TPTP Problem File: SWW526_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW526_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Huffman's Algorithm line 385
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla09] Blanchette (2009), Proof Pearl: Mechanizing the Textbo
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : huff_385 [Bla13]
% Status : Theorem
% Rating : 0.33 v8.2.0, 0.67 v7.4.0, 0.75 v7.1.0, 0.67 v6.4.0
% Syntax : Number of formulae : 174 ( 42 unt; 42 typ; 0 def)
% Number of atoms : 286 ( 91 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 185 ( 31 ~; 7 |; 16 &)
% ( 18 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 57 ( 28 >; 29 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 0 prp; 1-6 aty)
% Number of functors : 26 ( 26 usr; 3 con; 0-6 aty)
% Number of variables : 464 ( 413 !; 4 ?; 464 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:14:10
%------------------------------------------------------------------------------
%----Should-be-implicit typings (7)
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_Huffman__Mirabelle__lalbadcutu_Otree,type,
huffma1450048681e_tree: $tType > $tType ).
tff(ty_tc_Nat_Onat,type,
nat: $tType ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
tff(ty_tc_prod,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(ty_tc_sum,type,
sum_sum: ( $tType * $tType ) > $tType ).
%----Explicit typings (37)
tff(sy_cl_Lattices_Obounded__lattice,type,
bounded_lattice:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Obot,type,
bot:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Olattice,type,
lattice:
!>[A: $tType] : $o ).
tff(sy_cl_Finite__Set_Ofinite,type,
finite_finite1:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Osemilattice__inf,type,
semilattice_inf:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Osemilattice__sup,type,
semilattice_sup:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Obounded__lattice__bot,type,
bounded_lattice_bot:
!>[A: $tType] : $o ).
tff(sy_c_Big__Operators_Ocomm__monoid__big,type,
big_comm_monoid_big:
!>[A: $tType,B: $tType] : ( ( fun(A,fun(A,A)) * A * fun(fun(B,A),fun(fun(B,bool),A)) ) > $o ) ).
tff(sy_c_Big__Operators_Olattice__class_OSup__fin,type,
big_lattice_Sup_fin:
!>[A: $tType] : ( fun(A,bool) > A ) ).
tff(sy_c_COMBB,type,
combb:
!>[B: $tType,C: $tType,A: $tType] : ( ( fun(B,C) * fun(A,B) ) > fun(A,C) ) ).
tff(sy_c_COMBC,type,
combc:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(A,fun(B,C)) * B ) > fun(A,C) ) ).
tff(sy_c_COMBK,type,
combk:
!>[A: $tType,B: $tType] : ( A > fun(B,A) ) ).
tff(sy_c_COMBS,type,
combs:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(A,fun(B,C)) * fun(A,B) ) > fun(A,C) ) ).
tff(sy_c_Finite__Set_Ofinite,type,
finite_finite:
!>[A: $tType] : ( fun(A,bool) > $o ) ).
tff(sy_c_Finite__Set_Ofold__image,type,
finite_fold_image:
!>[B: $tType,A: $tType] : ( ( fun(B,fun(B,B)) * fun(A,B) * B * fun(A,bool) ) > B ) ).
tff(sy_c_Finite__Set_Ofolding__image__simple__idem,type,
finite908156982e_idem:
!>[A: $tType,B: $tType] : ( ( fun(A,fun(A,A)) * A * fun(B,A) * fun(fun(B,bool),A) ) > $o ) ).
tff(sy_c_Finite__Set_Ofolding__one__idem,type,
finite2073411215e_idem:
!>[A: $tType] : ( ( fun(A,fun(A,A)) * fun(fun(A,bool),A) ) > $o ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Oalphabet,type,
huffma675207370phabet:
!>[A: $tType] : ( huffma1450048681e_tree(A) > fun(A,bool) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Otree_OInnerNode,type,
huffma1146269203erNode:
!>[A: $tType] : ( ( nat * huffma1450048681e_tree(A) * huffma1450048681e_tree(A) ) > huffma1450048681e_tree(A) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Otree_Otree__case,type,
huffma107959123e_case:
!>[A: $tType,T: $tType] : ( ( fun(nat,fun(A,T)) * fun(nat,fun(huffma1450048681e_tree(A),fun(huffma1450048681e_tree(A),T))) * huffma1450048681e_tree(A) ) > T ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Otree_Otree__rec,type,
huffma1280178957ee_rec:
!>[A: $tType,T: $tType] : ( ( fun(nat,fun(A,T)) * fun(nat,fun(huffma1450048681e_tree(A),fun(huffma1450048681e_tree(A),fun(T,fun(T,T))))) * huffma1450048681e_tree(A) ) > T ) ).
tff(sy_c_Lattices_Oinf__class_Oinf,type,
inf_inf:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Lattices_Osup__class_Osup,type,
sup_sup:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Orderings_Obot__class_Obot,type,
bot_bot:
!>[A: $tType] : A ).
tff(sy_c_Predicate_Oinv__imagep,type,
inv_imagep:
!>[B: $tType,A: $tType] : ( ( fun(B,fun(B,bool)) * fun(A,B) * A * A ) > $o ) ).
tff(sy_c_Relation_OField,type,
field:
!>[A: $tType] : ( fun(product_prod(A,A),bool) > fun(A,bool) ) ).
tff(sy_c_Relation_Orefl__on,type,
refl_on:
!>[A: $tType] : ( ( fun(A,bool) * fun(product_prod(A,A),bool) ) > $o ) ).
tff(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( fun(A,bool) > fun(A,bool) ) ).
tff(sy_c_Set_OPow,type,
pow:
!>[A: $tType] : ( fun(A,bool) > fun(fun(A,bool),bool) ) ).
tff(sy_c_Sum__Type_OPlus,type,
sum_Plus:
!>[A: $tType,B: $tType] : ( ( fun(A,bool) * fun(B,bool) ) > fun(sum_sum(A,B),bool) ) ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_fdisj,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(sy_c_member,type,
member:
!>[A: $tType] : fun(A,fun(fun(A,bool),bool)) ).
tff(sy_c_pp,type,
pp: bool > $o ).
%----Relevant facts (100)
tff(fact_0_finite__code,axiom,
! [B: $tType] :
( finite_finite1(B)
=> ! [A1: fun(B,bool)] : finite_finite(B,A1) ) ).
tff(fact_1_finite,axiom,
! [B: $tType] :
( finite_finite1(B)
=> ! [A1: fun(B,bool)] : finite_finite(B,A1) ) ).
tff(fact_2_comm__monoid__big_Oinfinite,axiom,
! [C: $tType,B: $tType,G: fun(C,B),A1: fun(C,bool),F1: fun(fun(C,B),fun(fun(C,bool),B)),Z: B,F: fun(B,fun(B,B))] :
( big_comm_monoid_big(B,C,F,Z,F1)
=> ( ~ finite_finite(C,A1)
=> ( aa(fun(C,bool),B,aa(fun(C,B),fun(fun(C,bool),B),F1,G),A1) = Z ) ) ) ).
tff(fact_3_alphabet_Osimps_I2_J,axiom,
! [B: $tType,T_21: huffma1450048681e_tree(B),T_11: huffma1450048681e_tree(B),W: nat] : huffma675207370phabet(B,huffma1146269203erNode(B,W,T_11,T_21)) = sup_sup(fun(B,bool),huffma675207370phabet(B,T_11),huffma675207370phabet(B,T_21)) ).
tff(fact_4_folding__image__simple__idem_Oin__idem,axiom,
! [B: $tType,C: $tType,X: C,A1: fun(C,bool),F1: fun(fun(C,bool),B),G: fun(C,B),Z: B,F: fun(B,fun(B,B))] :
( finite908156982e_idem(B,C,F,Z,G,F1)
=> ( finite_finite(C,A1)
=> ( pp(aa(fun(C,bool),bool,aa(C,fun(fun(C,bool),bool),member(C),X),A1))
=> ( aa(B,B,aa(B,fun(B,B),F,aa(C,B,G,X)),aa(fun(C,bool),B,F1,A1)) = aa(fun(C,bool),B,F1,A1) ) ) ) ) ).
tff(fact_5_finite__Plus__iff,axiom,
! [B: $tType,C: $tType,B1: fun(C,bool),A1: fun(B,bool)] :
( finite_finite(sum_sum(B,C),sum_Plus(B,C,A1,B1))
<=> ( finite_finite(B,A1)
& finite_finite(C,B1) ) ) ).
tff(fact_6_folding__one__idem_Oin__idem,axiom,
! [B: $tType,X: B,A1: fun(B,bool),F1: fun(fun(B,bool),B),F: fun(B,fun(B,B))] :
( finite2073411215e_idem(B,F,F1)
=> ( finite_finite(B,A1)
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),A1))
=> ( aa(B,B,aa(B,fun(B,B),F,X),aa(fun(B,bool),B,F1,A1)) = aa(fun(B,bool),B,F1,A1) ) ) ) ) ).
tff(fact_7_finite__Plus,axiom,
! [B: $tType,C: $tType,B1: fun(C,bool),A1: fun(B,bool)] :
( finite_finite(B,A1)
=> ( finite_finite(C,B1)
=> finite_finite(sum_sum(B,C),sum_Plus(B,C,A1,B1)) ) ) ).
tff(fact_8_finite__PlusD_I1_J,axiom,
! [C: $tType,B: $tType,B1: fun(C,bool),A1: fun(B,bool)] :
( finite_finite(sum_sum(B,C),sum_Plus(B,C,A1,B1))
=> finite_finite(B,A1) ) ).
tff(fact_9_finite__PlusD_I2_J,axiom,
! [B: $tType,C: $tType,B1: fun(C,bool),A1: fun(B,bool)] :
( finite_finite(sum_sum(B,C),sum_Plus(B,C,A1,B1))
=> finite_finite(C,B1) ) ).
tff(fact_10_finite__Field,axiom,
! [B: $tType,R1: fun(product_prod(B,B),bool)] :
( finite_finite(product_prod(B,B),R1)
=> finite_finite(B,field(B,R1)) ) ).
tff(fact_11_finite__Pow__iff,axiom,
! [B: $tType,A1: fun(B,bool)] :
( finite_finite(fun(B,bool),pow(B,A1))
<=> finite_finite(B,A1) ) ).
tff(fact_12_tree_Osimps_I2_J,axiom,
! [B: $tType,Tree21: huffma1450048681e_tree(B),Tree11: huffma1450048681e_tree(B),Nat1: nat,Tree2: huffma1450048681e_tree(B),Tree1: huffma1450048681e_tree(B),Nat: nat] :
( ( huffma1146269203erNode(B,Nat,Tree1,Tree2) = huffma1146269203erNode(B,Nat1,Tree11,Tree21) )
<=> ( ( Nat = Nat1 )
& ( Tree1 = Tree11 )
& ( Tree2 = Tree21 ) ) ) ).
tff(fact_13_finite__Un,axiom,
! [B: $tType,G1: fun(B,bool),F1: fun(B,bool)] :
( finite_finite(B,sup_sup(fun(B,bool),F1,G1))
<=> ( finite_finite(B,F1)
& finite_finite(B,G1) ) ) ).
tff(fact_14_Field__Un,axiom,
! [B: $tType,S: fun(product_prod(B,B),bool),R1: fun(product_prod(B,B),bool)] : field(B,sup_sup(fun(product_prod(B,B),bool),R1,S)) = sup_sup(fun(B,bool),field(B,R1),field(B,S)) ).
tff(fact_15_Sup__fin_Oidem,axiom,
! [A: $tType] :
( lattice(A)
=> ! [X1: A] : sup_sup(A,X1,X1) = X1 ) ).
tff(fact_16_folding__one__idem_Oidem,axiom,
! [B: $tType,X: B,F1: fun(fun(B,bool),B),F: fun(B,fun(B,B))] :
( finite2073411215e_idem(B,F,F1)
=> ( aa(B,B,aa(B,fun(B,B),F,X),X) = X ) ) ).
tff(fact_17_folding__image__simple__idem_Oidem,axiom,
! [C: $tType,B: $tType,X: B,F1: fun(fun(C,bool),B),G: fun(C,B),Z: B,F: fun(B,fun(B,B))] :
( finite908156982e_idem(B,C,F,Z,G,F1)
=> ( aa(B,B,aa(B,fun(B,B),F,X),X) = X ) ) ).
tff(fact_18_folding__image__simple__idem_Ounion__idem,axiom,
! [B: $tType,C: $tType,B1: fun(C,bool),A1: fun(C,bool),F1: fun(fun(C,bool),B),G: fun(C,B),Z: B,F: fun(B,fun(B,B))] :
( finite908156982e_idem(B,C,F,Z,G,F1)
=> ( finite_finite(C,A1)
=> ( finite_finite(C,B1)
=> ( aa(fun(C,bool),B,F1,sup_sup(fun(C,bool),A1,B1)) = aa(B,B,aa(B,fun(B,B),F,aa(fun(C,bool),B,F1,A1)),aa(fun(C,bool),B,F1,B1)) ) ) ) ) ).
tff(fact_19_finite__UnI,axiom,
! [B: $tType,G1: fun(B,bool),F1: fun(B,bool)] :
( finite_finite(B,F1)
=> ( finite_finite(B,G1)
=> finite_finite(B,sup_sup(fun(B,bool),F1,G1)) ) ) ).
tff(fact_20_Un__iff,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),sup_sup(fun(B,bool),A1,B1)))
<=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
| pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1)) ) ) ).
tff(fact_21_UnE,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),sup_sup(fun(B,bool),A1,B1)))
=> ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1)) ) ) ).
tff(fact_22_sup1E,axiom,
! [B: $tType,X: B,B1: fun(B,bool),A1: fun(B,bool)] :
( pp(aa(B,bool,sup_sup(fun(B,bool),A1,B1),X))
=> ( ~ pp(aa(B,bool,A1,X))
=> pp(aa(B,bool,B1,X)) ) ) ).
tff(fact_23_sup1CI,axiom,
! [B: $tType,A1: fun(B,bool),X: B,B1: fun(B,bool)] :
( ( ~ pp(aa(B,bool,B1,X))
=> pp(aa(B,bool,A1,X)) )
=> pp(aa(B,bool,sup_sup(fun(B,bool),A1,B1),X)) ) ).
tff(fact_24_UnCI,axiom,
! [B: $tType,A1: fun(B,bool),B1: fun(B,bool),C1: B] :
( ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1)) )
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),sup_sup(fun(B,bool),A1,B1))) ) ).
tff(fact_25_sup_Oleft__idem,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [B2: A,A2: A] : sup_sup(A,A2,sup_sup(A,A2,B2)) = sup_sup(A,A2,B2) ) ).
tff(fact_26_sup__left__idem,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [Y: A,X1: A] : sup_sup(A,X1,sup_sup(A,X1,Y)) = sup_sup(A,X1,Y) ) ).
tff(fact_27_comm__monoid__big_OF__cong,axiom,
! [B: $tType,C: $tType,G: fun(C,B),H: fun(C,B),B1: fun(C,bool),A1: fun(C,bool),F1: fun(fun(C,B),fun(fun(C,bool),B)),Z: B,F: fun(B,fun(B,B))] :
( big_comm_monoid_big(B,C,F,Z,F1)
=> ( ( A1 = B1 )
=> ( ! [X3: C] :
( pp(aa(fun(C,bool),bool,aa(C,fun(fun(C,bool),bool),member(C),X3),B1))
=> ( aa(C,B,H,X3) = aa(C,B,G,X3) ) )
=> ( aa(fun(C,bool),B,aa(fun(C,B),fun(fun(C,bool),B),F1,H),A1) = aa(fun(C,bool),B,aa(fun(C,B),fun(fun(C,bool),B),F1,G),B1) ) ) ) ) ).
tff(fact_28_sup__fun__def,axiom,
! [C: $tType,B: $tType] :
( lattice(C)
=> ! [G: fun(B,C),F: fun(B,C),X2: B] : aa(B,C,sup_sup(fun(B,C),F,G),X2) = sup_sup(C,aa(B,C,F,X2),aa(B,C,G,X2)) ) ).
tff(fact_29_sup__assoc,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [Z1: A,Y: A,X1: A] : sup_sup(A,sup_sup(A,X1,Y),Z1) = sup_sup(A,X1,sup_sup(A,Y,Z1)) ) ).
tff(fact_30_inf__sup__aci_I6_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Z1: A,Y: A,X1: A] : sup_sup(A,sup_sup(A,X1,Y),Z1) = sup_sup(A,X1,sup_sup(A,Y,Z1)) ) ).
tff(fact_31_sup_Oassoc,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [C3: A,B2: A,A2: A] : sup_sup(A,sup_sup(A,A2,B2),C3) = sup_sup(A,A2,sup_sup(A,B2,C3)) ) ).
tff(fact_32_sup__left__commute,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [Z1: A,Y: A,X1: A] : sup_sup(A,X1,sup_sup(A,Y,Z1)) = sup_sup(A,Y,sup_sup(A,X1,Z1)) ) ).
tff(fact_33_inf__sup__aci_I7_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Z1: A,Y: A,X1: A] : sup_sup(A,X1,sup_sup(A,Y,Z1)) = sup_sup(A,Y,sup_sup(A,X1,Z1)) ) ).
tff(fact_34_sup_Oleft__commute,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [C3: A,A2: A,B2: A] : sup_sup(A,B2,sup_sup(A,A2,C3)) = sup_sup(A,A2,sup_sup(A,B2,C3)) ) ).
tff(fact_35_inf__sup__aci_I8_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Y: A,X1: A] : sup_sup(A,X1,sup_sup(A,X1,Y)) = sup_sup(A,X1,Y) ) ).
tff(fact_36_sup__commute,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [Y: A,X1: A] : sup_sup(A,X1,Y) = sup_sup(A,Y,X1) ) ).
tff(fact_37_inf__sup__aci_I5_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Y: A,X1: A] : sup_sup(A,X1,Y) = sup_sup(A,Y,X1) ) ).
tff(fact_38_sup_Ocommute,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [B2: A,A2: A] : sup_sup(A,A2,B2) = sup_sup(A,B2,A2) ) ).
tff(fact_39_sup__idem,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [X1: A] : sup_sup(A,X1,X1) = X1 ) ).
tff(fact_40_sup_Oidem,axiom,
! [A: $tType] :
( semilattice_sup(A)
=> ! [A2: A] : sup_sup(A,A2,A2) = A2 ) ).
tff(fact_41_UnI2,axiom,
! [B: $tType,A1: fun(B,bool),B1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),sup_sup(fun(B,bool),A1,B1))) ) ).
tff(fact_42_UnI1,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),sup_sup(fun(B,bool),A1,B1))) ) ).
tff(fact_43_sup1I2,axiom,
! [B: $tType,A1: fun(B,bool),X: B,B1: fun(B,bool)] :
( pp(aa(B,bool,B1,X))
=> pp(aa(B,bool,sup_sup(fun(B,bool),A1,B1),X)) ) ).
tff(fact_44_sup1I1,axiom,
! [B: $tType,B1: fun(B,bool),X: B,A1: fun(B,bool)] :
( pp(aa(B,bool,A1,X))
=> pp(aa(B,bool,sup_sup(fun(B,bool),A1,B1),X)) ) ).
tff(fact_45_ball__Un,axiom,
! [B: $tType,P1: fun(B,bool),B1: fun(B,bool),A1: fun(B,bool)] :
( ! [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),sup_sup(fun(B,bool),A1,B1)))
=> pp(aa(B,bool,P1,X4)) )
<=> ( ! [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),A1))
=> pp(aa(B,bool,P1,X4)) )
& ! [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),B1))
=> pp(aa(B,bool,P1,X4)) ) ) ) ).
tff(fact_46_bex__Un,axiom,
! [B: $tType,P1: fun(B,bool),B1: fun(B,bool),A1: fun(B,bool)] :
( ? [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),sup_sup(fun(B,bool),A1,B1)))
& pp(aa(B,bool,P1,X4)) )
<=> ( ? [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),A1))
& pp(aa(B,bool,P1,X4)) )
| ? [X4: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),B1))
& pp(aa(B,bool,P1,X4)) ) ) ) ).
tff(fact_47_Un__assoc,axiom,
! [B: $tType,C2: fun(B,bool),B1: fun(B,bool),A1: fun(B,bool)] : sup_sup(fun(B,bool),sup_sup(fun(B,bool),A1,B1),C2) = sup_sup(fun(B,bool),A1,sup_sup(fun(B,bool),B1,C2)) ).
tff(fact_48_Un__left__commute,axiom,
! [B: $tType,C2: fun(B,bool),B1: fun(B,bool),A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,sup_sup(fun(B,bool),B1,C2)) = sup_sup(fun(B,bool),B1,sup_sup(fun(B,bool),A1,C2)) ).
tff(fact_49_Un__left__absorb,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,sup_sup(fun(B,bool),A1,B1)) = sup_sup(fun(B,bool),A1,B1) ).
tff(fact_50_Un__commute,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,B1) = sup_sup(fun(B,bool),B1,A1) ).
tff(fact_51_Un__def,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,B1) = collect(B,combs(B,bool,bool,combb(bool,fun(bool,bool),B,fdisj,combc(B,fun(B,bool),bool,member(B),A1)),combc(B,fun(B,bool),bool,member(B),B1))) ).
tff(fact_52_Un__absorb,axiom,
! [B: $tType,A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,A1) = A1 ).
tff(fact_53_Pow__top,axiom,
! [B: $tType,A1: fun(B,bool)] : pp(aa(fun(fun(B,bool),bool),bool,aa(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),A1),pow(B,A1))) ).
tff(fact_54_sup__apply,axiom,
! [B: $tType,C: $tType] :
( lattice(B)
=> ! [X: C,G: fun(C,B),F: fun(C,B)] : aa(C,B,sup_sup(fun(C,B),F,G),X) = sup_sup(B,aa(C,B,F,X),aa(C,B,G,X)) ) ).
tff(fact_55_tree_Osimps_I6_J,axiom,
! [B: $tType,C: $tType,Tree2: huffma1450048681e_tree(C),Tree1: huffma1450048681e_tree(C),Nat: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B))),F11: fun(nat,fun(C,B))] : huffma107959123e_case(C,B,F11,F2,huffma1146269203erNode(C,Nat,Tree1,Tree2)) = aa(huffma1450048681e_tree(C),B,aa(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B),aa(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B)),F2,Nat),Tree1),Tree2) ).
tff(fact_56_tree_Orecs_I2_J,axiom,
! [B: $tType,C: $tType,Tree2: huffma1450048681e_tree(C),Tree1: huffma1450048681e_tree(C),Nat: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),fun(B,fun(B,B))))),F11: fun(nat,fun(C,B))] : huffma1280178957ee_rec(C,B,F11,F2,huffma1146269203erNode(C,Nat,Tree1,Tree2)) = aa(B,B,aa(B,fun(B,B),aa(huffma1450048681e_tree(C),fun(B,fun(B,B)),aa(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),fun(B,fun(B,B))),aa(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),fun(B,fun(B,B)))),F2,Nat),Tree1),Tree2),huffma1280178957ee_rec(C,B,F11,F2,Tree1)),huffma1280178957ee_rec(C,B,F11,F2,Tree2)) ).
tff(fact_57_folding__one__idem_Ounion__idem,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),F1: fun(fun(B,bool),B),F: fun(B,fun(B,B))] :
( finite2073411215e_idem(B,F,F1)
=> ( finite_finite(B,A1)
=> ( ( A1 != bot_bot(fun(B,bool)) )
=> ( finite_finite(B,B1)
=> ( ( B1 != bot_bot(fun(B,bool)) )
=> ( aa(fun(B,bool),B,F1,sup_sup(fun(B,bool),A1,B1)) = aa(B,B,aa(B,fun(B,B),F,aa(fun(B,bool),B,F1,A1)),aa(fun(B,bool),B,F1,B1)) ) ) ) ) ) ) ).
tff(fact_58_in__inv__imagep,axiom,
! [B: $tType,C: $tType,Y2: C,X: C,F: fun(C,B),R1: fun(B,fun(B,bool))] :
( inv_imagep(B,C,R1,F,X,Y2)
<=> pp(aa(B,bool,aa(B,fun(B,bool),R1,aa(C,B,F,X)),aa(C,B,F,Y2))) ) ).
tff(fact_59_comm__monoid__big_OF__eq,axiom,
! [C: $tType,B: $tType,G: fun(C,B),A1: fun(C,bool),F1: fun(fun(C,B),fun(fun(C,bool),B)),Z: B,F: fun(B,fun(B,B))] :
( big_comm_monoid_big(B,C,F,Z,F1)
=> ( ( finite_finite(C,A1)
=> ( aa(fun(C,bool),B,aa(fun(C,B),fun(fun(C,bool),B),F1,G),A1) = finite_fold_image(B,C,F,G,Z,A1) ) )
& ( ~ finite_finite(C,A1)
=> ( aa(fun(C,bool),B,aa(fun(C,B),fun(fun(C,bool),B),F1,G),A1) = Z ) ) ) ) ).
tff(fact_60_refl__on__Un,axiom,
! [B: $tType,S: fun(product_prod(B,B),bool),B1: fun(B,bool),R1: fun(product_prod(B,B),bool),A1: fun(B,bool)] :
( refl_on(B,A1,R1)
=> ( refl_on(B,B1,S)
=> refl_on(B,sup_sup(fun(B,bool),A1,B1),sup_sup(fun(product_prod(B,B),bool),R1,S)) ) ) ).
tff(fact_61_emptyE,axiom,
! [B: $tType,A3: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),A3),bot_bot(fun(B,bool)))) ).
tff(fact_62_Collect__empty__eq,axiom,
! [B: $tType,P1: fun(B,bool)] :
( ( collect(B,P1) = bot_bot(fun(B,bool)) )
<=> ! [X4: B] : ~ pp(aa(B,bool,P1,X4)) ) ).
tff(fact_63_empty__iff,axiom,
! [B: $tType,C1: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),bot_bot(fun(B,bool)))) ).
tff(fact_64_empty__Collect__eq,axiom,
! [B: $tType,P1: fun(B,bool)] :
( ( bot_bot(fun(B,bool)) = collect(B,P1) )
<=> ! [X4: B] : ~ pp(aa(B,bool,P1,X4)) ) ).
tff(fact_65_all__not__in__conv,axiom,
! [B: $tType,A1: fun(B,bool)] :
( ! [X4: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),A1))
<=> ( A1 = bot_bot(fun(B,bool)) ) ) ).
tff(fact_66_finite_OemptyI,axiom,
! [B: $tType] : finite_finite(B,bot_bot(fun(B,bool))) ).
tff(fact_67_sup__eq__bot__iff,axiom,
! [B: $tType] :
( bounded_lattice_bot(B)
=> ! [Y2: B,X: B] :
( ( sup_sup(B,X,Y2) = bot_bot(B) )
<=> ( ( X = bot_bot(B) )
& ( Y2 = bot_bot(B) ) ) ) ) ).
tff(fact_68_Un__empty,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool)] :
( ( sup_sup(fun(B,bool),A1,B1) = bot_bot(fun(B,bool)) )
<=> ( ( A1 = bot_bot(fun(B,bool)) )
& ( B1 = bot_bot(fun(B,bool)) ) ) ) ).
tff(fact_69_Field__empty,axiom,
! [B: $tType] : field(B,bot_bot(fun(product_prod(B,B),bool))) = bot_bot(fun(B,bool)) ).
tff(fact_70_equals0D,axiom,
! [B: $tType,A3: B,A1: fun(B,bool)] :
( ( A1 = bot_bot(fun(B,bool)) )
=> ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),A3),A1)) ) ).
tff(fact_71_ex__in__conv,axiom,
! [B: $tType,A1: fun(B,bool)] :
( ? [X4: B] : pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X4),A1))
<=> ( A1 != bot_bot(fun(B,bool)) ) ) ).
tff(fact_72_empty__def,axiom,
! [B: $tType] : bot_bot(fun(B,bool)) = collect(B,combk(bool,B,fFalse)) ).
tff(fact_73_bot__empty__eq,axiom,
! [B: $tType,X2: B] :
( pp(aa(B,bool,bot_bot(fun(B,bool)),X2))
<=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),bot_bot(fun(B,bool)))) ) ).
tff(fact_74_fold__image__empty,axiom,
! [C: $tType,B: $tType,Z: B,G: fun(C,B),F: fun(B,fun(B,B))] : finite_fold_image(B,C,F,G,Z,bot_bot(fun(C,bool))) = Z ).
tff(fact_75_ext,axiom,
! [C: $tType,B: $tType,G: fun(B,C),F: fun(B,C)] :
( ! [X3: B] : aa(B,C,F,X3) = aa(B,C,G,X3)
=> ( F = G ) ) ).
tff(fact_76_mem__def,axiom,
! [B: $tType,A1: fun(B,bool),X: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),A1))
<=> pp(aa(B,bool,A1,X)) ) ).
tff(fact_77_Collect__def,axiom,
! [B: $tType,P1: fun(B,bool)] : collect(B,P1) = P1 ).
tff(fact_78_refl__on__empty,axiom,
! [B: $tType] : refl_on(B,bot_bot(fun(B,bool)),bot_bot(fun(product_prod(B,B),bool))) ).
tff(fact_79_Un__empty__left,axiom,
! [B: $tType,B1: fun(B,bool)] : sup_sup(fun(B,bool),bot_bot(fun(B,bool)),B1) = B1 ).
tff(fact_80_Un__empty__right,axiom,
! [B: $tType,A1: fun(B,bool)] : sup_sup(fun(B,bool),A1,bot_bot(fun(B,bool))) = A1 ).
tff(fact_81_sup__bot__left,axiom,
! [A: $tType] :
( bounded_lattice_bot(A)
=> ! [X1: A] : sup_sup(A,bot_bot(A),X1) = X1 ) ).
tff(fact_82_sup__bot__right,axiom,
! [A: $tType] :
( bounded_lattice_bot(A)
=> ! [X1: A] : sup_sup(A,X1,bot_bot(A)) = X1 ) ).
tff(fact_83_Pow__bottom,axiom,
! [B: $tType,B1: fun(B,bool)] : pp(aa(fun(fun(B,bool),bool),bool,aa(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),bot_bot(fun(B,bool))),pow(B,B1))) ).
tff(fact_84_Pow__not__empty,axiom,
! [B: $tType,A1: fun(B,bool)] : pow(B,A1) != bot_bot(fun(fun(B,bool),bool)) ).
tff(fact_85_Plus__eq__empty__conv,axiom,
! [B: $tType,C: $tType,B1: fun(C,bool),A1: fun(B,bool)] :
( ( sum_Plus(B,C,A1,B1) = bot_bot(fun(sum_sum(B,C),bool)) )
<=> ( ( A1 = bot_bot(fun(B,bool)) )
& ( B1 = bot_bot(fun(C,bool)) ) ) ) ).
tff(fact_86_bot__fun__def,axiom,
! [B: $tType,C: $tType] :
( bot(C)
=> ! [X2: B] : aa(B,C,bot_bot(fun(B,C)),X2) = bot_bot(C) ) ).
tff(fact_87_bot__apply,axiom,
! [C: $tType,B: $tType] :
( bot(B)
=> ! [X: C] : aa(C,B,bot_bot(fun(C,B)),X) = bot_bot(B) ) ).
tff(fact_88_equals0I,axiom,
! [B: $tType,A1: fun(B,bool)] :
( ! [Y1: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Y1),A1))
=> ( A1 = bot_bot(fun(B,bool)) ) ) ).
tff(fact_89_Sup__fin_Ounion__idem,axiom,
! [B: $tType] :
( lattice(B)
=> ! [B1: fun(B,bool),A1: fun(B,bool)] :
( finite_finite(B,A1)
=> ( ( A1 != bot_bot(fun(B,bool)) )
=> ( finite_finite(B,B1)
=> ( ( B1 != bot_bot(fun(B,bool)) )
=> ( big_lattice_Sup_fin(B,sup_sup(fun(B,bool),A1,B1)) = sup_sup(B,big_lattice_Sup_fin(B,A1),big_lattice_Sup_fin(B,B1)) ) ) ) ) ) ) ).
tff(fact_90_Sup__fin_Oin__idem,axiom,
! [B: $tType] :
( lattice(B)
=> ! [X: B,A1: fun(B,bool)] :
( finite_finite(B,A1)
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),A1))
=> ( sup_sup(B,X,big_lattice_Sup_fin(B,A1)) = big_lattice_Sup_fin(B,A1) ) ) ) ) ).
tff(fact_91_Sup__fin_Ounion__disjoint,axiom,
! [B: $tType] :
( lattice(B)
=> ! [B1: fun(B,bool),A1: fun(B,bool)] :
( finite_finite(B,A1)
=> ( ( A1 != bot_bot(fun(B,bool)) )
=> ( finite_finite(B,B1)
=> ( ( B1 != bot_bot(fun(B,bool)) )
=> ( ( inf_inf(fun(B,bool),A1,B1) = bot_bot(fun(B,bool)) )
=> ( big_lattice_Sup_fin(B,sup_sup(fun(B,bool),A1,B1)) = sup_sup(B,big_lattice_Sup_fin(B,A1),big_lattice_Sup_fin(B,B1)) ) ) ) ) ) ) ) ).
tff(fact_92_Sup__fin_Ounion__inter,axiom,
! [B: $tType] :
( lattice(B)
=> ! [B1: fun(B,bool),A1: fun(B,bool)] :
( finite_finite(B,A1)
=> ( finite_finite(B,B1)
=> ( ( inf_inf(fun(B,bool),A1,B1) != bot_bot(fun(B,bool)) )
=> ( sup_sup(B,big_lattice_Sup_fin(B,sup_sup(fun(B,bool),A1,B1)),big_lattice_Sup_fin(B,inf_inf(fun(B,bool),A1,B1))) = sup_sup(B,big_lattice_Sup_fin(B,A1),big_lattice_Sup_fin(B,B1)) ) ) ) ) ) ).
tff(fact_93_inf_Oleft__idem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [B2: A,A2: A] : inf_inf(A,A2,inf_inf(A,A2,B2)) = inf_inf(A,A2,B2) ) ).
tff(fact_94_inf__left__idem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [Y: A,X1: A] : inf_inf(A,X1,inf_inf(A,X1,Y)) = inf_inf(A,X1,Y) ) ).
tff(fact_95_Int__iff,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),inf_inf(fun(B,bool),A1,B1)))
<=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
& pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1)) ) ) ).
tff(fact_96_inf1I,axiom,
! [B: $tType,B1: fun(B,bool),X: B,A1: fun(B,bool)] :
( pp(aa(B,bool,A1,X))
=> ( pp(aa(B,bool,B1,X))
=> pp(aa(B,bool,inf_inf(fun(B,bool),A1,B1),X)) ) ) ).
tff(fact_97_IntI,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),inf_inf(fun(B,bool),A1,B1))) ) ) ).
tff(fact_98_IntE,axiom,
! [B: $tType,B1: fun(B,bool),A1: fun(B,bool),C1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),inf_inf(fun(B,bool),A1,B1)))
=> ~ ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A1))
=> ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B1)) ) ) ).
tff(fact_99_inf1E,axiom,
! [B: $tType,X: B,B1: fun(B,bool),A1: fun(B,bool)] :
( pp(aa(B,bool,inf_inf(fun(B,bool),A1,B1),X))
=> ~ ( pp(aa(B,bool,A1,X))
=> ~ pp(aa(B,bool,B1,X)) ) ) ).
%----Arities (20)
tff(arity_HOL_Obool___Lattices_Obounded__lattice,axiom,
bounded_lattice(bool) ).
tff(arity_fun___Lattices_Obounded__lattice,axiom,
! [T_1: $tType,T_2: $tType] :
( bounded_lattice(T_2)
=> bounded_lattice(fun(T_1,T_2)) ) ).
tff(arity_fun___Lattices_Obounded__lattice__bot,axiom,
! [T_1: $tType,T_2: $tType] :
( bounded_lattice(T_2)
=> bounded_lattice_bot(fun(T_1,T_2)) ) ).
tff(arity_fun___Lattices_Osemilattice__sup,axiom,
! [T_1: $tType,T_2: $tType] :
( lattice(T_2)
=> semilattice_sup(fun(T_1,T_2)) ) ).
tff(arity_fun___Lattices_Osemilattice__inf,axiom,
! [T_1: $tType,T_2: $tType] :
( lattice(T_2)
=> semilattice_inf(fun(T_1,T_2)) ) ).
tff(arity_fun___Finite__Set_Ofinite,axiom,
! [T_1: $tType,T_2: $tType] :
( ( finite_finite1(T_2)
& finite_finite1(T_1) )
=> finite_finite1(fun(T_1,T_2)) ) ).
tff(arity_fun___Lattices_Olattice,axiom,
! [T_1: $tType,T_2: $tType] :
( lattice(T_2)
=> lattice(fun(T_1,T_2)) ) ).
tff(arity_fun___Orderings_Obot,axiom,
! [T_1: $tType,T_2: $tType] :
( bot(T_2)
=> bot(fun(T_1,T_2)) ) ).
tff(arity_Nat_Onat___Lattices_Osemilattice__sup,axiom,
semilattice_sup(nat) ).
tff(arity_Nat_Onat___Lattices_Osemilattice__inf,axiom,
semilattice_inf(nat) ).
tff(arity_Nat_Onat___Lattices_Olattice,axiom,
lattice(nat) ).
tff(arity_Nat_Onat___Orderings_Obot,axiom,
bot(nat) ).
tff(arity_HOL_Obool___Lattices_Obounded__lattice__bot,axiom,
bounded_lattice_bot(bool) ).
tff(arity_HOL_Obool___Lattices_Osemilattice__sup,axiom,
semilattice_sup(bool) ).
tff(arity_HOL_Obool___Lattices_Osemilattice__inf,axiom,
semilattice_inf(bool) ).
tff(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite1(bool) ).
tff(arity_HOL_Obool___Lattices_Olattice,axiom,
lattice(bool) ).
tff(arity_HOL_Obool___Orderings_Obot,axiom,
bot(bool) ).
tff(arity_sum___Finite__Set_Ofinite,axiom,
! [T_1: $tType,T_2: $tType] :
( ( finite_finite1(T_2)
& finite_finite1(T_1) )
=> finite_finite1(sum_sum(T_1,T_2)) ) ).
tff(arity_prod___Finite__Set_Ofinite,axiom,
! [T_1: $tType,T_2: $tType] :
( ( finite_finite1(T_2)
& finite_finite1(T_1) )
=> finite_finite1(product_prod(T_1,T_2)) ) ).
%----Helper facts (11)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
tff(help_COMBB_1_1_U,axiom,
! [C: $tType,B: $tType,A: $tType,R: A,Q: fun(A,B),P: fun(B,C)] : aa(A,C,combb(B,C,A,P,Q),R) = aa(B,C,P,aa(A,B,Q,R)) ).
tff(help_COMBC_1_1_U,axiom,
! [A: $tType,C: $tType,B: $tType,R: A,Q: B,P: fun(A,fun(B,C))] : aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q) ).
tff(help_COMBK_1_1_U,axiom,
! [B: $tType,A: $tType,Q: B,P: A] : aa(B,A,combk(A,B,P),Q) = P ).
tff(help_COMBS_1_1_U,axiom,
! [C: $tType,B: $tType,A: $tType,R: A,Q: fun(A,B),P: fun(A,fun(B,C))] : aa(A,C,combs(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),aa(A,B,Q,R)) ).
tff(help_fdisj_1_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(P)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q)) ) ).
tff(help_fdisj_2_1_U,axiom,
! [P: bool,Q: bool] :
( ~ pp(Q)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q)) ) ).
tff(help_fdisj_3_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q))
| pp(P)
| pp(Q) ) ).
tff(help_fFalse_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_fFalse_1_1_T,axiom,
! [P: bool] :
( ( P = fTrue )
| ( P = fFalse ) ) ).
%----Conjectures (1)
tff(conj_0,conjecture,
! [A: $tType,T: huffma1450048681e_tree(A)] : finite_finite(A,huffma675207370phabet(A,T)) ).
%------------------------------------------------------------------------------