TPTP Problem File: SWW548_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW548_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Huffman's Algorithm line 1217
% 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_1217 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 248 ( 79 unt; 70 typ; 0 def)
% Number of atoms : 335 ( 130 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 197 ( 40 ~; 7 |; 30 &)
% ( 16 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 64 ( 38 >; 26 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 0 prp; 1-2 aty)
% Number of functors : 49 ( 49 usr; 8 con; 0-6 aty)
% Number of variables : 485 ( 423 !; 2 ?; 485 :)
% ( 60 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:22:27
%------------------------------------------------------------------------------
%----Should-be-implicit typings (12)
tff(ty_t_a,type,
a1: $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_Datatype_Onode,type,
node: ( $tType * $tType ) > $tType ).
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_Huffman__Mirabelle__lalbadcutu_Otree,type,
huffma1450048681e_tree: $tType > $tType ).
tff(ty_tc_List_Olist,type,
list: $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 ).
tff(ty_tc_sum,type,
sum_sum: ( $tType * $tType ) > $tType ).
%----Explicit typings (58)
tff(sy_cl_Typerep_Otyperep,type,
typerep:
!>[A: $tType] : $o ).
tff(sy_cl_Enum_Oenum,type,
enum:
!>[A: $tType] : $o ).
tff(sy_cl_Code__Evaluation_Oterm__of,type,
code_term_of:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Obounded__lattice,type,
bounded_lattice:
!>[A: $tType] : $o ).
tff(sy_cl_HOL_Oequal,type,
cl_HOL_Oequal:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ozero,type,
zero:
!>[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_Quickcheck_Orandom,type,
random:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Olinorder,type,
linorder:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Osemilattice__inf,type,
semilattice_inf:
!>[A: $tType] : $o ).
tff(sy_cl_Lattices_Obounded__lattice__bot,type,
bounded_lattice_bot:
!>[A: $tType] : $o ).
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_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_HOL_Oequal__class_Oequal,type,
equal_equal:
!>[A: $tType] : fun(A,fun(A,bool)) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_ORep__tree,type,
huffma1756210660p_tree:
!>[A: $tType] : ( huffma1450048681e_tree(A) > fun(node(sum_sum(A,nat),product_unit),bool) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Oalphabet,type,
huffma675207370phabet:
!>[A: $tType] : ( huffma1450048681e_tree(A) > fun(A,bool) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Oalphabet_092_060_094isub_062F,type,
huffma1516701463abet_F:
!>[A: $tType] : ( list(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_Oconsistent_092_060_094isub_062F,type,
huffma594769176tent_F:
!>[A: $tType] : ( list(huffma1450048681e_tree(A)) > $o ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Ocost,type,
huffma1134658180e_cost:
!>[A: $tType] : ( huffma1450048681e_tree(A) > nat ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Odepth,type,
huffma410068972_depth:
!>[A: $tType] : ( ( huffma1450048681e_tree(A) * A ) > nat ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Ofreq,type,
huffma1352802255e_freq:
!>[A: $tType] : ( huffma1450048681e_tree(A) > fun(A,nat) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Ofreq_092_060_094isub_062F,type,
huffma409467474freq_F:
!>[A: $tType] : ( list(huffma1450048681e_tree(A)) > fun(A,nat) ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Oheight_092_060_094isub_062F,type,
huffma632063779ight_F:
!>[A: $tType] : ( list(huffma1450048681e_tree(A)) > nat ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_Ohuffman,type,
huffma607257910uffman:
!>[A: $tType] : ( list(huffma1450048681e_tree(A)) > huffma1450048681e_tree(A) ) ).
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_Osibling,type,
huffma1401021291ibling:
!>[A: $tType] : ( ( huffma1450048681e_tree(A) * A ) > A ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_OswapLeaves,type,
huffma414517318Leaves:
!>[A: $tType] : ( ( huffma1450048681e_tree(A) * nat * A * nat * A ) > huffma1450048681e_tree(A) ) ).
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_Huffman__Mirabelle__lalbadcutu_Otree_Otree__rec,type,
huffma1280178957ee_rec:
!>[A: $tType,T1: $tType] : ( ( fun(nat,fun(A,T1)) * fun(nat,fun(huffma1450048681e_tree(A),fun(huffma1450048681e_tree(A),fun(T1,fun(T1,T1))))) * huffma1450048681e_tree(A) ) > T1 ) ).
tff(sy_c_Huffman__Mirabelle__lalbadcutu_OuniteTrees,type,
huffma921447403eTrees:
!>[A: $tType] : ( ( huffma1450048681e_tree(A) * huffma1450048681e_tree(A) ) > huffma1450048681e_tree(A) ) ).
tff(sy_c_Lattices_Oinf__class_Oinf,type,
inf_inf:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_List_Olinorder__class_Osorted__list__of__set,type,
linord467138063of_set:
!>[A: $tType] : ( fun(A,bool) > list(A) ) ).
tff(sy_c_List_Olist_ONil,type,
nil:
!>[A: $tType] : list(A) ).
tff(sy_c_List_Olist_Olist__case,type,
list_case:
!>[T1: $tType,A: $tType] : ( ( T1 * fun(A,fun(list(A),T1)) * list(A) ) > T1 ) ).
tff(sy_c_List_Oset,type,
set:
!>[A: $tType] : ( list(A) > fun(A,bool) ) ).
tff(sy_c_Nat_Osize__class_Osize,type,
size_size:
!>[A: $tType] : ( A > nat ) ).
tff(sy_c_Orderings_Obot__class_Obot,type,
bot_bot:
!>[A: $tType] : A ).
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,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
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_fequal,type,
fequal:
!>[A: $tType] : fun(A,fun(A,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_a,type,
a: a1 ).
tff(sy_v_b,type,
b: a1 ).
tff(sy_v_t,type,
t: huffma1450048681e_tree(a1) ).
tff(sy_v_w_092_060_094isub_062a,type,
w_a: nat ).
tff(sy_v_w_092_060_094isub_062b,type,
w_b: nat ).
%----Relevant facts (99)
tff(fact_0_swapLeaves__id,axiom,
! [A: $tType,A1: A,T: huffma1450048681e_tree(A)] :
( huffma1518433673istent(A,T)
=> ( huffma414517318Leaves(A,T,aa(A,nat,huffma1352802255e_freq(A,T),A1),A1,aa(A,nat,huffma1352802255e_freq(A,T),A1),A1) = T ) ) ).
tff(fact_1_swapLeaves_Osimps_I1_J,axiom,
! [A: $tType,B1: A,W_b: nat,W_a: nat,W_c: nat,A1: A,C1: A] :
( ( ( C1 = A1 )
=> ( huffma414517318Leaves(A,huffma2021818691e_Leaf(A,W_c,C1),W_a,A1,W_b,B1) = huffma2021818691e_Leaf(A,W_b,B1) ) )
& ( ( C1 != A1 )
=> ( ( ( C1 = B1 )
=> ( huffma414517318Leaves(A,huffma2021818691e_Leaf(A,W_c,C1),W_a,A1,W_b,B1) = huffma2021818691e_Leaf(A,W_a,A1) ) )
& ( ( C1 != B1 )
=> ( huffma414517318Leaves(A,huffma2021818691e_Leaf(A,W_c,C1),W_a,A1,W_b,B1) = huffma2021818691e_Leaf(A,W_c,C1) ) ) ) ) ) ).
tff(fact_2_swapLeaves_Osimps_I2_J,axiom,
! [A: $tType,B1: A,W_b: nat,A1: A,W_a: nat,T_22: huffma1450048681e_tree(A),T_12: huffma1450048681e_tree(A),W1: nat] : huffma414517318Leaves(A,huffma1146269203erNode(A,W1,T_12,T_22),W_a,A1,W_b,B1) = huffma1146269203erNode(A,W1,huffma414517318Leaves(A,T_12,W_a,A1,W_b,B1),huffma414517318Leaves(A,T_22,W_a,A1,W_b,B1)) ).
tff(fact_3_consistent_Osimps_I1_J,axiom,
! [A: $tType,A1: A,W1: nat] : huffma1518433673istent(A,huffma2021818691e_Leaf(A,W1,A1)) ).
tff(fact_4_sibling__sibling__id,axiom,
! [A: $tType,A1: A,T: huffma1450048681e_tree(A)] :
( huffma1518433673istent(A,T)
=> ( huffma1401021291ibling(A,T,huffma1401021291ibling(A,T,A1)) = A1 ) ) ).
tff(fact_5_sibling__reciprocal,axiom,
! [A: $tType,B1: A,A1: A,T: huffma1450048681e_tree(A)] :
( huffma1518433673istent(A,T)
=> ( ( huffma1401021291ibling(A,T,A1) = B1 )
=> ( huffma1401021291ibling(A,T,B1) = A1 ) ) ) ).
tff(fact_6_swapLeaves__id__when__notin__alphabet,axiom,
! [B: $tType,W2: nat,W: nat,Ta: huffma1450048681e_tree(B),Aa: B] :
( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,Ta)))
=> ( huffma414517318Leaves(B,Ta,W,Aa,W2,Aa) = Ta ) ) ).
tff(fact_7_depth__sibling,axiom,
! [A: $tType,A1: A,T: huffma1450048681e_tree(A)] :
( huffma1518433673istent(A,T)
=> ( huffma410068972_depth(A,T,huffma1401021291ibling(A,T,A1)) = huffma410068972_depth(A,T,A1) ) ) ).
tff(fact_8_random__tree__def,axiom,
! [B: $tType] :
( random(B)
=> ! [I: code_code_numeral] : random_random(huffma1450048681e_tree(B),I) = huffma928900296x_tree(B,I,I) ) ).
tff(fact_9_consistent__huffman,axiom,
! [A: $tType,Ts1: list(huffma1450048681e_tree(A))] :
( huffma594769176tent_F(A,Ts1)
=> ( ( Ts1 != nil(huffma1450048681e_tree(A)) )
=> huffma1518433673istent(A,huffma607257910uffman(A,Ts1)) ) ) ).
tff(fact_10_equal__tree__def,axiom,
! [B: $tType,Y1: huffma1450048681e_tree(B),X2: huffma1450048681e_tree(B)] :
( pp(aa(huffma1450048681e_tree(B),bool,aa(huffma1450048681e_tree(B),fun(huffma1450048681e_tree(B),bool),equal_equal(huffma1450048681e_tree(B)),X2),Y1))
<=> ( X2 = Y1 ) ) ).
tff(fact_11_Rep__tree__inject,axiom,
! [B: $tType,Y1: huffma1450048681e_tree(B),X2: huffma1450048681e_tree(B)] :
( ( huffma1756210660p_tree(B,X2) = huffma1756210660p_tree(B,Y1) )
<=> ( X2 = Y1 ) ) ).
tff(fact_12_tree_Osimps_I2_J,axiom,
! [B: $tType,Tree23: huffma1450048681e_tree(B),Tree13: huffma1450048681e_tree(B),Nat4: nat,Tree2: huffma1450048681e_tree(B),Tree1: huffma1450048681e_tree(B),Nat1: nat] :
( ( huffma1146269203erNode(B,Nat1,Tree1,Tree2) = huffma1146269203erNode(B,Nat4,Tree13,Tree23) )
<=> ( ( Nat1 = Nat4 )
& ( Tree1 = Tree13 )
& ( Tree2 = Tree23 ) ) ) ).
tff(fact_13_tree_Osimps_I1_J,axiom,
! [B: $tType,A4: B,Nat4: nat,Aa: B,Nat1: nat] :
( ( huffma2021818691e_Leaf(B,Nat1,Aa) = huffma2021818691e_Leaf(B,Nat4,A4) )
<=> ( ( Nat1 = Nat4 )
& ( Aa = A4 ) ) ) ).
tff(fact_14_consistent_092_060_094isub_062F_Osimps_I1_J,axiom,
! [A: $tType] : huffma594769176tent_F(A,nil(huffma1450048681e_tree(A))) ).
tff(fact_15_sibling_Osimps_I4_J,axiom,
! [B: $tType,Vb: huffma1450048681e_tree(B),Va: huffma1450048681e_tree(B),V: nat,W: nat,T_11: huffma1450048681e_tree(B),Aa: B] :
( ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_11)))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,T_11,huffma1146269203erNode(B,V,Va,Vb)),Aa) = huffma1401021291ibling(B,T_11,Aa) ) )
& ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_11)))
=> ( ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,huffma1146269203erNode(B,V,Va,Vb))))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,T_11,huffma1146269203erNode(B,V,Va,Vb)),Aa) = huffma1401021291ibling(B,huffma1146269203erNode(B,V,Va,Vb),Aa) ) )
& ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,huffma1146269203erNode(B,V,Va,Vb))))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,T_11,huffma1146269203erNode(B,V,Va,Vb)),Aa) = Aa ) ) ) ) ) ).
tff(fact_16_sibling_Osimps_I3_J,axiom,
! [B: $tType,T_21: huffma1450048681e_tree(B),W: nat,Vb: huffma1450048681e_tree(B),Va: huffma1450048681e_tree(B),V: nat,Aa: B] :
( ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,huffma1146269203erNode(B,V,Va,Vb))))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,huffma1146269203erNode(B,V,Va,Vb),T_21),Aa) = huffma1401021291ibling(B,huffma1146269203erNode(B,V,Va,Vb),Aa) ) )
& ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,huffma1146269203erNode(B,V,Va,Vb))))
=> ( ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_21)))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,huffma1146269203erNode(B,V,Va,Vb),T_21),Aa) = huffma1401021291ibling(B,T_21,Aa) ) )
& ( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_21)))
=> ( huffma1401021291ibling(B,huffma1146269203erNode(B,W,huffma1146269203erNode(B,V,Va,Vb),T_21),Aa) = Aa ) ) ) ) ) ).
tff(fact_17_sibling_Osimps_I2_J,axiom,
! [A: $tType,C1: A,W_c: nat,W_b: nat,W1: nat,B1: A,A1: A] :
( ( ( A1 = B1 )
=> ( huffma1401021291ibling(A,huffma1146269203erNode(A,W1,huffma2021818691e_Leaf(A,W_b,B1),huffma2021818691e_Leaf(A,W_c,C1)),A1) = C1 ) )
& ( ( A1 != B1 )
=> ( ( ( A1 = C1 )
=> ( huffma1401021291ibling(A,huffma1146269203erNode(A,W1,huffma2021818691e_Leaf(A,W_b,B1),huffma2021818691e_Leaf(A,W_c,C1)),A1) = B1 ) )
& ( ( A1 != C1 )
=> ( huffma1401021291ibling(A,huffma1146269203erNode(A,W1,huffma2021818691e_Leaf(A,W_b,B1),huffma2021818691e_Leaf(A,W_c,C1)),A1) = A1 ) ) ) ) ) ).
tff(fact_18_tree_Osimps_I3_J,axiom,
! [A: $tType,Tree22: huffma1450048681e_tree(A),Tree12: huffma1450048681e_tree(A),Nat3: nat,A1: A,Nat: nat] : huffma2021818691e_Leaf(A,Nat,A1) != huffma1146269203erNode(A,Nat3,Tree12,Tree22) ).
tff(fact_19_tree_Osimps_I4_J,axiom,
! [A: $tType,A1: A,Nat: nat,Tree22: huffma1450048681e_tree(A),Tree12: huffma1450048681e_tree(A),Nat3: nat] : huffma1146269203erNode(A,Nat3,Tree12,Tree22) != huffma2021818691e_Leaf(A,Nat,A1) ).
tff(fact_20_sibling_Osimps_I1_J,axiom,
! [A: $tType,A1: A,B1: A,W_b: nat] : huffma1401021291ibling(A,huffma2021818691e_Leaf(A,W_b,B1),A1) = A1 ).
tff(fact_21_notin__alphabet__imp__sibling__id,axiom,
! [B: $tType,Ta: huffma1450048681e_tree(B),Aa: B] :
( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,Ta)))
=> ( huffma1401021291ibling(B,Ta,Aa) = Aa ) ) ).
tff(fact_22_sibling__ne__imp__sibling__in__alphabet,axiom,
! [B: $tType,Aa: B,Ta: huffma1450048681e_tree(B)] :
( ( huffma1401021291ibling(B,Ta,Aa) != Aa )
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),huffma1401021291ibling(B,Ta,Aa)),huffma675207370phabet(B,Ta))) ) ).
tff(fact_23_in__alphabet__imp__sibling__in__alphabet,axiom,
! [B: $tType,Ta: huffma1450048681e_tree(B),Aa: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,Ta)))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),huffma1401021291ibling(B,Ta,Aa)),huffma675207370phabet(B,Ta))) ) ).
tff(fact_24_freq__huffman,axiom,
! [B: $tType,Ts: list(huffma1450048681e_tree(B))] :
( ( Ts != nil(huffma1450048681e_tree(B)) )
=> ( huffma1352802255e_freq(B,huffma607257910uffman(B,Ts)) = huffma409467474freq_F(B,Ts) ) ) ).
tff(fact_25_alphabet__huffman,axiom,
! [B: $tType,Ts: list(huffma1450048681e_tree(B))] :
( ( Ts != nil(huffma1450048681e_tree(B)) )
=> ( huffma675207370phabet(B,huffma607257910uffman(B,Ts)) = huffma1516701463abet_F(B,Ts) ) ) ).
tff(fact_26_tree_Osimps_I5_J,axiom,
! [B: $tType,C: $tType,Aa: C,Nat1: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B))),F1: fun(nat,fun(C,B))] : huffma107959123e_case(C,B,F1,F2,huffma2021818691e_Leaf(C,Nat1,Aa)) = aa(C,B,aa(nat,fun(C,B),F1,Nat1),Aa) ).
tff(fact_27_tree_Osimps_I6_J,axiom,
! [B: $tType,C: $tType,Tree2: huffma1450048681e_tree(C),Tree1: huffma1450048681e_tree(C),Nat1: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),B))),F1: fun(nat,fun(C,B))] : huffma107959123e_case(C,B,F1,F2,huffma1146269203erNode(C,Nat1,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,Nat1),Tree1),Tree2) ).
tff(fact_28_exists__in__alphabet,axiom,
! [B: $tType,Ta: huffma1450048681e_tree(B)] :
? [A3: B] : pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),A3),huffma675207370phabet(B,Ta))) ).
tff(fact_29_tree_Oexhaust,axiom,
! [A: $tType,Y: huffma1450048681e_tree(A)] :
( ! [Nat2: nat,A3: A] : Y != huffma2021818691e_Leaf(A,Nat2,A3)
=> ~ ! [Nat2: nat,Tree11: huffma1450048681e_tree(A),Tree21: huffma1450048681e_tree(A)] : Y != huffma1146269203erNode(A,Nat2,Tree11,Tree21) ) ).
tff(fact_30_equal,axiom,
! [B: $tType] :
( cl_HOL_Oequal(B)
=> ( equal_equal(B) = fequal(B) ) ) ).
tff(fact_31_equal__refl,axiom,
! [A: $tType] :
( cl_HOL_Oequal(A)
=> ! [X: A] : pp(aa(A,bool,aa(A,fun(A,bool),equal_equal(A),X),X)) ) ).
tff(fact_32_equal__eq,axiom,
! [B: $tType] :
( cl_HOL_Oequal(B)
=> ! [Y1: B,X2: B] :
( pp(aa(B,bool,aa(B,fun(B,bool),equal_equal(B),X2),Y1))
<=> ( X2 = Y1 ) ) ) ).
tff(fact_33_eq__equal,axiom,
! [B: $tType] :
( cl_HOL_Oequal(B)
=> ( fequal(B) = equal_equal(B) ) ) ).
tff(fact_34_freq_092_060_094isub_062F_Osimps_I1_J,axiom,
! [A: $tType,X4: A] : aa(A,nat,huffma409467474freq_F(A,nil(huffma1450048681e_tree(A))),X4) = zero_zero(nat) ).
tff(fact_35_alphabet_092_060_094isub_062F_Osimps_I1_J,axiom,
! [B: $tType] : huffma1516701463abet_F(B,nil(huffma1450048681e_tree(B))) = bot_bot(fun(B,bool)) ).
tff(fact_36_tree_Orecs_I1_J,axiom,
! [B: $tType,C: $tType,Aa: C,Nat1: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),fun(B,fun(B,B))))),F1: fun(nat,fun(C,B))] : huffma1280178957ee_rec(C,B,F1,F2,huffma2021818691e_Leaf(C,Nat1,Aa)) = aa(C,B,aa(nat,fun(C,B),F1,Nat1),Aa) ).
tff(fact_37_tree_Orecs_I2_J,axiom,
! [B: $tType,C: $tType,Tree2: huffma1450048681e_tree(C),Tree1: huffma1450048681e_tree(C),Nat1: nat,F2: fun(nat,fun(huffma1450048681e_tree(C),fun(huffma1450048681e_tree(C),fun(B,fun(B,B))))),F1: fun(nat,fun(C,B))] : huffma1280178957ee_rec(C,B,F1,F2,huffma1146269203erNode(C,Nat1,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,Nat1),Tree1),Tree2),huffma1280178957ee_rec(C,B,F1,F2,Tree1)),huffma1280178957ee_rec(C,B,F1,F2,Tree2)) ).
tff(fact_38_depth_Osimps_I1_J,axiom,
! [A: $tType,A1: A,B1: A,W1: nat] : huffma410068972_depth(A,huffma2021818691e_Leaf(A,W1,B1),A1) = zero_zero(nat) ).
tff(fact_39_freq_Osimps_I1_J,axiom,
! [A: $tType,W1: nat,A1: A,X4: A] :
( ( ( X4 = A1 )
=> ( aa(A,nat,huffma1352802255e_freq(A,huffma2021818691e_Leaf(A,W1,A1)),X4) = W1 ) )
& ( ( X4 != A1 )
=> ( aa(A,nat,huffma1352802255e_freq(A,huffma2021818691e_Leaf(A,W1,A1)),X4) = zero_zero(nat) ) ) ) ).
tff(fact_40_notin__alphabet__imp__freq__0,axiom,
! [B: $tType,Ta: huffma1450048681e_tree(B),Aa: B] :
( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,Ta)))
=> ( aa(B,nat,huffma1352802255e_freq(B,Ta),Aa) = zero_zero(nat) ) ) ).
tff(fact_41_notin__alphabet_092_060_094isub_062F__imp__freq_092_060_094isub_062F__0,axiom,
! [B: $tType,Ts: list(huffma1450048681e_tree(B)),Aa: B] :
( ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma1516701463abet_F(B,Ts)))
=> ( aa(B,nat,huffma409467474freq_F(B,Ts),Aa) = zero_zero(nat) ) ) ).
tff(fact_42_tree_Osize_I3_J,axiom,
! [A: $tType,A1: A,Nat: nat] : size_size(huffma1450048681e_tree(A),huffma2021818691e_Leaf(A,Nat,A1)) = zero_zero(nat) ).
tff(fact_43_height_092_060_094isub_062F_Osimps_I1_J,axiom,
! [A: $tType] : huffma632063779ight_F(A,nil(huffma1450048681e_tree(A))) = zero_zero(nat) ).
tff(fact_44_all__not__in__conv,axiom,
! [B: $tType,A2: fun(B,bool)] :
( ! [X1: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X1),A2))
<=> ( A2 = bot_bot(fun(B,bool)) ) ) ).
tff(fact_45_empty__Collect__eq,axiom,
! [B: $tType,P1: fun(B,bool)] :
( ( bot_bot(fun(B,bool)) = collect(B,P1) )
<=> ! [X1: B] : ~ pp(aa(B,bool,P1,X1)) ) ).
tff(fact_46_empty__iff,axiom,
! [B: $tType,C3: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),bot_bot(fun(B,bool)))) ).
tff(fact_47_emptyE,axiom,
! [B: $tType,Aa: B] : ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),bot_bot(fun(B,bool)))) ).
tff(fact_48_Collect__empty__eq,axiom,
! [B: $tType,P1: fun(B,bool)] :
( ( collect(B,P1) = bot_bot(fun(B,bool)) )
<=> ! [X1: B] : ~ pp(aa(B,bool,P1,X1)) ) ).
tff(fact_49_equals0D,axiom,
! [B: $tType,Aa: B,A2: fun(B,bool)] :
( ( A2 = bot_bot(fun(B,bool)) )
=> ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),A2)) ) ).
tff(fact_50_ex__in__conv,axiom,
! [B: $tType,A2: fun(B,bool)] :
( ? [X1: B] : pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X1),A2))
<=> ( A2 != bot_bot(fun(B,bool)) ) ) ).
tff(fact_51_empty__def,axiom,
! [B: $tType] : bot_bot(fun(B,bool)) = collect(B,combk(bool,B,fFalse)) ).
tff(fact_52_height_092_060_094isub_062F__0__imp__Leaf__freq_092_060_094isub_062F__in__set,axiom,
! [B: $tType,Aa: B,Ts: list(huffma1450048681e_tree(B))] :
( huffma594769176tent_F(B,Ts)
=> ( ( huffma632063779ight_F(B,Ts) = zero_zero(nat) )
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma1516701463abet_F(B,Ts)))
=> pp(aa(fun(huffma1450048681e_tree(B),bool),bool,aa(huffma1450048681e_tree(B),fun(fun(huffma1450048681e_tree(B),bool),bool),member(huffma1450048681e_tree(B)),huffma2021818691e_Leaf(B,aa(B,nat,huffma409467474freq_F(B,Ts),Aa),Aa)),set(huffma1450048681e_tree(B),Ts))) ) ) ) ).
tff(fact_53_cost_Osimps_I1_J,axiom,
! [A: $tType,A1: A,W1: nat] : huffma1134658180e_cost(A,huffma2021818691e_Leaf(A,W1,A1)) = zero_zero(nat) ).
tff(fact_54_bot__apply,axiom,
! [C: $tType,B: $tType] :
( bot(B)
=> ! [X2: C] : aa(C,B,bot_bot(fun(C,B)),X2) = bot_bot(B) ) ).
tff(fact_55_zero__reorient,axiom,
! [B: $tType] :
( zero(B)
=> ! [X2: B] :
( ( zero_zero(B) = X2 )
<=> ( X2 = zero_zero(B) ) ) ) ).
tff(fact_56_bot__fun__def,axiom,
! [B: $tType,C: $tType] :
( bot(C)
=> ! [X4: B] : aa(B,C,bot_bot(fun(B,C)),X4) = bot_bot(C) ) ).
tff(fact_57_set__empty,axiom,
! [B: $tType,Xs: list(B)] :
( ( set(B,Xs) = bot_bot(fun(B,bool)) )
<=> ( Xs = nil(B) ) ) ).
tff(fact_58_set__empty2,axiom,
! [B: $tType,Xs: list(B)] :
( ( bot_bot(fun(B,bool)) = set(B,Xs) )
<=> ( Xs = nil(B) ) ) ).
tff(fact_59_List_Oset_Osimps_I1_J,axiom,
! [B: $tType] : set(B,nil(B)) = bot_bot(fun(B,bool)) ).
tff(fact_60_sorted__list__of__set__empty,axiom,
! [B: $tType] :
( linorder(B)
=> ( linord467138063of_set(B,bot_bot(fun(B,bool))) = nil(B) ) ) ).
tff(fact_61_consistent_Osimps_I2_J,axiom,
! [B: $tType,T_21: huffma1450048681e_tree(B),T_11: huffma1450048681e_tree(B),W: nat] :
( huffma1518433673istent(B,huffma1146269203erNode(B,W,T_11,T_21))
<=> ( huffma1518433673istent(B,T_11)
& huffma1518433673istent(B,T_21)
& ( inf_inf(fun(B,bool),huffma675207370phabet(B,T_11),huffma675207370phabet(B,T_21)) = bot_bot(fun(B,bool)) ) ) ) ).
tff(fact_62_list_Osimps_I4_J,axiom,
! [C: $tType,B: $tType,F2: fun(C,fun(list(C),B)),F1: B] : list_case(B,C,F1,F2,nil(C)) = F1 ).
tff(fact_63_IntE,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool),C3: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),inf_inf(fun(B,bool),A2,B2)))
=> ~ ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),A2))
=> ~ pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),B2)) ) ) ).
tff(fact_64_IntI,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool),C3: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),A2))
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),B2))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),inf_inf(fun(B,bool),A2,B2))) ) ) ).
tff(fact_65_Int__iff,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool),C3: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),inf_inf(fun(B,bool),A2,B2)))
<=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),A2))
& pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),B2)) ) ) ).
tff(fact_66_IntD2,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool),C3: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),inf_inf(fun(B,bool),A2,B2)))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),B2)) ) ).
tff(fact_67_IntD1,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool),C3: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),inf_inf(fun(B,bool),A2,B2)))
=> pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C3),A2)) ) ).
tff(fact_68_Int__assoc,axiom,
! [B: $tType,C2: fun(B,bool),B2: fun(B,bool),A2: fun(B,bool)] : inf_inf(fun(B,bool),inf_inf(fun(B,bool),A2,B2),C2) = inf_inf(fun(B,bool),A2,inf_inf(fun(B,bool),B2,C2)) ).
tff(fact_69_Int__left__commute,axiom,
! [B: $tType,C2: fun(B,bool),B2: fun(B,bool),A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,inf_inf(fun(B,bool),B2,C2)) = inf_inf(fun(B,bool),B2,inf_inf(fun(B,bool),A2,C2)) ).
tff(fact_70_Int__left__absorb,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,inf_inf(fun(B,bool),A2,B2)) = inf_inf(fun(B,bool),A2,B2) ).
tff(fact_71_Int__commute,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,B2) = inf_inf(fun(B,bool),B2,A2) ).
tff(fact_72_Int__def,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,B2) = collect(B,combs(B,bool,bool,combb(bool,fun(bool,bool),B,fconj,combc(B,fun(B,bool),bool,member(B),A2)),combc(B,fun(B,bool),bool,member(B),B2))) ).
tff(fact_73_Int__absorb,axiom,
! [B: $tType,A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,A2) = A2 ).
tff(fact_74_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_75_mem__def,axiom,
! [B: $tType,A2: fun(B,bool),X2: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2))
<=> pp(aa(B,bool,A2,X2)) ) ).
tff(fact_76_Collect__def,axiom,
! [B: $tType,P1: fun(B,bool)] : collect(B,P1) = P1 ).
tff(fact_77_disjoint__iff__not__equal,axiom,
! [B: $tType,B2: fun(B,bool),A2: fun(B,bool)] :
( ( inf_inf(fun(B,bool),A2,B2) = bot_bot(fun(B,bool)) )
<=> ! [X1: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X1),A2))
=> ! [Xa: B] :
( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Xa),B2))
=> ( X1 != Xa ) ) ) ) ).
tff(fact_78_Int__empty__right,axiom,
! [B: $tType,A2: fun(B,bool)] : inf_inf(fun(B,bool),A2,bot_bot(fun(B,bool))) = bot_bot(fun(B,bool)) ).
tff(fact_79_Int__empty__left,axiom,
! [B: $tType,B2: fun(B,bool)] : inf_inf(fun(B,bool),bot_bot(fun(B,bool)),B2) = bot_bot(fun(B,bool)) ).
tff(fact_80_freq__0__left,axiom,
! [B: $tType,Aa: B,T_21: huffma1450048681e_tree(B),T_11: huffma1450048681e_tree(B)] :
( ( inf_inf(fun(B,bool),huffma675207370phabet(B,T_11),huffma675207370phabet(B,T_21)) = bot_bot(fun(B,bool)) )
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_21)))
=> ( aa(B,nat,huffma1352802255e_freq(B,T_11),Aa) = zero_zero(nat) ) ) ) ).
tff(fact_81_freq__0__right,axiom,
! [B: $tType,Aa: B,T_21: huffma1450048681e_tree(B),T_11: huffma1450048681e_tree(B)] :
( ( inf_inf(fun(B,bool),huffma675207370phabet(B,T_11),huffma675207370phabet(B,T_21)) = bot_bot(fun(B,bool)) )
=> ( pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),Aa),huffma675207370phabet(B,T_11)))
=> ( aa(B,nat,huffma1352802255e_freq(B,T_21),Aa) = zero_zero(nat) ) ) ) ).
tff(fact_82_inf__bot__left,axiom,
! [A: $tType] :
( bounded_lattice_bot(A)
=> ! [X: A] : inf_inf(A,bot_bot(A),X) = bot_bot(A) ) ).
tff(fact_83_inf__bot__right,axiom,
! [A: $tType] :
( bounded_lattice_bot(A)
=> ! [X: A] : inf_inf(A,X,bot_bot(A)) = bot_bot(A) ) ).
tff(fact_84_consistent__uniteTrees,axiom,
! [B: $tType,T_21: huffma1450048681e_tree(B),T_11: huffma1450048681e_tree(B)] :
( huffma1518433673istent(B,T_11)
=> ( huffma1518433673istent(B,T_21)
=> ( ( inf_inf(fun(B,bool),huffma675207370phabet(B,T_11),huffma675207370phabet(B,T_21)) = bot_bot(fun(B,bool)) )
=> huffma1518433673istent(B,huffma921447403eTrees(B,T_11,T_21)) ) ) ) ).
tff(fact_85_inf__left__idem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [Y: A,X: A] : inf_inf(A,X,inf_inf(A,X,Y)) = inf_inf(A,X,Y) ) ).
tff(fact_86_inf_Oleft__idem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [B1: A,A1: A] : inf_inf(A,A1,inf_inf(A,A1,B1)) = inf_inf(A,A1,B1) ) ).
tff(fact_87_inf__assoc,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [Z: A,Y: A,X: A] : inf_inf(A,inf_inf(A,X,Y),Z) = inf_inf(A,X,inf_inf(A,Y,Z)) ) ).
tff(fact_88_inf__sup__aci_I2_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Z: A,Y: A,X: A] : inf_inf(A,inf_inf(A,X,Y),Z) = inf_inf(A,X,inf_inf(A,Y,Z)) ) ).
tff(fact_89_inf_Oassoc,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [C1: A,B1: A,A1: A] : inf_inf(A,inf_inf(A,A1,B1),C1) = inf_inf(A,A1,inf_inf(A,B1,C1)) ) ).
tff(fact_90_inf__left__commute,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [Z: A,Y: A,X: A] : inf_inf(A,X,inf_inf(A,Y,Z)) = inf_inf(A,Y,inf_inf(A,X,Z)) ) ).
tff(fact_91_inf__sup__aci_I3_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Z: A,Y: A,X: A] : inf_inf(A,X,inf_inf(A,Y,Z)) = inf_inf(A,Y,inf_inf(A,X,Z)) ) ).
tff(fact_92_inf_Oleft__commute,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [C1: A,A1: A,B1: A] : inf_inf(A,B1,inf_inf(A,A1,C1)) = inf_inf(A,A1,inf_inf(A,B1,C1)) ) ).
tff(fact_93_inf__sup__aci_I4_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Y: A,X: A] : inf_inf(A,X,inf_inf(A,X,Y)) = inf_inf(A,X,Y) ) ).
tff(fact_94_inf__commute,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [Y: A,X: A] : inf_inf(A,X,Y) = inf_inf(A,Y,X) ) ).
tff(fact_95_inf__sup__aci_I1_J,axiom,
! [A: $tType] :
( lattice(A)
=> ! [Y: A,X: A] : inf_inf(A,X,Y) = inf_inf(A,Y,X) ) ).
tff(fact_96_inf_Ocommute,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [B1: A,A1: A] : inf_inf(A,A1,B1) = inf_inf(A,B1,A1) ) ).
tff(fact_97_inf__idem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [X: A] : inf_inf(A,X,X) = X ) ).
tff(fact_98_inf_Oidem,axiom,
! [A: $tType] :
( semilattice_inf(A)
=> ! [A1: A] : inf_inf(A,A1,A1) = A1 ) ).
%----Arities (64)
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_Code__Numeral_Ocode__numeral___Code__Evaluation_Oterm__of,axiom,
code_term_of(code_code_numeral) ).
tff(arity_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of,axiom,
code_term_of(code_term) ).
tff(arity_Product__Type_Ounit___Code__Evaluation_Oterm__of,axiom,
code_term_of(product_unit) ).
tff(arity_Product__Type_Ounit___Enum_Oenum,axiom,
enum(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___Enum_Oenum,axiom,
! [T_1: $tType,T_2: $tType] :
( ( enum(T_2)
& enum(T_1) )
=> enum(product_prod(T_1,T_2)) ) ).
tff(arity_sum___Code__Evaluation_Oterm__of,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> code_term_of(sum_sum(T_1,T_2)) ) ).
tff(arity_sum___Enum_Oenum,axiom,
! [T_1: $tType,T_2: $tType] :
( ( enum(T_2)
& enum(T_1) )
=> enum(sum_sum(T_1,T_2)) ) ).
tff(arity_List_Olist___Code__Evaluation_Oterm__of,axiom,
! [T_1: $tType] :
( typerep(T_1)
=> code_term_of(list(T_1)) ) ).
tff(arity_HOL_Obool___Lattices_Obounded__lattice,axiom,
bounded_lattice(bool) ).
tff(arity_HOL_Obool___Code__Evaluation_Oterm__of,axiom,
code_term_of(bool) ).
tff(arity_HOL_Obool___Enum_Oenum,axiom,
enum(bool) ).
tff(arity_Nat_Onat___Code__Evaluation_Oterm__of,axiom,
code_term_of(nat) ).
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___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___Enum_Oenum,axiom,
! [T_1: $tType,T_2: $tType] :
( ( enum(T_2)
& enum(T_1) )
=> enum(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_Nat_Onat___Typerep_Otyperep,axiom,
typerep(nat) ).
tff(arity_HOL_Obool___Typerep_Otyperep,axiom,
typerep(bool) ).
tff(arity_List_Olist___Typerep_Otyperep,axiom,
! [T_1: $tType] :
( typerep(T_1)
=> typerep(list(T_1)) ) ).
tff(arity_sum___Typerep_Otyperep,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> typerep(sum_sum(T_1,T_2)) ) ).
tff(arity_Datatype_Onode___Typerep_Otyperep,axiom,
! [T_1: $tType,T_2: $tType] :
( ( typerep(T_2)
& typerep(T_1) )
=> typerep(node(T_1,T_2)) ) ).
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_Product__Type_Ounit___Typerep_Otyperep,axiom,
typerep(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___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__inf,axiom,
! [T_1: $tType,T_2: $tType] :
( lattice(T_2)
=> semilattice_inf(fun(T_1,T_2)) ) ).
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_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_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_Nat_Onat___Lattices_Osemilattice__inf,axiom,
semilattice_inf(nat) ).
tff(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat) ).
tff(arity_Nat_Onat___Quickcheck_Orandom,axiom,
random(nat) ).
tff(arity_Nat_Onat___Lattices_Olattice,axiom,
lattice(nat) ).
tff(arity_Nat_Onat___Orderings_Obot,axiom,
bot(nat) ).
tff(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat) ).
tff(arity_Nat_Onat___HOL_Oequal,axiom,
cl_HOL_Oequal(nat) ).
tff(arity_HOL_Obool___Lattices_Obounded__lattice__bot,axiom,
bounded_lattice_bot(bool) ).
tff(arity_HOL_Obool___Lattices_Osemilattice__inf,axiom,
semilattice_inf(bool) ).
tff(arity_HOL_Obool___Orderings_Olinorder,axiom,
linorder(bool) ).
tff(arity_HOL_Obool___Quickcheck_Orandom,axiom,
random(bool) ).
tff(arity_HOL_Obool___Lattices_Olattice,axiom,
lattice(bool) ).
tff(arity_HOL_Obool___Orderings_Obot,axiom,
bot(bool) ).
tff(arity_HOL_Obool___HOL_Oequal,axiom,
cl_HOL_Oequal(bool) ).
tff(arity_List_Olist___Quickcheck_Orandom,axiom,
! [T_1: $tType] :
( random(T_1)
=> random(list(T_1)) ) ).
tff(arity_List_Olist___HOL_Oequal,axiom,
! [T_1: $tType] : cl_HOL_Oequal(list(T_1)) ).
tff(arity_sum___Quickcheck_Orandom,axiom,
! [T_1: $tType,T_2: $tType] :
( ( random(T_2)
& random(T_1) )
=> random(sum_sum(T_1,T_2)) ) ).
tff(arity_sum___HOL_Oequal,axiom,
! [T_1: $tType,T_2: $tType] : cl_HOL_Oequal(sum_sum(T_1,T_2)) ).
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_prod___HOL_Oequal,axiom,
! [T_1: $tType,T_2: $tType] : cl_HOL_Oequal(product_prod(T_1,T_2)) ).
tff(arity_Product__Type_Ounit___Quickcheck_Orandom,axiom,
random(product_unit) ).
tff(arity_Product__Type_Ounit___HOL_Oequal,axiom,
cl_HOL_Oequal(product_unit) ).
tff(arity_Code__Evaluation_Oterm___Quickcheck_Orandom,axiom,
random(code_term) ).
tff(arity_Code__Evaluation_Oterm___HOL_Oequal,axiom,
cl_HOL_Oequal(code_term) ).
tff(arity_Code__Numeral_Ocode__numeral___Orderings_Olinorder,axiom,
linorder(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___HOL_Oequal,axiom,
cl_HOL_Oequal(code_code_numeral) ).
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___Quickcheck_Orandom,axiom,
! [T_1: $tType] :
( random(T_1)
=> random(huffma1450048681e_tree(T_1)) ) ).
tff(arity_Huffman__Mirabelle__lalbadcutu_Otree___HOL_Oequal,axiom,
! [T_1: $tType] : cl_HOL_Oequal(huffma1450048681e_tree(T_1)) ).
%----Helper facts (13)
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_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_fFalse_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_fFalse_1_1_T,axiom,
! [P: bool] :
( ( P = fTrue )
| ( P = fFalse ) ) ).
tff(help_fequal_1_1_T,axiom,
! [A: $tType,Y: A,X: A] :
( ~ pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_T,axiom,
! [A: $tType,Y: A,X: A] :
( ( X != Y )
| pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X),Y)) ) ).
%----Conjectures (2)
tff(conj_0,hypothesis,
huffma1518433673istent(a1,t) ).
tff(conj_1,conjecture,
huffma1518433673istent(a1,huffma414517318Leaves(a1,t,w_a,a,w_b,b)) ).
%------------------------------------------------------------------------------