ITP001 Axioms: ITP038_5.ax
%------------------------------------------------------------------------------
% File : ITP038_5 : TPTP v9.0.0. 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 : 159 ( 33 unt; 54 typ; 0 def)
% Number of atoms : 2038 ( 90 equ)
% Maximal formula atoms : 11 ( 12 avg)
% Number of connectives : 129 ( 1 ~; 0 |; 3 &)
% ( 0 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1805 (1805 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 166 ( 54 >; 112 *; 0 +; 0 <<)
% Number of predicates : 48 ( 47 usr; 16 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 0 con; 1-6 aty)
% Number of variables : 419 ( 419 !; 0 ?; 419 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Estate__transformer_2EBIND,type,
c_2Estate__transformer_2EBIND: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EBIND,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EEXT,type,
c_2Estate__transformer_2EEXT: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EEXT,axiom,
! [A_27b: del,A_27c: del,A_27s: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EFOR,type,
c_2Estate__transformer_2EFOR: del > $i ).
tff(mem_c_2Estate__transformer_2EFOR,axiom,
! [A_27state: del] : 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)))) ).
tff(tp_c_2Estate__transformer_2EFOREACH,type,
c_2Estate__transformer_2EFOREACH: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EFOREACH,axiom,
! [A_27a: del,A_27state: del] : 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)))) ).
tff(tp_c_2Estate__transformer_2EIGNORE__BIND,type,
c_2Estate__transformer_2EIGNORE__BIND: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EIGNORE__BIND,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EJOIN,type,
c_2Estate__transformer_2EJOIN: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EJOIN,axiom,
! [A_27a: del,A_27b: del] : 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)))) ).
tff(tp_c_2Estate__transformer_2EMCOMP,type,
c_2Estate__transformer_2EMCOMP: ( del * del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EMCOMP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27s: del] : 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)))))) ).
tff(tp_c_2Estate__transformer_2EMMAP,type,
c_2Estate__transformer_2EMMAP: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EMMAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EMWHILE,type,
c_2Estate__transformer_2EMWHILE: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EMWHILE,axiom,
! [A_27a: del,A_27b: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2ENARROW,type,
c_2Estate__transformer_2ENARROW: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2ENARROW,axiom,
! [A_27a: del,A_27b: del,A_27state: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EREAD,type,
c_2Estate__transformer_2EREAD: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EREAD,axiom,
! [A_27a: del,A_27state: del] : 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)))) ).
tff(tp_c_2Estate__transformer_2EUNIT,type,
c_2Estate__transformer_2EUNIT: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EUNIT,axiom,
! [A_27a: del,A_27b: del] : mem(c_2Estate__transformer_2EUNIT(A_27a,A_27b),arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) ).
tff(tp_c_2Estate__transformer_2EWIDEN,type,
c_2Estate__transformer_2EWIDEN: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EWIDEN,axiom,
! [A_27a: del,A_27b: del,A_27state: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2EWRITE,type,
c_2Estate__transformer_2EWRITE: del > $i ).
tff(mem_c_2Estate__transformer_2EWRITE,axiom,
! [A_27state: del] : mem(c_2Estate__transformer_2EWRITE(A_27state),arr(arr(A_27state,A_27state),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) ).
tff(tp_c_2Estate__transformer_2EmapM,type,
c_2Estate__transformer_2EmapM: ( del * del * del ) > $i ).
tff(mem_c_2Estate__transformer_2EmapM,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : 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))))) ).
tff(tp_c_2Estate__transformer_2Esequence,type,
c_2Estate__transformer_2Esequence: ( del * del ) > $i ).
tff(mem_c_2Estate__transformer_2Esequence,axiom,
! [A_27a: del,A_27b: del] : 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)))) ).
tff(lamtp_f497,type,
f497: ( del * del * $i ) > $i ).
tff(lameq_f497,axiom,
! [A_27b: del,A_27a: del,V0x: $i] :
( mem(V0x,A_27b)
=> ! [V1s: $i] : ( ap(f497(A_27b,A_27a,V0x),V1s) = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V0x),V1s) ) ) ).
tff(ax_thm_2Estate__transformer_2EUNIT__DEF,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( mem(V0x,A_27b)
=> ( ap(c_2Estate__transformer_2EUNIT(A_27a,A_27b),V0x) = f497(A_27b,A_27a,V0x) ) ) ).
tff(ax_thm_2Estate__transformer_2EBIND__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1f: $i] :
( 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) ) ) ) ).
tff(ax_thm_2Estate__transformer_2EIGNORE__BIND__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))
=> ! [V1g: $i] :
( 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)) ) ) ) ).
tff(ax_thm_2Estate__transformer_2EMMAP__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1m: $i] :
( 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)) ) ) ) ).
tff(ax_thm_2Estate__transformer_2EJOIN__DEF,axiom,
! [A_27a: del,A_27b: del,V0z: $i] :
( 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)))) ) ) ).
tff(ax_thm_2Estate__transformer_2EEXT__DEF,axiom,
! [A_27b: del,A_27c: del,A_27s: del,V0f: $i] :
( mem(V0f,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))
=> ! [V1m: $i] :
( 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) ) ) ) ).
tff(ax_thm_2Estate__transformer_2EMCOMP__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27s: del,V0g: $i] :
( mem(V0g,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))
=> ! [V1f: $i] :
( 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) ) ) ) ).
tff(lamtp_f498,type,
f498: ( del * $i * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f498,axiom,
! [A_27state: del,V1a: $i] :
( mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V0R: $i] :
( 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: tp__ty_2Enum_2Enum,V3i: tp__ty_2Enum_2Enum] : ( ap(f498(A_27state,V1a,V0R,V2j),inj__ty_2Enum_2Enum(V3i)) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V3i)),inj__ty_2Enum_2Enum(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,inj__ty_2Enum_2Enum(V3i)),inj__ty_2Enum_2Enum(V2j))),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V3i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V3i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__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)))),inj__ty_2Enum_2Enum(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))))),inj__ty_2Enum_2Enum(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)))),inj__ty_2Enum_2Enum(V2j)),V1a)))) ) ) ) ).
tff(lamtp_f499,type,
f499: ( del * $i * $i ) > $i ).
tff(lameq_f499,axiom,
! [A_27state: del,V0R: $i] :
( 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: $i] :
( mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V2j: tp__ty_2Enum_2Enum] : ( ap(f499(A_27state,V0R,V1a),inj__ty_2Enum_2Enum(V2j)) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f498(A_27state,V1a,V0R,V2j)) ) ) ) ).
tff(lamtp_f500,type,
f500: ( del * $i ) > $i ).
tff(lameq_f500,axiom,
! [A_27state: del,V0R: $i] :
( 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: $i] : ( ap(f500(A_27state,V0R),V1a) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f499(A_27state,V0R,V1a)) ) ) ).
tff(lamtp_f501,type,
f501: del > $i ).
tff(lameq_f501,axiom,
! [A_27state: del,V0R: $i] : ( 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))) ) ).
tff(lamtp_f502,type,
f502: ( del * tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f502,axiom,
! [A_27state: del,V6i: tp__ty_2Enum_2Enum,V8j: tp__ty_2Enum_2Enum,V4FOR: $i] :
( 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: $i] : ( 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),inj__ty_2Enum_2Enum(V6i)),inj__ty_2Enum_2Enum(V8j))),ap(V9a,inj__ty_2Enum_2Enum(V6i))),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V9a,inj__ty_2Enum_2Enum(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,inj__ty_2Enum_2Enum(V6i)),inj__ty_2Enum_2Enum(V8j))),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V6i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V6i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__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)))),inj__ty_2Enum_2Enum(V8j)),V9a))))))) ) ) ).
tff(lamtp_f503,type,
f503: ( del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f503,axiom,
! [A_27state: del,V6i: tp__ty_2Enum_2Enum,V4FOR: $i] :
( 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: tp__ty_2Enum_2Enum] : ( ap(f503(A_27state,V6i,V4FOR),inj__ty_2Enum_2Enum(V8j)) = f502(A_27state,V6i,V8j,V4FOR) ) ) ).
tff(lamtp_f504,type,
f504: ( del * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f504,axiom,
! [A_27state: del,V4FOR: $i] :
( 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: tp__ty_2Enum_2Enum,V7v1: $i] : ( 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)) ) ) ).
tff(lamtp_f505,type,
f505: ( del * $i ) > $i ).
tff(lameq_f505,axiom,
! [A_27state: del,V4FOR: $i] :
( 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: tp__ty_2Enum_2Enum] : ( ap(f505(A_27state,V4FOR),inj__ty_2Enum_2Enum(V6i)) = f504(A_27state,V4FOR,V6i) ) ) ).
tff(lamtp_f506,type,
f506: ( del * $i ) > $i ).
tff(lameq_f506,axiom,
! [A_27state: del,V4FOR: $i] :
( 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: $i] : ( 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)) ) ) ).
tff(lamtp_f507,type,
f507: del > $i ).
tff(lameq_f507,axiom,
! [A_27state: del,V4FOR: $i] : ( ap(f507(A_27state),V4FOR) = f506(A_27state,V4FOR) ) ).
tff(ax_thm_2Estate__transformer_2EFOR__primitive__def,axiom,
! [A_27state: del] : ( 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)) ) ).
tff(conj_thm_2Estate__transformer_2EFOR__ind,axiom,
! [A_27state: del,V0P: $i] :
( 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: tp__ty_2Enum_2Enum,V2j: tp__ty_2Enum_2Enum,V3a: $i] :
( 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,inj__ty_2Enum_2Enum(V1i)),inj__ty_2Enum_2Enum(V2j))),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__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)))),inj__ty_2Enum_2Enum(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))))),inj__ty_2Enum_2Enum(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)))),inj__ty_2Enum_2Enum(V2j)),V3a)))) ) )
=> ! [V4v: tp__ty_2Enum_2Enum,V5v1: tp__ty_2Enum_2Enum,V6v2: $i] :
( 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))))),inj__ty_2Enum_2Enum(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)))),inj__ty_2Enum_2Enum(V5v1)),V6v2)))) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EFOR__def,axiom,
! [A_27state: del,V0j: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2a: $i] :
( 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))))),inj__ty_2Enum_2Enum(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)))),inj__ty_2Enum_2Enum(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),inj__ty_2Enum_2Enum(V1i)),inj__ty_2Enum_2Enum(V0j))),ap(V2a,inj__ty_2Enum_2Enum(V1i))),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V2a,inj__ty_2Enum_2Enum(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,inj__ty_2Enum_2Enum(V1i)),inj__ty_2Enum_2Enum(V0j))),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1i)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__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)))),inj__ty_2Enum_2Enum(V0j)),V2a)))))) ) ) ).
tff(lamtp_f508,type,
f508: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f508,axiom,
! [A_27state: del,A_27a: del,V0R: $i] :
( 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: $i] :
( mem(V1h,A_27a)
=> ! [V2a: $i] :
( mem(V2a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V3t: $i] : ( 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)) ) ) ) ) ).
tff(lamtp_f509,type,
f509: ( del * del * $i * $i ) > $i ).
tff(lameq_f509,axiom,
! [A_27state: del,A_27a: del,V1h: $i] :
( mem(V1h,A_27a)
=> ! [V0R: $i] :
( 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: $i] : ( 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)) ) ) ) ).
tff(lamtp_f510,type,
f510: ( del * del * $i ) > $i ).
tff(lameq_f510,axiom,
! [A_27state: del,A_27a: del,V0R: $i] :
( 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: $i] : ( 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)) ) ) ).
tff(lamtp_f511,type,
f511: ( del * del ) > $i ).
tff(lameq_f511,axiom,
! [A_27state: del,A_27a: del,V0R: $i] : ( 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))) ) ).
tff(lamtp_f512,type,
f512: ( del * del * $i * $i * $i ) > $i ).
tff(lameq_f512,axiom,
! [A_27state: del,A_27a: del,V7a: $i] :
( mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V8h: $i] :
( mem(V8h,A_27a)
=> ! [V4FOREACH: $i] :
( 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: $i] : ( 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))))) ) ) ) ) ).
tff(lamtp_f513,type,
f513: ( del * del * $i * $i ) > $i ).
tff(lameq_f513,axiom,
! [A_27state: del,A_27a: del,V7a: $i] :
( mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))
=> ! [V4FOREACH: $i] :
( 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: $i] : ( ap(f513(A_27state,A_27a,V7a,V4FOREACH),V8h) = f512(A_27state,A_27a,V7a,V8h,V4FOREACH) ) ) ) ).
tff(lamtp_f514,type,
f514: ( del * del * $i * $i ) > $i ).
tff(lameq_f514,axiom,
! [A_27state: del,A_27a: del,V4FOREACH: $i] :
( 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: $i] :
( mem(V6v,ty_2Elist_2Elist(A_27a))
=> ! [V7a: $i] : ( 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),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)))),f513(A_27state,A_27a,V7a,V4FOREACH)) ) ) ) ).
tff(lamtp_f515,type,
f515: ( del * del * $i ) > $i ).
tff(lameq_f515,axiom,
! [A_27state: del,A_27a: del,V4FOREACH: $i] :
( 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: $i] : ( ap(f515(A_27state,A_27a,V4FOREACH),V6v) = f514(A_27state,A_27a,V4FOREACH,V6v) ) ) ).
tff(lamtp_f516,type,
f516: ( del * del * $i ) > $i ).
tff(lameq_f516,axiom,
! [A_27state: del,A_27a: del,V4FOREACH: $i] :
( 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: $i] : ( 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)) ) ) ).
tff(lamtp_f517,type,
f517: ( del * del ) > $i ).
tff(lameq_f517,axiom,
! [A_27state: del,A_27a: del,V4FOREACH: $i] : ( ap(f517(A_27state,A_27a),V4FOREACH) = f516(A_27state,A_27a,V4FOREACH) ) ).
tff(ax_thm_2Estate__transformer_2EFOREACH__primitive__def,axiom,
! [A_27a: del,A_27state: del] : ( 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)) ) ).
tff(conj_thm_2Estate__transformer_2EFOREACH__ind,axiom,
! [A_27a: del,A_27state: del,V0P: $i] :
( 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: $i] :
( 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: $i] :
( mem(V2h,A_27a)
=> ! [V3t: $i] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ! [V4a: $i] :
( 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: $i] :
( mem(V5v,ty_2Elist_2Elist(A_27a))
=> ! [V6v1: $i] :
( 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))) ) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EFOREACH__def,axiom,
! [A_27a: del,A_27state: del] :
( ! [V0a: $i] :
( 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),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)) ) )
& ! [V1t: $i] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ! [V2h: $i] :
( mem(V2h,A_27a)
=> ! [V3a: $i] :
( 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)))) ) ) ) ) ) ).
tff(lamtp_f518,type,
f518: ( del * del * $i ) > $i ).
tff(lameq_f518,axiom,
! [A_27a: del,A_27state: del,V0f: $i] :
( mem(V0f,arr(A_27state,A_27a))
=> ! [V1s: $i] : ( ap(f518(A_27a,A_27state,V0f),V1s) = ap(ap(c_2Epair_2E_2C(A_27a,A_27state),ap(V0f,V1s)),V1s) ) ) ).
tff(ax_thm_2Estate__transformer_2EREAD__def,axiom,
! [A_27a: del,A_27state: del,V0f: $i] :
( mem(V0f,arr(A_27state,A_27a))
=> ( ap(c_2Estate__transformer_2EREAD(A_27a,A_27state),V0f) = f518(A_27a,A_27state,V0f) ) ) ).
tff(lamtp_f519,type,
f519: ( del * $i ) > $i ).
tff(lameq_f519,axiom,
! [A_27state: del,V0f: $i] :
( mem(V0f,arr(A_27state,A_27state))
=> ! [V1s: $i] : ( ap(f519(A_27state,V0f),V1s) = ap(ap(c_2Epair_2E_2C(ty_2Eone_2Eone,A_27state),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone)),ap(V0f,V1s)) ) ) ).
tff(ax_thm_2Estate__transformer_2EWRITE__def,axiom,
! [A_27state: del,V0f: $i] :
( mem(V0f,arr(A_27state,A_27state))
=> ( ap(c_2Estate__transformer_2EWRITE(A_27state),V0f) = f519(A_27state,V0f) ) ) ).
tff(lamtp_f520,type,
f520: ( del * del * del * $i ) > $i ).
tff(lameq_f520,axiom,
! [A_27a: del,A_27b: del,A_27state: del,V3r: $i] :
( mem(V3r,A_27a)
=> ! [V4s1: $i] : ( 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)) ) ) ).
tff(lamtp_f521,type,
f521: ( del * del * del ) > $i ).
tff(lameq_f521,axiom,
! [A_27state: del,A_27b: del,A_27a: del,V3r: $i] : ( ap(f521(A_27state,A_27b,A_27a),V3r) = f520(A_27a,A_27b,A_27state,V3r) ) ).
tff(lamtp_f522,type,
f522: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f522,axiom,
! [A_27b: del,A_27a: del,A_27state: del,V1f: $i] :
( mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))
=> ! [V0v: $i] :
( mem(V0v,A_27b)
=> ! [V2s: $i] : ( 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))) ) ) ) ).
tff(ax_thm_2Estate__transformer_2ENARROW__def,axiom,
! [A_27a: del,A_27b: del,A_27state: del,V0v: $i] :
( mem(V0v,A_27b)
=> ! [V1f: $i] :
( 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) ) ) ) ).
tff(lamtp_f523,type,
f523: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f523,axiom,
! [A_27b: del,A_27a: del,A_27state: del,V1s1: $i] :
( mem(V1s1,A_27b)
=> ! [V3r: $i] :
( mem(V3r,A_27a)
=> ! [V4s3: $i] : ( 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)) ) ) ) ).
tff(lamtp_f524,type,
f524: ( del * del * del * $i ) > $i ).
tff(lameq_f524,axiom,
! [A_27state: del,A_27b: del,A_27a: del,V1s1: $i] :
( mem(V1s1,A_27b)
=> ! [V3r: $i] : ( ap(f524(A_27state,A_27b,A_27a,V1s1),V3r) = f523(A_27b,A_27a,A_27state,V1s1,V3r) ) ) ).
tff(lamtp_f525,type,
f525: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f525,axiom,
! [A_27a: del,A_27b: del,A_27state: del,V0f: $i] :
( mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))
=> ! [V1s1: $i] :
( mem(V1s1,A_27b)
=> ! [V2s2: $i] : ( 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)) ) ) ) ).
tff(lamtp_f526,type,
f526: ( del * del * del * $i ) > $i ).
tff(lameq_f526,axiom,
! [A_27state: del,A_27a: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))
=> ! [V1s1: $i] : ( ap(f526(A_27state,A_27a,A_27b,V0f),V1s1) = f525(A_27a,A_27b,A_27state,V0f,V1s1) ) ) ).
tff(ax_thm_2Estate__transformer_2EWIDEN__def,axiom,
! [A_27a: del,A_27b: del,A_27state: del,V0f: $i] :
( 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)) ) ) ).
tff(lamtp_f527,type,
f527: ( del * del * $i ) > $i ).
tff(lameq_f527,axiom,
! [A_27a: del,A_27b: del,V2x: $i] :
( mem(V2x,A_27b)
=> ! [V3xs: $i] : ( 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)) ) ) ).
tff(lamtp_f528,type,
f528: ( del * del * $i ) > $i ).
tff(lameq_f528,axiom,
! [A_27a: del,A_27b: del,V1ms: $i] :
( mem(V1ms,arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V2x: $i] : ( 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)) ) ) ).
tff(lamtp_f529,type,
f529: ( del * del * $i ) > $i ).
tff(lameq_f529,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1ms: $i] : ( 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)) ) ) ).
tff(lamtp_f530,type,
f530: ( del * del ) > $i ).
tff(lameq_f530,axiom,
! [A_27a: del,A_27b: del,V0m: $i] : ( ap(f530(A_27a,A_27b),V0m) = f529(A_27a,A_27b,V0m) ) ).
tff(ax_thm_2Estate__transformer_2Esequence__def,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(ax_thm_2Estate__transformer_2EmapM__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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)) ) ) ).
tff(lamtp_f531,type,
f531: ( del * del * $i * $i ) > $i ).
tff(lameq_f531,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)))
=> ! [V1b: $i] :
( mem(V1b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V2gv: tp__o] : ( ap(f531(A_27a,A_27b,V0g,V1b),inj__o(V2gv)) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))),inj__o(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),inj__ty_2Eone_2Eone(fo__c_2Eone_2Eone))) ) ) ) ).
tff(ax_thm_2Estate__transformer_2EMWHILE__DEF,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)))
=> ! [V1b: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EUNIT__CURRY,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(conj_thm_2Estate__transformer_2EMCOMP__ALT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
( mem(V0g,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1f: $i] :
( 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))) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EMCOMP__ID,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,V0g: $i] :
( mem(V0g,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1f: $i] :
( 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 ) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EMCOMP__ASSOC,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,V0f: $i] :
( mem(V0f,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1g: $i] :
( mem(V1g,arr(A_27e,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b))))
=> ! [V2h: $i] :
( 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) ) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EEXT__UNIT,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(conj_thm_2Estate__transformer_2EEXT__MCOMP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
( mem(V0g,arr(A_27d,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V1f: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EEXT__o__UNIT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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 ) ) ).
tff(conj_thm_2Estate__transformer_2EUNIT__o__MCOMP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
( mem(V0g,arr(A_27d,A_27c))
=> ! [V1f: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EBIND__EXT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0m: $i] :
( mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))
=> ! [V1f: $i] :
( 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) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EMMAP__EXT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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)) ) ) ).
tff(conj_thm_2Estate__transformer_2EJOIN__EXT,axiom,
! [A_27a: del,A_27b: del] : ( 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)))) ) ).
tff(conj_thm_2Estate__transformer_2EEXT__JM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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)) ) ) ).
tff(conj_thm_2Estate__transformer_2EBIND__LEFT__UNIT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0k: $i] :
( mem(V0k,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))))
=> ! [V1x: $i] :
( 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) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EUNIT__UNCURRY,axiom,
! [A_27a: del,A_27b: del,V0s: $i] :
( 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 ) ) ).
tff(conj_thm_2Estate__transformer_2EBIND__RIGHT__UNIT,axiom,
! [A_27a: del,A_27b: del,V0k: $i] :
( 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 ) ) ).
tff(lamtp_f532,type,
f532: ( del * del * del * del * $i * $i ) > $i ).
tff(lameq_f532,axiom,
! [A_27c: del,A_27d: del,A_27a: del,A_27b: del,V1m: $i] :
( mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V2n: $i] :
( mem(V2n,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))))
=> ! [V3a: $i] : ( 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) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EBIND__ASSOC,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0k: $i] :
( mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1m: $i] :
( mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))
=> ! [V2n: $i] :
( 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) ) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EMMAP__ID,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(conj_thm_2Estate__transformer_2EMMAP__COMP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
( mem(V0f,arr(A_27c,A_27d))
=> ! [V1g: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EMMAP__UNIT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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) ) ) ).
tff(conj_thm_2Estate__transformer_2EEXT__o__JOIN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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)) ) ) ).
tff(conj_thm_2Estate__transformer_2EMMAP__JOIN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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))) ) ) ).
tff(conj_thm_2Estate__transformer_2EJOIN__UNIT,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(conj_thm_2Estate__transformer_2EJOIN__MMAP__UNIT,axiom,
! [A_27a: del,A_27b: del] : ( 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))) ) ).
tff(conj_thm_2Estate__transformer_2EJOIN__MAP__JOIN,axiom,
! [A_27a: del,A_27b: del] : ( 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)))) ) ).
tff(conj_thm_2Estate__transformer_2EJOIN__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0k: $i] :
( mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))
=> ! [V1m: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EFST__o__UNIT,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( 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) ) ) ).
tff(conj_thm_2Estate__transformer_2ESND__o__UNIT,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( 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) ) ) ).
tff(conj_thm_2Estate__transformer_2EFST__o__MMAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1g: $i] :
( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2Esequence__nil,axiom,
! [A_27a: del,A_27b: del] : ( 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)) ) ).
tff(conj_thm_2Estate__transformer_2EmapM__nil,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( 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)) ) ) ).
tff(lamtp_f533,type,
f533: ( del * del * $i ) > $i ).
tff(lameq_f533,axiom,
! [A_27a: del,A_27b: del,V3y: $i] :
( mem(V3y,A_27b)
=> ! [V4ys: $i] : ( 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)) ) ) ).
tff(lamtp_f534,type,
f534: ( del * del * del * $i * $i ) > $i ).
tff(lameq_f534,axiom,
! [A_27a: del,A_27c: del,A_27b: del,V0f: $i] :
( mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ! [V2xs: $i] :
( mem(V2xs,ty_2Elist_2Elist(A_27c))
=> ! [V3y: $i] : ( 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)) ) ) ) ).
tff(conj_thm_2Estate__transformer_2EmapM__cons,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))
=> ! [V1x: $i] :
( mem(V1x,A_27c)
=> ! [V2xs: $i] :
( 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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