_2EREAD(A_27a,A_27state),V0f) = f518(A_27a,A_27state,V0f) ) ) ) ).
fof(lameq_f519,axiom,
! [A_27state,V0f] :
( mem(V0f,arr(A_27state,A_27state))
=> ! [V1s] : ap(f519(A_27state,V0f),V1s) = ap(ap(c_2Epair_2E_2C(ty_2Eone_2Eone,A_27state),c_2Eone_2Eone),ap(V0f,V1s)) ) ).
fof(ax_thm_2Estate__transformer_2EWRITE__def,axiom,
! [A_27state] :
( ne(A_27state)
=> ! [V0f] :
( mem(V0f,arr(A_27state,A_27state))
=> ap(c_2Estate__transformer_2EWRITE(A_27state),V0f) = f519(A_27state,V0f) ) ) ).
fof(lameq_f520,axiom,
! [A_27a,A_27b,A_27state,V3r] :
( mem(V3r,A_27a)
=> ! [V4s1] : ap(f520(A_27a,A_27b,A_27state,V3r),V4s1) = ap(ap(c_2Epair_2E_2C(A_27a,A_27state),V3r),ap(c_2Epair_2ESND(A_27b,A_27state),V4s1)) ) ).
fof(lameq_f521,axiom,
! [A_27state,A_27b,A_27a,V3r] : ap(f521(A_27state,A_27b,A_27a),V3r) = f520(A_27a,A_27b,A_27state,V3r) ).
fof(lameq_f522,axiom,
! [A_27b,A_27a,A_27state,V1f] :
( mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))
=> ! [V0v] :
( mem(V0v,A_27b)
=> ! [V2s] : ap(f522(A_27b,A_27a,A_27state,V1f,V0v),V2s) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),ty_2Epair_2Eprod(A_27a,A_27state)),ap(c_2Epair_2EUNCURRY(A_27a,ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,A_27state)),f521(A_27state,A_27b,A_27a))),ap(V1f,ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V0v),V2s))) ) ) ).
fof(ax_thm_2Estate__transformer_2ENARROW__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27state] :
( ne(A_27state)
=> ! [V0v] :
( mem(V0v,A_27b)
=> ! [V1f] :
( mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))
=> ap(ap(c_2Estate__transformer_2ENARROW(A_27a,A_27b,A_27state),V0v),V1f) = f522(A_27b,A_27a,A_27state,V1f,V0v) ) ) ) ) ) ).
fof(lameq_f523,axiom,
! [A_27b,A_27a,A_27state,V1s1] :
( mem(V1s1,A_27b)
=> ! [V3r] :
( mem(V3r,A_27a)
=> ! [V4s3] : ap(f523(A_27b,A_27a,A_27state,V1s1,V3r),V4s3) = ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),V3r),ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V1s1),V4s3)) ) ) ).
fof(lameq_f524,axiom,
! [A_27state,A_27b,A_27a,V1s1] :
( mem(V1s1,A_27b)
=> ! [V3r] : ap(f524(A_27state,A_27b,A_27a,V1s1),V3r) = f523(A_27b,A_27a,A_27state,V1s1,V3r) ) ).
fof(lameq_f525,axiom,
! [A_27a,A_27b,A_27state,V0f] :
( mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))
=> ! [V1s1] :
( mem(V1s1,A_27b)
=> ! [V2s2] : ap(f525(A_27a,A_27b,A_27state,V0f,V1s1),V2s2) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),ap(c_2Epair_2EUNCURRY(A_27a,A_27state,ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),f524(A_27state,A_27b,A_27a,V1s1))),ap(V0f,V2s2)) ) ) ).
fof(lameq_f526,axiom,
! [A_27state,A_27a,A_27b,V0f] :
( mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))
=> ! [V1s1] : ap(f526(A_27state,A_27a,A_27b,V0f),V1s1) = f525(A_27a,A_27b,A_27state,V0f,V1s1) ) ).
fof(ax_thm_2Estate__transformer_2EWIDEN__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27state] :
( ne(A_27state)
=> ! [V0f] :
( mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))
=> ap(c_2Estate__transformer_2EWIDEN(A_27a,A_27b,A_27state),V0f) = ap(c_2Epair_2EUNCURRY(A_27b,A_27state,ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),f526(A_27state,A_27a,A_27b,V0f)) ) ) ) ) ).
fof(lameq_f527,axiom,
! [A_27a,A_27b,V2x] :
( mem(V2x,A_27b)
=> ! [V3xs] : ap(f527(A_27a,A_27b,V2x),V3xs) = ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V2x),V3xs)) ) ).
fof(lameq_f528,axiom,
! [A_27a,A_27b,V1ms] :
( mem(V1ms,arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V2x] : ap(f528(A_27a,A_27b,V1ms),V2x) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),V1ms),f527(A_27a,A_27b,V2x)) ) ).
fof(lameq_f529,axiom,
! [A_27a,A_27b,V0m] :
( mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1ms] : ap(f529(A_27a,A_27b,V0m),V1ms) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),V0m),f528(A_27a,A_27b,V1ms)) ) ).
fof(lameq_f530,axiom,
! [A_27a,A_27b,V0m] : ap(f530(A_27a,A_27b),V0m) = f529(A_27a,A_27b,V0m) ).
fof(ax_thm_2Estate__transformer_2Esequence__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Estate__transformer_2Esequence(A_27a,A_27b) = ap(ap(c_2Elist_2EFOLDR(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a))),f530(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b))) ) ) ).
fof(ax_thm_2Estate__transformer_2EmapM__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ap(c_2Estate__transformer_2EmapM(A_27a,A_27b,A_27c),V0f) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b)),ty_2Elist_2Elist(arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2Esequence(A_27b,A_27c)),ap(c_2Elist_2EMAP(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))),V0f)) ) ) ) ) ).
fof(lameq_f531,axiom,
! [A_27a,A_27b,V0g] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)))
=> ! [V1b] :
( mem(V1b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V2gv] : ap(f531(A_27a,A_27b,V0g,V1b),V2gv) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))),V2gv),ap(ap(c_2Estate__transformer_2EIGNORE__BIND(A_27a,ty_2Eone_2Eone,A_27b),V1b),ap(ap(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),V0g),V1b))),ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Eone_2Eone),c_2Eone_2Eone)) ) ) ).
fof(ax_thm_2Estate__transformer_2EMWHILE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0g] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)))
=> ! [V1b] :
( mem(V1b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ap(ap(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),V0g),V1b) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,bool,ty_2Eone_2Eone),V0g),f531(A_27a,A_27b,V0g,V1b)) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EUNIT__CURRY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Estate__transformer_2EUNIT(A_27b,A_27a) = ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI(ty_2Epair_2Eprod(A_27a,A_27b))) ) ) ).
fof(conj_thm_2Estate__transformer_2EMCOMP__ALT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0g] :
( mem(V0g,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b))))
=> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),V0g),V1f) = ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27b),ty_2Epair_2Eprod(A_27d,A_27b)),ap(c_2Epair_2EUNCURRY(A_27d,A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),V0g)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27d,A_27b)),V1f))) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMCOMP__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [V0g] :
( mem(V0g,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1f] :
( mem(V1f,arr(A_27d,arr(A_27e,ty_2Epair_2Eprod(A_27f,A_27e))))
=> ( ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27a,A_27c,A_27b),V0g),c_2Estate__transformer_2EUNIT(A_27b,A_27a)) = V0g
& ap(ap(c_2Estate__transformer_2EMCOMP(A_27d,A_27f,A_27f,A_27e),c_2Estate__transformer_2EUNIT(A_27e,A_27f)),V1f) = V1f ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMCOMP__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [V0f] :
( mem(V0f,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1g] :
( mem(V1g,arr(A_27e,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b))))
=> ! [V2h] :
( mem(V2h,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27e,A_27b))))
=> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),V0f),ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27e,A_27d,A_27b),V1g),V2h)) = ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27e,A_27c,A_27b),ap(ap(c_2Estate__transformer_2EMCOMP(A_27e,A_27d,A_27c,A_27b),V0f),V1g)),V2h) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EEXT__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Estate__transformer_2EEXT(A_27b,A_27b,A_27a),c_2Estate__transformer_2EUNIT(A_27a,A_27b)) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) ) ) ).
fof(conj_thm_2Estate__transformer_2EEXT__MCOMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0g] :
( mem(V0g,arr(A_27d,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))))
=> ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),ap(ap(c_2Estate__transformer_2EMCOMP(A_27b,A_27d,A_27c,A_27a),V0g),V1f)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))),ap(c_2Estate__transformer_2EEXT(A_27d,A_27c,A_27a),V0g)),ap(c_2Estate__transformer_2EEXT(A_27b,A_27d,A_27a),V1f)) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EEXT__o__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),ap(c_2Estate__transformer_2EEXT(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EUNIT(A_27b,A_27a)) = V0f ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EUNIT__o__MCOMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0g] :
( mem(V0g,arr(A_27d,A_27c))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27d))
=> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),A_27c),c_2Estate__transformer_2EUNIT(A_27b,A_27c)),V0g)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b)),A_27d),c_2Estate__transformer_2EUNIT(A_27b,A_27d)),V1f)) = ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),A_27c),c_2Estate__transformer_2EUNIT(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27d),V0g),V1f)) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EBIND__EXT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0m] :
( mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))
=> ! [V1f] :
( mem(V1f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V0m),V1f) = ap(ap(c_2Estate__transformer_2EEXT(A_27c,A_27b,A_27a),V1f),V0m) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMMAP__EXT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f) = ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27c),c_2Estate__transformer_2EUNIT(A_27a,A_27c)),V0f)) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EJOIN__EXT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Estate__transformer_2EJOIN(A_27a,A_27b) = ap(c_2Estate__transformer_2EEXT(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b,A_27a),c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ) ) ).
fof(conj_thm_2Estate__transformer_2EEXT__JM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27c)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27b),V0f)) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EBIND__LEFT__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0k] :
( mem(V0k,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(c_2Estate__transformer_2EBIND(A_27b,A_27a,A_27c),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V1x)),V0k) = ap(V0k,V1x) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EUNIT__UNCURRY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,ty_2Epair_2Eprod(A_27a,A_27b))
=> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT(A_27b,A_27a)),V0s) = V0s ) ) ) ).
fof(conj_thm_2Estate__transformer_2EBIND__RIGHT__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0k] :
( mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27b),V0k),c_2Estate__transformer_2EUNIT(A_27a,A_27b)) = V0k ) ) ) ).
fof(lameq_f532,axiom,
! [A_27c,A_27d,A_27a,A_27b,V1m] :
( mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V2n] :
( mem(V2n,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))))
=> ! [V3a] : ap(f532(A_27c,A_27d,A_27a,A_27b,V1m,V2n),V3a) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27d),ap(V1m,V3a)),V2n) ) ) ).
fof(conj_thm_2Estate__transformer_2EBIND__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0k] :
( mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1m] :
( mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V2n] :
( mem(V2n,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))))
=> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27d),V0k),f532(A_27c,A_27d,A_27a,A_27b,V1m,V2n)) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27d),ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0k),V1m)),V2n) ) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMMAP__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) ) ) ).
fof(conj_thm_2Estate__transformer_2EMMAP__COMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0f] :
( mem(V0f,arr(A_27c,A_27d))
=> ! [V1g] :
( mem(V1g,arr(A_27b,A_27c))
=> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27d,A_27b),ap(ap(c_2Ecombin_2Eo(A_27b,A_27d,A_27c),V0f),V1g)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27d,A_27c),V0f)),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V1g)) ) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMMAP__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EUNIT(A_27a,A_27b)) = ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27c),c_2Estate__transformer_2EUNIT(A_27a,A_27c)),V0f) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EEXT__o__JOIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f)),c_2Estate__transformer_2EJOIN(A_27a,A_27b)) = ap(c_2Estate__transformer_2EEXT(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27c,A_27a),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f)) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EMMAP__JOIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EJOIN(A_27a,A_27b)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27c)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f))) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EJOIN__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),c_2Estate__transformer_2EUNIT(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) ) ) ).
fof(conj_thm_2Estate__transformer_2EJOIN__MMAP__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),c_2Estate__transformer_2EUNIT(A_27a,A_27b))) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) ) ) ).
fof(conj_thm_2Estate__transformer_2EJOIN__MAP__JOIN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),c_2Estate__transformer_2EJOIN(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ) ) ).
fof(conj_thm_2Estate__transformer_2EJOIN__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0k] :
( mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1m] :
( mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0k),V1m) = ap(c_2Estate__transformer_2EJOIN(A_27a,A_27c),ap(ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27b),V1m),V0k)) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EFST__o__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(ap(c_2Ecombin_2Eo(A_27b,A_27a,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2EFST(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V0x)) = ap(c_2Ecombin_2EK(A_27a,A_27b),V0x) ) ) ) ).
fof(conj_thm_2Estate__transformer_2ESND__o__UNIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(ap(c_2Ecombin_2Eo(A_27b,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2ESND(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V0x)) = c_2Ecombin_2EI(A_27b) ) ) ) ).
fof(conj_thm_2Estate__transformer_2EFST__o__MMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1g] :
( mem(V1g,arr(A_27c,ty_2Epair_2Eprod(A_27a,A_27c)))
=> ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,ty_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2EFST(A_27b,A_27c)),ap(ap(c_2Estate__transformer_2EMMAP(A_27c,A_27b,A_27a),V0f),V1g)) = ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,ty_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2EFST(A_27a,A_27c)),V1g)) ) ) ) ) ) ).
fof(conj_thm_2Estate__transformer_2Esequence__nil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Estate__transformer_2Esequence(A_27a,A_27b),c_2Elist_2ENIL(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) = ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)) ) ) ).
fof(conj_thm_2Estate__transformer_2EmapM__nil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27c)) = ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)) ) ) ) ) ).
fof(lameq_f533,axiom,
! [A_27a,A_27b,V3y] :
( mem(V3y,A_27b)
=> ! [V4ys] : ap(f533(A_27a,A_27b,V3y),V4ys) = ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V3y),V4ys)) ) ).
fof(lameq_f534,axiom,
! [A_27a,A_27c,A_27b,V0f] :
( mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27c))
=> ! [V3y] : ap(f534(A_27a,A_27c,A_27b,V0f,V2xs),V3y) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),V2xs)),f533(A_27a,A_27b,V3y)) ) ) ).
fof(conj_thm_2Estate__transformer_2EmapM__cons,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ! [V1x] :
( mem(V1x,A_27c)
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27c))
=> ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),ap(ap(c_2Elist_2ECONS(A_27c),V1x),V2xs)) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),ap(V0f,V1x)),f534(A_27a,A_27c,A_27b,V0f,V2xs)) ) ) ) ) ) ) ).
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