TPTP Problem File: SWW529_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW529_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Huffman's Algorithm line 545
% 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_545 [Bla13]
% Status : Theorem
% Rating : 0.00 v7.5.0, 0.33 v7.4.0, 0.25 v7.1.0, 0.33 v6.4.0
% Syntax : Number of formulae : 217 ( 84 unt; 55 typ; 0 def)
% Number of atoms : 299 ( 89 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 161 ( 24 ~; 11 |; 26 &)
% ( 31 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 43 ( 25 >; 18 *; 0 +; 0 <<)
% Number of predicates : 19 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 7 con; 0-5 aty)
% Number of variables : 431 ( 378 !; 7 ?; 431 :)
% ( 46 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:15:38
%------------------------------------------------------------------------------
%----Should-be-implicit typings (9)
tff(ty_t_a,type,
a: $tType ).
tff(ty_tc_Code__Evaluation_Oterm,type,
code_term: $tType ).
tff(ty_tc_Code__Numeral_Ocode__numeral,type,
code_code_numeral: $tType ).
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_Product__Type_Ounit,type,
product_unit: $tType ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
tff(ty_tc_prod,type,
product_prod: ( $tType * $tType ) > $tType ).
%----Explicit typings (46)
tff(sy_cl_Enum_Oenum,type,
enum:
!>[A: $tType] : $o ).
tff(sy_cl_Typerep_Otyperep,type,
typerep:
!>[A: $tType] : $o ).
tff(sy_cl_HOL_Oequal,type,
cl_HOL_Oequal:
!>[A: $tType] : $o ).
tff(sy_cl_Code__Evaluation_Oterm__of,type,
code_term_of:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Oone,type,
one:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
tff(sy_cl_Quickcheck_Orandom,type,
random:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Oab__semigroup__add,type,
ab_semigroup_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ocancel__semigroup__add,type,
cancel_semigroup_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
cancel146912293up_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
ordere236663937imp_le:
!>[A: $tType] : $o ).
tff(sy_c_COMBB,type,
combb:
!>[B1: $tType,C: $tType,A: $tType] : ( ( fun(B1,C) * fun(A,B1) ) > fun(A,C) ) ).
tff(sy_c_COMBC,type,
combc:
!>[A: $tType,B1: $tType,C: $tType] : ( ( fun(A,fun(B1,C)) * B1 ) > fun(A,C) ) ).
tff(sy_c_COMBK,type,
combk:
!>[A: $tType,B1: $tType] : ( A > fun(B1,A) ) ).
tff(sy_c_COMBS,type,
combs:
!>[A: $tType,B1: $tType,C: $tType] : ( ( fun(A,fun(B1,C)) * fun(A,B1) ) > fun(A,C) ) ).
tff(sy_c_Finite__Set_Ofinite,type,
finite_finite:
!>[A: $tType] : ( fun(A,bool) > $o ) ).
tff(sy_c_Groups_Oone__class_Oone,type,
one_one:
!>[A: $tType] : A ).
tff(sy_c_Groups_Oplus__class_Oplus,type,
plus_plus:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_HOL_Oequal__class_Oequal,type,
equal_equal:
!>[A: $tType] : ( ( A * 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_Oconsistent,type,
huffma1518433673istent:
!>[A: $tType] : ( huffma1450048681e_tree(A) > $o ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Odepth,type,
huffma410068972_depth:
!>[A: $tType] : ( ( huffma1450048681e_tree(A) * A ) > nat ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Oheight,type,
huffma945805758height:
!>[A: $tType] : ( huffma1450048681e_tree(A) > nat ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Orandom__aux__tree,type,
huffma928900296x_tree:
!>[A: $tType] : ( ( code_code_numeral * code_code_numeral ) > fun(product_prod(code_code_numeral,code_code_numeral),product_prod(product_prod(huffma1450048681e_tree(A),fun(product_unit,code_term)),product_prod(code_code_numeral,code_code_numeral))) ) ).
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_OLeaf,type,
huffma2021818691e_Leaf:
!>[A: $tType] : ( ( nat * A ) > huffma1450048681e_tree(A) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Otree_Otree__case,type,
huffma107959123e_case:
!>[A: $tType,T1: $tType] : ( ( fun(nat,fun(A,T1)) * fun(nat,fun(huffma1450048681e_tree(A),fun(huffma1450048681e_tree(A),T1))) * huffma1450048681e_tree(A) ) > T1 ) ).
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_Orderings_Oord__class_Oless__eq,type,
ord_less_eq:
!>[A: $tType] : ( ( A * A ) > $o ) ).
tff(sy_c_Quickcheck_Orandom__class_Orandom,type,
random_random:
!>[A: $tType] : ( code_code_numeral > fun(product_prod(code_code_numeral,code_code_numeral),product_prod(product_prod(A,fun(product_unit,code_term)),product_prod(code_code_numeral,code_code_numeral))) ) ).
tff(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( fun(A,bool) > fun(A,bool) ) ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B1: $tType] : ( ( fun(A,B1) * A ) > B1 ) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_fconj,type,
fconj: fun(bool,fun(bool,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 ).
tff(sy_v_t_092_060_094isub_0621____,type,
t_1: huffma1450048681e_tree(a) ).
tff(sy_v_t_092_060_094isub_0622____,type,
t_2: huffma1450048681e_tree(a) ).
tff(sy_v_thesis____,type,
thesis: $o ).
tff(sy_v_w____,type,
w: nat ).
%----Relevant facts (98)
tff(fact_0_InnerNode_Oprems,axiom,
huffma1518433673istent(a,huffma1146269203erNode(a,w,t_1,t_2)) ).
tff(fact_1_InnerNode_I2_J,axiom,
( huffma1518433673istent(a,t_2)
=> ? [X3: a] :
( pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,t_2)))
& ( huffma410068972_depth(a,t_2,X3) = huffma945805758height(a,t_2) ) ) ) ).
tff(fact_2_InnerNode_I1_J,axiom,
( huffma1518433673istent(a,t_1)
=> ? [X3: a] :
( pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,t_1)))
& ( huffma410068972_depth(a,t_1,X3) = huffma945805758height(a,t_1) ) ) ) ).
tff(fact_3_tree_Osimps_I2_J,axiom,
! [B1: $tType,Tree22: huffma1450048681e_tree(B1),Tree12: huffma1450048681e_tree(B1),Nat3: nat,Tree21: huffma1450048681e_tree(B1),Tree11: huffma1450048681e_tree(B1),Nat: nat] :
( ( huffma1146269203erNode(B1,Nat,Tree11,Tree21) = huffma1146269203erNode(B1,Nat3,Tree12,Tree22) )
<=> ( ( Nat = Nat3 )
& ( Tree11 = Tree12 )
& ( Tree21 = Tree22 ) ) ) ).
tff(fact_4_exists__in__alphabet,axiom,
! [B1: $tType,Ta: huffma1450048681e_tree(B1)] :
? [A5: B1] : pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A5),huffma675207370phabet(B1,Ta))) ).
tff(fact_5_depth__le__height,axiom,
! [A: $tType,A3: A,T: huffma1450048681e_tree(A)] : ord_less_eq(nat,huffma410068972_depth(A,T,A3),huffma945805758height(A,T)) ).
tff(fact_6_finite__alphabet,axiom,
! [B1: $tType,Ta: huffma1450048681e_tree(B1)] : finite_finite(B1,huffma675207370phabet(B1,Ta)) ).
tff(fact_7_alphabet_Osimps_I2_J,axiom,
! [B1: $tType,T_21: huffma1450048681e_tree(B1),T_11: huffma1450048681e_tree(B1),Wa: nat] : huffma675207370phabet(B1,huffma1146269203erNode(B1,Wa,T_11,T_21)) = sup_sup(fun(B1,bool),huffma675207370phabet(B1,T_11),huffma675207370phabet(B1,T_21)) ).
tff(fact_8_depth_Osimps_I1_J,axiom,
! [A: $tType,A3: A,B3: A,W: nat] : huffma410068972_depth(A,huffma2021818691e_Leaf(A,W,B3),A3) = zero_zero(nat) ).
tff(fact_9_height_Osimps_I1_J,axiom,
! [A: $tType,A3: A,W: nat] : huffma945805758height(A,huffma2021818691e_Leaf(A,W,A3)) = zero_zero(nat) ).
tff(fact_10_depth_Osimps_I2_J,axiom,
! [B1: $tType,T_21: huffma1450048681e_tree(B1),Wa: nat,T_11: huffma1450048681e_tree(B1),A2: B1] :
( ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),huffma675207370phabet(B1,T_11)))
=> ( huffma410068972_depth(B1,huffma1146269203erNode(B1,Wa,T_11,T_21),A2) = plus_plus(nat,huffma410068972_depth(B1,T_11,A2),one_one(nat)) ) )
& ( ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),huffma675207370phabet(B1,T_11)))
=> ( ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),huffma675207370phabet(B1,T_21)))
=> ( huffma410068972_depth(B1,huffma1146269203erNode(B1,Wa,T_11,T_21),A2) = plus_plus(nat,huffma410068972_depth(B1,T_21,A2),one_one(nat)) ) )
& ( ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),huffma675207370phabet(B1,T_21)))
=> ( huffma410068972_depth(B1,huffma1146269203erNode(B1,Wa,T_11,T_21),A2) = zero_zero(nat) ) ) ) ) ) ).
tff(fact_11_random__tree__def,axiom,
! [B1: $tType] :
( random(B1)
=> ! [I1: code_code_numeral] : random_random(huffma1450048681e_tree(B1),I1) = huffma928900296x_tree(B1,I1,I1) ) ).
tff(fact_12_tree_Osimps_I6_J,axiom,
! [B1: $tType,C: $tType,Tree21: huffma1450048681e_tree(C),Tree11: huffma1450048681e_tree(C),Nat: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B1))),F1: fun(nat,fun(C,B1))] : huffma107959123e_case(C,B1,F1,F2,huffma1146269203erNode(C,Nat,Tree11,Tree21)) = aa(huffma1450048681e_tree(C),B1,aa(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B1),aa(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B1)),F2,Nat),Tree11),Tree21) ).
tff(fact_13_consistent_Osimps_I2_J,axiom,
! [B1: $tType,T_21: huffma1450048681e_tree(B1),T_11: huffma1450048681e_tree(B1),Wa: nat] :
( huffma1518433673istent(B1,huffma1146269203erNode(B1,Wa,T_11,T_21))
<=> ( huffma1518433673istent(B1,T_11)
& huffma1518433673istent(B1,T_21)
& ( inf_inf(fun(B1,bool),huffma675207370phabet(B1,T_11),huffma675207370phabet(B1,T_21)) = bot_bot(fun(B1,bool)) ) ) ) ).
tff(fact_14_equal__tree__def,axiom,
! [B1: $tType,Y1: huffma1450048681e_tree(B1),X2: huffma1450048681e_tree(B1)] :
( equal_equal(huffma1450048681e_tree(B1),X2,Y1)
<=> ( X2 = Y1 ) ) ).
tff(fact_15_tree_Osimps_I1_J,axiom,
! [B1: $tType,A4: B1,Nat3: nat,A2: B1,Nat: nat] :
( ( huffma2021818691e_Leaf(B1,Nat,A2) = huffma2021818691e_Leaf(B1,Nat3,A4) )
<=> ( ( Nat = Nat3 )
& ( A2 = A4 ) ) ) ).
tff(fact_16_consistent_Osimps_I1_J,axiom,
! [A: $tType,A3: A,W: nat] : huffma1518433673istent(A,huffma2021818691e_Leaf(A,W,A3)) ).
tff(fact_17_tree_Osimps_I3_J,axiom,
! [A: $tType,Tree2: huffma1450048681e_tree(A),Tree1: huffma1450048681e_tree(A),Nat1: nat,A3: A,Nat2: nat] : huffma2021818691e_Leaf(A,Nat2,A3) != huffma1146269203erNode(A,Nat1,Tree1,Tree2) ).
tff(fact_18_tree_Osimps_I4_J,axiom,
! [A: $tType,A3: A,Nat2: nat,Tree2: huffma1450048681e_tree(A),Tree1: huffma1450048681e_tree(A),Nat1: nat] : huffma1146269203erNode(A,Nat1,Tree1,Tree2) != huffma2021818691e_Leaf(A,Nat2,A3) ).
tff(fact_19_tree_Osimps_I5_J,axiom,
! [B1: $tType,C: $tType,A2: C,Nat: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B1))),F1: fun(nat,fun(C,B1))] : huffma107959123e_case(C,B1,F1,F2,huffma2021818691e_Leaf(C,Nat,A2)) = aa(C,B1,aa(nat,fun(C,B1),F1,Nat),A2) ).
tff(fact_20_zero__le__double__add__iff__zero__le__single__add,axiom,
! [B1: $tType] :
( linord219039673up_add(B1)
=> ! [A2: B1] :
( ord_less_eq(B1,zero_zero(B1),plus_plus(B1,A2,A2))
<=> ord_less_eq(B1,zero_zero(B1),A2) ) ) ).
tff(fact_21_double__add__le__zero__iff__single__add__le__zero,axiom,
! [B1: $tType] :
( linord219039673up_add(B1)
=> ! [A2: B1] :
( ord_less_eq(B1,plus_plus(B1,A2,A2),zero_zero(B1))
<=> ord_less_eq(B1,A2,zero_zero(B1)) ) ) ).
tff(fact_22_nat__add__left__cancel__le,axiom,
! [N1: nat,M1: nat,K1: nat] :
( ord_less_eq(nat,plus_plus(nat,K1,M1),plus_plus(nat,K1,N1))
<=> ord_less_eq(nat,M1,N1) ) ).
tff(fact_23_Int__Un__distrib,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,sup_sup(fun(B1,bool),B2,C1)) = sup_sup(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),inf_inf(fun(B1,bool),A1,C1)) ).
tff(fact_24_Int__Un__distrib2,axiom,
! [B1: $tType,A1: fun(B1,bool),C1: fun(B1,bool),B2: fun(B1,bool)] : inf_inf(fun(B1,bool),sup_sup(fun(B1,bool),B2,C1),A1) = sup_sup(fun(B1,bool),inf_inf(fun(B1,bool),B2,A1),inf_inf(fun(B1,bool),C1,A1)) ).
tff(fact_25_le0,axiom,
! [N: nat] : ord_less_eq(nat,zero_zero(nat),N) ).
tff(fact_26_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ord_less_eq(nat,zero_zero(nat),N) ).
tff(fact_27_le__0__eq,axiom,
! [N1: nat] :
( ord_less_eq(nat,N1,zero_zero(nat))
<=> ( N1 = zero_zero(nat) ) ) ).
tff(fact_28_add__right__cancel,axiom,
! [B1: $tType] :
( cancel_semigroup_add(B1)
=> ! [C2: B1,A2: B1,B4: B1] :
( ( plus_plus(B1,B4,A2) = plus_plus(B1,C2,A2) )
<=> ( B4 = C2 ) ) ) ).
tff(fact_29_add__left__cancel,axiom,
! [B1: $tType] :
( cancel_semigroup_add(B1)
=> ! [C2: B1,B4: B1,A2: B1] :
( ( plus_plus(B1,A2,B4) = plus_plus(B1,A2,C2) )
<=> ( B4 = C2 ) ) ) ).
tff(fact_30_subset__empty,axiom,
! [B1: $tType,A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,bot_bot(fun(B1,bool)))
<=> ( A1 = bot_bot(fun(B1,bool)) ) ) ).
tff(fact_31_empty__subsetI,axiom,
! [B1: $tType,A1: fun(B1,bool)] : ord_less_eq(fun(B1,bool),bot_bot(fun(B1,bool)),A1) ).
tff(fact_32_emptyE,axiom,
! [B1: $tType,A2: B1] : ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),bot_bot(fun(B1,bool)))) ).
tff(fact_33_Collect__empty__eq,axiom,
! [B1: $tType,P1: fun(B1,bool)] :
( ( collect(B1,P1) = bot_bot(fun(B1,bool)) )
<=> ! [X: B1] : ~ pp(aa(B1,bool,P1,X)) ) ).
tff(fact_34_empty__iff,axiom,
! [B1: $tType,C2: B1] : ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),bot_bot(fun(B1,bool)))) ).
tff(fact_35_empty__Collect__eq,axiom,
! [B1: $tType,P1: fun(B1,bool)] :
( ( bot_bot(fun(B1,bool)) = collect(B1,P1) )
<=> ! [X: B1] : ~ pp(aa(B1,bool,P1,X)) ) ).
tff(fact_36_all__not__in__conv,axiom,
! [B1: $tType,A1: fun(B1,bool)] :
( ! [X: B1] : ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),A1))
<=> ( A1 = bot_bot(fun(B1,bool)) ) ) ).
tff(fact_37_nat__add__right__cancel,axiom,
! [N1: nat,K1: nat,M1: nat] :
( ( plus_plus(nat,M1,K1) = plus_plus(nat,N1,K1) )
<=> ( M1 = N1 ) ) ).
tff(fact_38_nat__add__left__cancel,axiom,
! [N1: nat,M1: nat,K1: nat] :
( ( plus_plus(nat,K1,M1) = plus_plus(nat,K1,N1) )
<=> ( M1 = N1 ) ) ).
tff(fact_39_IntE,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),inf_inf(fun(B1,bool),A1,B2)))
=> ~ ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
=> ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2)) ) ) ).
tff(fact_40_IntI,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
=> ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),inf_inf(fun(B1,bool),A1,B2))) ) ) ).
tff(fact_41_Int__iff,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),inf_inf(fun(B1,bool),A1,B2)))
<=> ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
& pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2)) ) ) ).
tff(fact_42_UnCI,axiom,
! [B1: $tType,A1: fun(B1,bool),B2: fun(B1,bool),C2: B1] :
( ( ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1)) )
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),sup_sup(fun(B1,bool),A1,B2))) ) ).
tff(fact_43_UnE,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),sup_sup(fun(B1,bool),A1,B2)))
=> ( ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2)) ) ) ).
tff(fact_44_Un__iff,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),sup_sup(fun(B1,bool),A1,B2)))
<=> ( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
| pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2)) ) ) ).
tff(fact_45_add__le__cancel__left,axiom,
! [B1: $tType] :
( ordere236663937imp_le(B1)
=> ! [B4: B1,A2: B1,C2: B1] :
( ord_less_eq(B1,plus_plus(B1,C2,A2),plus_plus(B1,C2,B4))
<=> ord_less_eq(B1,A2,B4) ) ) ).
tff(fact_46_add__le__cancel__right,axiom,
! [B1: $tType] :
( ordere236663937imp_le(B1)
=> ! [B4: B1,C2: B1,A2: B1] :
( ord_less_eq(B1,plus_plus(B1,A2,C2),plus_plus(B1,B4,C2))
<=> ord_less_eq(B1,A2,B4) ) ) ).
tff(fact_47_double__zero__sym,axiom,
! [B1: $tType] :
( linord219039673up_add(B1)
=> ! [A2: B1] :
( ( zero_zero(B1) = plus_plus(B1,A2,A2) )
<=> ( A2 = zero_zero(B1) ) ) ) ).
tff(fact_48_Un__empty,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] :
( ( sup_sup(fun(B1,bool),A1,B2) = bot_bot(fun(B1,bool)) )
<=> ( ( A1 = bot_bot(fun(B1,bool)) )
& ( B2 = bot_bot(fun(B1,bool)) ) ) ) ).
tff(fact_49_add__is__0,axiom,
! [N1: nat,M1: nat] :
( ( plus_plus(nat,M1,N1) = zero_zero(nat) )
<=> ( ( M1 = zero_zero(nat) )
& ( N1 = zero_zero(nat) ) ) ) ).
tff(fact_50_Un__upper1,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : ord_less_eq(fun(B1,bool),A1,sup_sup(fun(B1,bool),A1,B2)) ).
tff(fact_51_Un__upper2,axiom,
! [B1: $tType,A1: fun(B1,bool),B2: fun(B1,bool)] : ord_less_eq(fun(B1,bool),B2,sup_sup(fun(B1,bool),A1,B2)) ).
tff(fact_52_Int__lower1,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : ord_less_eq(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),A1) ).
tff(fact_53_Int__lower2,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : ord_less_eq(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),B2) ).
tff(fact_54_subset__Un__eq,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,B2)
<=> ( sup_sup(fun(B1,bool),A1,B2) = B2 ) ) ).
tff(fact_55_Int__absorb2,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,B2)
=> ( inf_inf(fun(B1,bool),A1,B2) = A1 ) ) ).
tff(fact_56_Un__absorb1,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,B2)
=> ( sup_sup(fun(B1,bool),A1,B2) = B2 ) ) ).
tff(fact_57_Int__absorb1,axiom,
! [B1: $tType,A1: fun(B1,bool),B2: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),B2,A1)
=> ( inf_inf(fun(B1,bool),A1,B2) = B2 ) ) ).
tff(fact_58_Un__absorb2,axiom,
! [B1: $tType,A1: fun(B1,bool),B2: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),B2,A1)
=> ( sup_sup(fun(B1,bool),A1,B2) = A1 ) ) ).
tff(fact_59_Int__greatest,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),C1,A1)
=> ( ord_less_eq(fun(B1,bool),C1,B2)
=> ord_less_eq(fun(B1,bool),C1,inf_inf(fun(B1,bool),A1,B2)) ) ) ).
tff(fact_60_Un__least,axiom,
! [B1: $tType,B2: fun(B1,bool),C1: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,C1)
=> ( ord_less_eq(fun(B1,bool),B2,C1)
=> ord_less_eq(fun(B1,bool),sup_sup(fun(B1,bool),A1,B2),C1) ) ) ).
tff(fact_61_Int__mono,axiom,
! [B1: $tType,D: fun(B1,bool),B2: fun(B1,bool),C1: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,C1)
=> ( ord_less_eq(fun(B1,bool),B2,D)
=> ord_less_eq(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),inf_inf(fun(B1,bool),C1,D)) ) ) ).
tff(fact_62_Un__mono,axiom,
! [B1: $tType,D: fun(B1,bool),B2: fun(B1,bool),C1: fun(B1,bool),A1: fun(B1,bool)] :
( ord_less_eq(fun(B1,bool),A1,C1)
=> ( ord_less_eq(fun(B1,bool),B2,D)
=> ord_less_eq(fun(B1,bool),sup_sup(fun(B1,bool),A1,B2),sup_sup(fun(B1,bool),C1,D)) ) ) ).
tff(fact_63_Un__Int__assoc__eq,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] :
( ( sup_sup(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),C1) = inf_inf(fun(B1,bool),A1,sup_sup(fun(B1,bool),B2,C1)) )
<=> ord_less_eq(fun(B1,bool),C1,A1) ) ).
tff(fact_64_zero__reorient,axiom,
! [B1: $tType] :
( zero(B1)
=> ! [X2: B1] :
( ( zero_zero(B1) = X2 )
<=> ( X2 = zero_zero(B1) ) ) ) ).
tff(fact_65_add__right__imp__eq,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C3: A,A3: A,B3: A] :
( ( plus_plus(A,B3,A3) = plus_plus(A,C3,A3) )
=> ( B3 = C3 ) ) ) ).
tff(fact_66_add__imp__eq,axiom,
! [A: $tType] :
( cancel146912293up_add(A)
=> ! [C3: A,B3: A,A3: A] :
( ( plus_plus(A,A3,B3) = plus_plus(A,A3,C3) )
=> ( B3 = C3 ) ) ) ).
tff(fact_67_add__left__imp__eq,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C3: A,B3: A,A3: A] :
( ( plus_plus(A,A3,B3) = plus_plus(A,A3,C3) )
=> ( B3 = C3 ) ) ) ).
tff(fact_68_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: $tType] :
( ab_semigroup_add(A)
=> ! [C3: A,B3: A,A3: A] : plus_plus(A,plus_plus(A,A3,B3),C3) = plus_plus(A,A3,plus_plus(A,B3,C3)) ) ).
tff(fact_69_equals0D,axiom,
! [B1: $tType,A2: B1,A1: fun(B1,bool)] :
( ( A1 = bot_bot(fun(B1,bool)) )
=> ~ pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),A2),A1)) ) ).
tff(fact_70_ex__in__conv,axiom,
! [B1: $tType,A1: fun(B1,bool)] :
( ? [X: B1] : pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),A1))
<=> ( A1 != bot_bot(fun(B1,bool)) ) ) ).
tff(fact_71_empty__def,axiom,
! [B1: $tType] : bot_bot(fun(B1,bool)) = collect(B1,combk(bool,B1,fFalse)) ).
tff(fact_72_one__reorient,axiom,
! [B1: $tType] :
( one(B1)
=> ! [X2: B1] :
( ( one_one(B1) = X2 )
<=> ( X2 = one_one(B1) ) ) ) ).
tff(fact_73_mem__def,axiom,
! [B1: $tType,A1: fun(B1,bool),X2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X2),A1))
<=> pp(aa(B1,bool,A1,X2)) ) ).
tff(fact_74_Collect__def,axiom,
! [B1: $tType,P1: fun(B1,bool)] : collect(B1,P1) = P1 ).
tff(fact_75_nat__add__assoc,axiom,
! [K: nat,N: nat,M: nat] : plus_plus(nat,plus_plus(nat,M,N),K) = plus_plus(nat,M,plus_plus(nat,N,K)) ).
tff(fact_76_nat__add__left__commute,axiom,
! [Z: nat,Y: nat,X1: nat] : plus_plus(nat,X1,plus_plus(nat,Y,Z)) = plus_plus(nat,Y,plus_plus(nat,X1,Z)) ).
tff(fact_77_nat__add__commute,axiom,
! [N: nat,M: nat] : plus_plus(nat,M,N) = plus_plus(nat,N,M) ).
tff(fact_78_IntD2,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),inf_inf(fun(B1,bool),A1,B2)))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2)) ) ).
tff(fact_79_IntD1,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),inf_inf(fun(B1,bool),A1,B2)))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1)) ) ).
tff(fact_80_Int__assoc,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),inf_inf(fun(B1,bool),A1,B2),C1) = inf_inf(fun(B1,bool),A1,inf_inf(fun(B1,bool),B2,C1)) ).
tff(fact_81_Int__left__commute,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,inf_inf(fun(B1,bool),B2,C1)) = inf_inf(fun(B1,bool),B2,inf_inf(fun(B1,bool),A1,C1)) ).
tff(fact_82_Int__left__absorb,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,inf_inf(fun(B1,bool),A1,B2)) = inf_inf(fun(B1,bool),A1,B2) ).
tff(fact_83_Int__commute,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,B2) = inf_inf(fun(B1,bool),B2,A1) ).
tff(fact_84_Int__def,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,B2) = collect(B1,combs(B1,bool,bool,combb(bool,fun(bool,bool),B1,fconj,combc(B1,fun(B1,bool),bool,member(B1),A1)),combc(B1,fun(B1,bool),bool,member(B1),B2))) ).
tff(fact_85_Int__absorb,axiom,
! [B1: $tType,A1: fun(B1,bool)] : inf_inf(fun(B1,bool),A1,A1) = A1 ).
tff(fact_86_UnI2,axiom,
! [B1: $tType,A1: fun(B1,bool),B2: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),B2))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),sup_sup(fun(B1,bool),A1,B2))) ) ).
tff(fact_87_UnI1,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool),C2: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),A1))
=> pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),C2),sup_sup(fun(B1,bool),A1,B2))) ) ).
tff(fact_88_ball__Un,axiom,
! [B1: $tType,P1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] :
( ! [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),sup_sup(fun(B1,bool),A1,B2)))
=> pp(aa(B1,bool,P1,X)) )
<=> ( ! [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),A1))
=> pp(aa(B1,bool,P1,X)) )
& ! [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),B2))
=> pp(aa(B1,bool,P1,X)) ) ) ) ).
tff(fact_89_bex__Un,axiom,
! [B1: $tType,P1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] :
( ? [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),sup_sup(fun(B1,bool),A1,B2)))
& pp(aa(B1,bool,P1,X)) )
<=> ( ? [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),A1))
& pp(aa(B1,bool,P1,X)) )
| ? [X: B1] :
( pp(aa(fun(B1,bool),bool,aa(B1,fun(fun(B1,bool),bool),member(B1),X),B2))
& pp(aa(B1,bool,P1,X)) ) ) ) ).
tff(fact_90_Un__assoc,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] : sup_sup(fun(B1,bool),sup_sup(fun(B1,bool),A1,B2),C1) = sup_sup(fun(B1,bool),A1,sup_sup(fun(B1,bool),B2,C1)) ).
tff(fact_91_Un__left__commute,axiom,
! [B1: $tType,C1: fun(B1,bool),B2: fun(B1,bool),A1: fun(B1,bool)] : sup_sup(fun(B1,bool),A1,sup_sup(fun(B1,bool),B2,C1)) = sup_sup(fun(B1,bool),B2,sup_sup(fun(B1,bool),A1,C1)) ).
tff(fact_92_Un__left__absorb,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : sup_sup(fun(B1,bool),A1,sup_sup(fun(B1,bool),A1,B2)) = sup_sup(fun(B1,bool),A1,B2) ).
tff(fact_93_Un__commute,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : sup_sup(fun(B1,bool),A1,B2) = sup_sup(fun(B1,bool),B2,A1) ).
tff(fact_94_Un__def,axiom,
! [B1: $tType,B2: fun(B1,bool),A1: fun(B1,bool)] : sup_sup(fun(B1,bool),A1,B2) = collect(B1,combs(B1,bool,bool,combb(bool,fun(bool,bool),B1,fdisj,combc(B1,fun(B1,bool),bool,member(B1),A1)),combc(B1,fun(B1,bool),bool,member(B1),B2))) ).
tff(fact_95_Un__absorb,axiom,
! [B1: $tType,A1: fun(B1,bool)] : sup_sup(fun(B1,bool),A1,A1) = A1 ).
tff(fact_96_le__antisym,axiom,
! [N: nat,M: nat] :
( ord_less_eq(nat,M,N)
=> ( ord_less_eq(nat,N,M)
=> ( M = N ) ) ) ).
tff(fact_97_le__trans,axiom,
! [K: nat,J: nat,I: nat] :
( ord_less_eq(nat,I,J)
=> ( ord_less_eq(nat,J,K)
=> ord_less_eq(nat,I,K) ) ) ).
%----Arities (48)
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___Code__Evaluation_Oterm__of,axiom,
! [T_1: $tType] :
( typerep(T_1)
=> code_term_of(huffma1450048681e_tree(T_1)) ) ).
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___HOL_Oequal,axiom,
! [T_1: $tType] : cl_HOL_Oequal(huffma1450048681e_tree(T_1)) ).
tff(arity_Code__Numeral_Ocode__numeral___Code__Evaluation_Oterm__of,axiom,
code_term_of(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___HOL_Oequal,axiom,
cl_HOL_Oequal(code_code_numeral) ).
tff(arity_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of,axiom,
code_term_of(code_term) ).
tff(arity_Code__Evaluation_Oterm___HOL_Oequal,axiom,
cl_HOL_Oequal(code_term) ).
tff(arity_Product__Type_Ounit___Code__Evaluation_Oterm__of,axiom,
code_term_of(product_unit) ).
tff(arity_Product__Type_Ounit___HOL_Oequal,axiom,
cl_HOL_Oequal(product_unit) ).
tff(arity_prod___Code__Evaluation_Oterm__of,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> code_term_of(product_prod(T_1,T_2)) ) ).
tff(arity_prod___HOL_Oequal,axiom,
! [T_1: $tType,T_2: $tType] : cl_HOL_Oequal(product_prod(T_1,T_2)) ).
tff(arity_HOL_Obool___Code__Evaluation_Oterm__of,axiom,
code_term_of(bool) ).
tff(arity_HOL_Obool___HOL_Oequal,axiom,
cl_HOL_Oequal(bool) ).
tff(arity_Nat_Onat___Code__Evaluation_Oterm__of,axiom,
code_term_of(nat) ).
tff(arity_Nat_Onat___HOL_Oequal,axiom,
cl_HOL_Oequal(nat) ).
tff(arity_fun___Code__Evaluation_Oterm__of,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> code_term_of(fun(T_1,T_2)) ) ).
tff(arity_fun___HOL_Oequal,axiom,
! [T_1: $tType,T_2: $tType] :
( ( cl_HOL_Oequal(T_2)
& enum(T_1) )
=> cl_HOL_Oequal(fun(T_1,T_2)) ) ).
tff(arity_fun___Typerep_Otyperep,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> typerep(fun(T_1,T_2)) ) ).
tff(arity_fun___Enum_Oenum,axiom,
! [T_1: $tType,T_2: $tType] :
( ( enum(T_2)
& enum(T_1) )
=> enum(fun(T_1,T_2)) ) ).
tff(arity_Nat_Onat___Typerep_Otyperep,axiom,
typerep(nat) ).
tff(arity_HOL_Obool___Typerep_Otyperep,axiom,
typerep(bool) ).
tff(arity_HOL_Obool___Enum_Oenum,axiom,
enum(bool) ).
tff(arity_prod___Typerep_Otyperep,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> typerep(product_prod(T_1,T_2)) ) ).
tff(arity_prod___Enum_Oenum,axiom,
! [T_1: $tType,T_2: $tType] :
( ( enum(T_2)
& enum(T_1) )
=> enum(product_prod(T_1,T_2)) ) ).
tff(arity_Product__Type_Ounit___Typerep_Otyperep,axiom,
typerep(product_unit) ).
tff(arity_Product__Type_Ounit___Enum_Oenum,axiom,
enum(product_unit) ).
tff(arity_Code__Evaluation_Oterm___Typerep_Otyperep,axiom,
typerep(code_term) ).
tff(arity_Code__Numeral_Ocode__numeral___Typerep_Otyperep,axiom,
typerep(code_code_numeral) ).
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___Typerep_Otyperep,axiom,
! [T_1: $tType] :
( typerep(T_1)
=> typerep(huffma1450048681e_tree(T_1)) ) ).
tff(arity_fun___Quickcheck_Orandom,axiom,
! [T_1: $tType,T_2: $tType] :
( ( random(T_2)
& cl_HOL_Oequal(T_1)
& code_term_of(T_1) )
=> random(fun(T_1,T_2)) ) ).
tff(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat) ).
tff(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(nat) ).
tff(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat) ).
tff(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(nat) ).
tff(arity_Nat_Onat___Quickcheck_Orandom,axiom,
random(nat) ).
tff(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat) ).
tff(arity_Nat_Onat___Groups_Oone,axiom,
one(nat) ).
tff(arity_HOL_Obool___Quickcheck_Orandom,axiom,
random(bool) ).
tff(arity_prod___Quickcheck_Orandom,axiom,
! [T_1: $tType,T_2: $tType] :
( ( random(T_2)
& random(T_1) )
=> random(product_prod(T_1,T_2)) ) ).
tff(arity_Product__Type_Ounit___Quickcheck_Orandom,axiom,
random(product_unit) ).
tff(arity_Code__Evaluation_Oterm___Quickcheck_Orandom,axiom,
random(code_term) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Quickcheck_Orandom,axiom,
random(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Ozero,axiom,
zero(code_code_numeral) ).
tff(arity_Code__Numeral_Ocode__numeral___Groups_Oone,axiom,
one(code_code_numeral) ).
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___Quickcheck_Orandom,axiom,
! [T_1: $tType] :
( random(T_1)
=> random(huffma1450048681e_tree(T_1)) ) ).
%----Helper facts (14)
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,B1: $tType,A: $tType,R: A,Q: fun(A,B1),P: fun(B1,C)] : aa(A,C,combb(B1,C,A,P,Q),R) = aa(B1,C,P,aa(A,B1,Q,R)) ).
tff(help_COMBC_1_1_U,axiom,
! [A: $tType,C: $tType,B1: $tType,R: A,Q: B1,P: fun(A,fun(B1,C))] : aa(A,C,combc(A,B1,C,P,Q),R) = aa(B1,C,aa(A,fun(B1,C),P,R),Q) ).
tff(help_COMBK_1_1_U,axiom,
! [B1: $tType,A: $tType,Q: B1,P: A] : aa(B1,A,combk(A,B1,P),Q) = P ).
tff(help_COMBS_1_1_U,axiom,
! [C: $tType,B1: $tType,A: $tType,R: A,Q: fun(A,B1),P: fun(A,fun(B1,C))] : aa(A,C,combs(A,B1,C,P,Q),R) = aa(B1,C,aa(A,fun(B1,C),P,R),aa(A,B1,Q,R)) ).
tff(help_fconj_1_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(P)
| ~ pp(Q)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q)) ) ).
tff(help_fconj_2_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q))
| pp(P) ) ).
tff(help_fconj_3_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q))
| pp(Q) ) ).
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 (2)
tff(conj_0,hypothesis,
! [B: a] :
( pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),B),huffma675207370phabet(a,t_1)))
=> ( ( huffma410068972_depth(a,t_1,B) = huffma945805758height(a,t_1) )
=> thesis ) ) ).
tff(conj_1,conjecture,
thesis ).
%------------------------------------------------------------------------------