TPTP Problem File: COM162^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : COM162^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Computing Theory
% Problem : Binary decision diagram 38
% Version : [Bla16] axioms : Especial.
% English :
% Refs : [OS08] Ortner & Schirmer (2008), BDD Normalisation
% : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% Source : [Bla16]
% Names : bindag__38.p [Bla16]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.00 v7.1.0
% Syntax : Number of formulae : 473 ( 238 unt; 103 typ; 0 def)
% Number of atoms : 642 ( 385 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 2965 ( 61 ~; 8 |; 44 &;2665 @)
% ( 0 <=>; 187 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 246 ( 246 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 94 usr; 8 con; 0-7 aty)
% Number of variables : 802 ( 43 ^; 673 !; 11 ?; 802 :)
% ( 75 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2016-07-13 14:44:49.360
%------------------------------------------------------------------------------
%----Could-be-implicit typings (16)
thf(ty_t_BinDag__Mirabelle__rybootvolr_Odag,type,
binDag_Mirabelle_dag: $tType ).
thf(ty_t_Record_Otuple__isomorphism,type,
tuple_isomorphism: $tType > $tType > $tType > $tType ).
thf(ty_t_Code__Numeral_Onatural,type,
code_natural: $tType ).
thf(ty_t_Code__Evaluation_Oterm,type,
code_term: $tType ).
thf(ty_t_Product__Type_Ounit,type,
product_unit: $tType ).
thf(ty_t_Product__Type_Oprod,type,
product_prod: $tType > $tType > $tType ).
thf(ty_t_Typerep_Otyperep,type,
typerep: $tType ).
thf(ty_t_Simpl__Heap_Oref,type,
simpl_ref: $tType ).
thf(ty_t_String_Oliteral,type,
literal: $tType ).
thf(ty_t_Sum__Type_Osum,type,
sum_sum: $tType > $tType > $tType ).
thf(ty_t_Option_Ooption,type,
option: $tType > $tType ).
thf(ty_t_List_Olist,type,
list: $tType > $tType ).
thf(ty_t_Set_Oset,type,
set: $tType > $tType ).
thf(ty_t_Num_Onum,type,
num: $tType ).
thf(ty_t_Nat_Onat,type,
nat: $tType ).
thf(ty_t_itself,type,
itself: $tType > $tType ).
%----Explicit typings (87)
thf(sy_cl_Enum_Oenum,type,
enum:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Typerep_Otyperep,type,
typerep2:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_HOL_Otype,type,
type:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_HOL_Oequal,type,
cl_HOL_Oequal:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Code__Evaluation_Oterm__of,type,
code_term_of:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Nat_Osize,type,
size:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Oone,type,
one:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Num_Onumeral,type,
numeral:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Fields_Ofield,type,
field:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Num_Oneg__numeral,type,
neg_numeral:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ogroup__add,type,
group_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Omonoid__add,type,
monoid_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Rings_Ozero__neq__one,type,
zero_neq_one:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Nat_Osemiring__char__0,type,
semiring_char_0:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Divides_Osemiring__div,type,
semiring_div:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Fields_Odivision__ring,type,
division_ring:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Osemigroup__add,type,
semigroup_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Rings_Osemidom__divide,type,
semidom_divide:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Rings_Ocomm__semiring__1,type,
comm_semiring_1:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ocomm__monoid__add,type,
comm_monoid_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Fields_Olinordered__field,type,
linordered_field:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Oab__semigroup__add,type,
ab_semigroup_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Quickcheck__Random_Orandom,type,
quickcheck_random:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Divides_Osemiring__div__parity,type,
semiring_div_parity:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ocancel__semigroup__add,type,
cancel_semigroup_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
cancel1352612707id_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
ordere779506340up_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
canoni770627133id_add:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
semiri456707255roduct:
!>[A: $tType] : ( ( itself @ A ) > $o ) ).
thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
bNF_Greatest_Shift:
!>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
thf(sy_c_Basic__BNF__LFPs_Osum_Osize__sum,type,
basic_BNF_size_sum:
!>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( sum_sum @ A @ B ) > nat ) ).
thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_ONode,type,
binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).
thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_OTip,type,
binDag_Mirabelle_Tip: binDag_Mirabelle_dag ).
thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Ocase__dag,type,
binDag1297733282se_dag:
!>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A ) > binDag_Mirabelle_dag > A ) ).
thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Orec__dag,type,
binDag1442713106ec_dag:
!>[A: $tType] : ( A > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A ) > binDag_Mirabelle_dag > A ) ).
thf(sy_c_BinDag__Mirabelle__rybootvolr_Odag_Osize__dag,type,
binDag1924123185ze_dag: binDag_Mirabelle_dag > nat ).
thf(sy_c_Code__Numeral_OSuc,type,
code_Suc: code_natural > code_natural ).
thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
code_case_natural:
!>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
code_rec_natural:
!>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
code_size_natural: code_natural > nat ).
thf(sy_c_Groups_Oone__class_Oone,type,
one_one:
!>[A: $tType] : A ).
thf(sy_c_Groups_Oplus__class_Oplus,type,
plus_plus:
!>[A: $tType] : ( A > A > A ) ).
thf(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
thf(sy_c_HOL_Obool_Osize__bool,type,
size_bool: $o > nat ).
thf(sy_c_HOL_Odefault__class_Odefault,type,
default_default:
!>[A: $tType] : A ).
thf(sy_c_HOL_Oundefined,type,
undefined:
!>[A: $tType] : A ).
thf(sy_c_If,type,
if:
!>[A: $tType] : ( $o > A > A > A ) ).
thf(sy_c_List_Ogen__length,type,
gen_length:
!>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
thf(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_List_Olist_Osize__list,type,
size_list:
!>[A: $tType] : ( ( A > nat ) > ( list @ A ) > nat ) ).
thf(sy_c_List_Osplice,type,
splice:
!>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_Nat_OSuc,type,
suc: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize,type,
size_size:
!>[A: $tType] : ( A > nat ) ).
thf(sy_c_Num_Oinc,type,
inc: num > num ).
thf(sy_c_Num_Onat__of__num,type,
nat_of_num: num > nat ).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
neg_numeral_dbl_inc:
!>[A: $tType] : ( A > A ) ).
thf(sy_c_Num_Onum_OBit0,type,
bit0: num > num ).
thf(sy_c_Num_Onum_OBit1,type,
bit1: num > num ).
thf(sy_c_Num_Onum_OOne,type,
one2: num ).
thf(sy_c_Num_Onum_Osize__num,type,
size_num: num > nat ).
thf(sy_c_Num_Onumeral__class_Onumeral,type,
numeral_numeral:
!>[A: $tType] : ( num > A ) ).
thf(sy_c_Option_Ooption_ONone,type,
none:
!>[A: $tType] : ( option @ A ) ).
thf(sy_c_Option_Ooption_OSome,type,
some:
!>[A: $tType] : ( A > ( option @ A ) ) ).
thf(sy_c_Option_Ooption_Ocase__option,type,
case_option:
!>[B: $tType,A: $tType] : ( B > ( A > B ) > ( option @ A ) > B ) ).
thf(sy_c_Option_Ooption_Osize__option,type,
size_option:
!>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
thf(sy_c_Option_Ooption_Othe,type,
the:
!>[A: $tType] : ( ( option @ A ) > A ) ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
product_rec_bool:
!>[T: $tType] : ( T > T > $o > T ) ).
thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
product_rec_unit:
!>[T: $tType] : ( T > product_unit > T ) ).
thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
product_case_unit:
!>[A: $tType] : ( A > product_unit > A ) ).
thf(sy_c_Product__Type_Ounit_Osize__unit,type,
product_size_unit: product_unit > nat ).
thf(sy_c_Pure_Otype,type,
type2:
!>[A: $tType] : ( itself @ A ) ).
thf(sy_c_Record_Otuple__isomorphism_OTuple__Isomorphism,type,
tuple_742722141rphism:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( ( product_prod @ B @ C ) > A ) > ( tuple_isomorphism @ A @ B @ C ) ) ).
thf(sy_c_Record_Otuple__isomorphism_Osize__tuple__isomorphism,type,
tuple_1907371454rphism:
!>[A: $tType,B: $tType,C: $tType] : ( ( A > nat ) > ( B > nat ) > ( C > nat ) > ( tuple_isomorphism @ A @ B @ C ) > nat ) ).
thf(sy_c_Rings_Odivide__class_Odivide,type,
divide_divide:
!>[A: $tType] : ( A > A > A ) ).
thf(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
thf(sy_c_Sum__Type_OInl,type,
sum_Inl:
!>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
thf(sy_c_Sum__Type_OInr,type,
sum_Inr:
!>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
thf(sy_c_Transitive__Closure_Ontrancl,type,
transitive_ntrancl:
!>[A: $tType] : ( nat > ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
thf(sy_c_Typerep_Otyperep_OTyperep,type,
typerep3: literal > ( list @ typerep ) > typerep ).
thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
size_typerep: typerep > nat ).
thf(sy_c_member,type,
member:
!>[A: $tType] : ( A > ( set @ A ) > $o ) ).
thf(sy_v_a,type,
a: simpl_ref ).
thf(sy_v_lt,type,
lt: binDag_Mirabelle_dag ).
thf(sy_v_rt,type,
rt: binDag_Mirabelle_dag ).
%----Relevant facts (251)
thf(fact_0_dag_Oinject,axiom,
! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag,Y21: binDag_Mirabelle_dag,Y22: simpl_ref,Y23: binDag_Mirabelle_dag] :
( ( ( binDag476092410e_Node @ X21 @ X22 @ X23 )
= ( binDag476092410e_Node @ Y21 @ Y22 @ Y23 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 )
& ( X23 = Y23 ) ) ) ).
% dag.inject
thf(fact_1_dag_Odistinct_I1_J,axiom,
! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
( binDag_Mirabelle_Tip
!= ( binDag476092410e_Node @ X21 @ X22 @ X23 ) ) ).
% dag.distinct(1)
thf(fact_2_dag_Oinduct,axiom,
! [P: binDag_Mirabelle_dag > $o,Dag: binDag_Mirabelle_dag] :
( ( P @ binDag_Mirabelle_Tip )
=> ( ! [X1: binDag_Mirabelle_dag,X2: simpl_ref,X3: binDag_Mirabelle_dag] :
( ( P @ X1 )
=> ( ( P @ X3 )
=> ( P @ ( binDag476092410e_Node @ X1 @ X2 @ X3 ) ) ) )
=> ( P @ Dag ) ) ) ).
% dag.induct
thf(fact_3_dag_Oexhaust,axiom,
! [Y: binDag_Mirabelle_dag] :
( ( Y != binDag_Mirabelle_Tip )
=> ~ ! [X212: binDag_Mirabelle_dag,X222: simpl_ref,X232: binDag_Mirabelle_dag] :
( Y
!= ( binDag476092410e_Node @ X212 @ X222 @ X232 ) ) ) ).
% dag.exhaust
thf(fact_4_dag_Osimps_I7_J,axiom,
! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
= ( F2 @ X21 @ X22 @ X23 @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X21 ) @ ( binDag1442713106ec_dag @ A @ F1 @ F2 @ X23 ) ) ) ).
% dag.simps(7)
thf(fact_5_dag_Osimps_I5_J,axiom,
! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
( ( binDag1297733282se_dag @ A @ F1 @ F2 @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
= ( F2 @ X21 @ X22 @ X23 ) ) ).
% dag.simps(5)
thf(fact_6_dag_Osimps_I6_J,axiom,
! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A > A > A] :
( ( binDag1442713106ec_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
= F1 ) ).
% dag.simps(6)
thf(fact_7_dag_Osimps_I4_J,axiom,
! [A: $tType,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A] :
( ( binDag1297733282se_dag @ A @ F1 @ F2 @ binDag_Mirabelle_Tip )
= F1 ) ).
% dag.simps(4)
thf(fact_8_dag_Osize__gen_I1_J,axiom,
( ( binDag1924123185ze_dag @ binDag_Mirabelle_Tip )
= ( zero_zero @ nat ) ) ).
% dag.size_gen(1)
thf(fact_9_dag_Osize_I3_J,axiom,
( ( size_size @ binDag_Mirabelle_dag @ binDag_Mirabelle_Tip )
= ( zero_zero @ nat ) ) ).
% dag.size(3)
thf(fact_10_dag_Ocase__distrib,axiom,
! [B: $tType,A: $tType,H: A > B,F1: A,F2: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > A,Dag: binDag_Mirabelle_dag] :
( ( H @ ( binDag1297733282se_dag @ A @ F1 @ F2 @ Dag ) )
= ( binDag1297733282se_dag @ B @ ( H @ F1 )
@ ^ [X12: binDag_Mirabelle_dag,X24: simpl_ref,X32: binDag_Mirabelle_dag] : ( H @ ( F2 @ X12 @ X24 @ X32 ) )
@ Dag ) ) ).
% dag.case_distrib
thf(fact_11_fun__cong__unused__0,axiom,
! [A: $tType,B: $tType,C: $tType] :
( ( zero @ B @ ( type2 @ B ) )
=> ! [F: ( A > B ) > C,G: C] :
( ( F
= ( ^ [X: A > B] : G ) )
=> ( ( F
@ ^ [X: A] : ( zero_zero @ B ) )
= G ) ) ) ).
% fun_cong_unused_0
thf(fact_12_size__ne__size__imp__ne,axiom,
! [A: $tType] :
( ( size @ A @ ( type2 @ A ) )
=> ! [X4: A,Y: A] :
( ( ( size_size @ A @ X4 )
!= ( size_size @ A @ Y ) )
=> ( X4 != Y ) ) ) ).
% size_ne_size_imp_ne
thf(fact_13_zero__natural_Orsp,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ) ).
% zero_natural.rsp
thf(fact_14_zero__reorient,axiom,
! [A: $tType] :
( ( zero @ A @ ( type2 @ A ) )
=> ! [X4: A] :
( ( ( zero_zero @ A )
= X4 )
= ( X4
= ( zero_zero @ A ) ) ) ) ).
% zero_reorient
thf(fact_15_bool_Osize_I1_J,axiom,
( ( size_bool @ $true )
= ( zero_zero @ nat ) ) ).
% bool.size(1)
thf(fact_16_bool_Osize_I2_J,axiom,
( ( size_bool @ $false )
= ( zero_zero @ nat ) ) ).
% bool.size(2)
thf(fact_17_dag_Osize__gen_I2_J,axiom,
! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
( ( binDag1924123185ze_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( binDag1924123185ze_dag @ X21 ) @ ( binDag1924123185ze_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% dag.size_gen(2)
thf(fact_18_dag_Osize_I4_J,axiom,
! [X21: binDag_Mirabelle_dag,X22: simpl_ref,X23: binDag_Mirabelle_dag] :
( ( size_size @ binDag_Mirabelle_dag @ ( binDag476092410e_Node @ X21 @ X22 @ X23 ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ binDag_Mirabelle_dag @ X21 ) @ ( size_size @ binDag_Mirabelle_dag @ X23 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% dag.size(4)
thf(fact_19_ntrancl__Zero,axiom,
! [A: $tType,R: set @ ( product_prod @ A @ A )] :
( ( transitive_ntrancl @ A @ ( zero_zero @ nat ) @ R )
= R ) ).
% ntrancl_Zero
thf(fact_20_add__left__cancel,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
= ( B2 = C2 ) ) ) ).
% add_left_cancel
thf(fact_21_add__right__cancel,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
= ( B2 = C2 ) ) ) ).
% add_right_cancel
thf(fact_22_natural_Osize_I3_J,axiom,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ) ).
% natural.size(3)
thf(fact_23_bool_Osize_I4_J,axiom,
( ( size_size @ $o @ $false )
= ( zero_zero @ nat ) ) ).
% bool.size(4)
thf(fact_24_bool_Osize_I3_J,axiom,
( ( size_size @ $o @ $true )
= ( zero_zero @ nat ) ) ).
% bool.size(3)
thf(fact_25_nat_Oinject,axiom,
! [X25: nat,Y2: nat] :
( ( ( suc @ X25 )
= ( suc @ Y2 ) )
= ( X25 = Y2 ) ) ).
% nat.inject
thf(fact_26_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_27_add_Oleft__neutral,axiom,
! [A: $tType] :
( ( monoid_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% add.left_neutral
thf(fact_28_add_Oright__neutral,axiom,
! [A: $tType] :
( ( monoid_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% add.right_neutral
thf(fact_29_double__zero,axiom,
! [A: $tType] :
( ( linord219039673up_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( ( plus_plus @ A @ A2 @ A2 )
= ( zero_zero @ A ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% double_zero
thf(fact_30_double__zero__sym,axiom,
! [A: $tType] :
( ( linord219039673up_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( ( zero_zero @ A )
= ( plus_plus @ A @ A2 @ A2 ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% double_zero_sym
thf(fact_31_add__cancel__left__left,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= A2 )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_left_left
thf(fact_32_add__cancel__left__right,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= A2 )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_left_right
thf(fact_33_add__cancel__right__left,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( A2
= ( plus_plus @ A @ B2 @ A2 ) )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_right_left
thf(fact_34_add__cancel__right__right,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( A2
= ( plus_plus @ A @ A2 @ B2 ) )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_right_right
thf(fact_35_add__is__0,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus @ nat @ M @ N )
= ( zero_zero @ nat ) )
= ( ( M
= ( zero_zero @ nat ) )
& ( N
= ( zero_zero @ nat ) ) ) ) ).
% add_is_0
thf(fact_36_Nat_Oadd__0__right,axiom,
! [M: nat] :
( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
= M ) ).
% Nat.add_0_right
thf(fact_37_add__Suc__right,axiom,
! [M: nat,N: nat] :
( ( plus_plus @ nat @ M @ ( suc @ N ) )
= ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% add_Suc_right
thf(fact_38_one__is__add,axiom,
! [M: nat,N: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ M @ N ) )
= ( ( ( M
= ( suc @ ( zero_zero @ nat ) ) )
& ( N
= ( zero_zero @ nat ) ) )
| ( ( M
= ( zero_zero @ nat ) )
& ( N
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% one_is_add
thf(fact_39_add__is__1,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus @ nat @ M @ N )
= ( suc @ ( zero_zero @ nat ) ) )
= ( ( ( M
= ( suc @ ( zero_zero @ nat ) ) )
& ( N
= ( zero_zero @ nat ) ) )
| ( ( M
= ( zero_zero @ nat ) )
& ( N
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% add_is_1
thf(fact_40_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_41_add__mono__thms__linordered__semiring_I4_J,axiom,
! [A: $tType] :
( ( ordere779506340up_add @ A @ ( type2 @ A ) )
=> ! [I: A,J: A,K: A,L: A] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus @ A @ I @ K )
= ( plus_plus @ A @ J @ L ) ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_42_mem__Collect__eq,axiom,
! [A: $tType,A2: A,P: A > $o] :
( ( member @ A @ A2 @ ( collect @ A @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_43_Collect__mem__eq,axiom,
! [A: $tType,A3: set @ A] :
( ( collect @ A
@ ^ [X: A] : ( member @ A @ X @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_44_Collect__cong,axiom,
! [A: $tType,P: A > $o,Q: A > $o] :
( ! [X5: A] :
( ( P @ X5 )
= ( Q @ X5 ) )
=> ( ( collect @ A @ P )
= ( collect @ A @ Q ) ) ) ).
% Collect_cong
thf(fact_45_ext,axiom,
! [B: $tType,A: $tType,F: A > B,G: A > B] :
( ! [X5: A] :
( ( F @ X5 )
= ( G @ X5 ) )
=> ( F = G ) ) ).
% ext
thf(fact_46_Suc__inject,axiom,
! [X4: nat,Y: nat] :
( ( ( suc @ X4 )
= ( suc @ Y ) )
=> ( X4 = Y ) ) ).
% Suc_inject
thf(fact_47_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_48_add__Suc__shift,axiom,
! [M: nat,N: nat] :
( ( plus_plus @ nat @ ( suc @ M ) @ N )
= ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% add_Suc_shift
thf(fact_49_add__Suc,axiom,
! [M: nat,N: nat] :
( ( plus_plus @ nat @ ( suc @ M ) @ N )
= ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% add_Suc
thf(fact_50_nat__add__left__cancel,axiom,
! [K: nat,M: nat,N: nat] :
( ( ( plus_plus @ nat @ K @ M )
= ( plus_plus @ nat @ K @ N ) )
= ( M = N ) ) ).
% nat_add_left_cancel
thf(fact_51_nat__add__right__cancel,axiom,
! [M: nat,K: nat,N: nat] :
( ( ( plus_plus @ nat @ M @ K )
= ( plus_plus @ nat @ N @ K ) )
= ( M = N ) ) ).
% nat_add_right_cancel
thf(fact_52_add_Oassoc,axiom,
! [A: $tType] :
( ( semigroup_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% add.assoc
thf(fact_53_add_Oleft__cancel,axiom,
! [A: $tType] :
( ( group_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
= ( B2 = C2 ) ) ) ).
% add.left_cancel
thf(fact_54_add_Oright__cancel,axiom,
! [A: $tType] :
( ( group_add @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
= ( B2 = C2 ) ) ) ).
% add.right_cancel
thf(fact_55_add_Ocommute,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A @ ( type2 @ A ) )
=> ( ( plus_plus @ A )
= ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% add.commute
thf(fact_56_add_Oleft__commute,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A,C2: A] :
( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% add.left_commute
thf(fact_57_add__left__imp__eq,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
=> ( B2 = C2 ) ) ) ).
% add_left_imp_eq
thf(fact_58_add__right__imp__eq,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
=> ( B2 = C2 ) ) ) ).
% add_right_imp_eq
thf(fact_59_comm__monoid__add__class_Oadd__0,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% comm_monoid_add_class.add_0
thf(fact_60_add_Ocomm__neutral,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% add.comm_neutral
thf(fact_61_add_Ogroup__left__neutral,axiom,
! [A: $tType] :
( ( group_add @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% add.group_left_neutral
thf(fact_62_add__eq__0__iff__both__eq__0,axiom,
! [A: $tType] :
( ( canoni770627133id_add @ A @ ( type2 @ A ) )
=> ! [X4: A,Y: A] :
( ( ( plus_plus @ A @ X4 @ Y )
= ( zero_zero @ A ) )
= ( ( X4
= ( zero_zero @ A ) )
& ( Y
= ( zero_zero @ A ) ) ) ) ) ).
% add_eq_0_iff_both_eq_0
thf(fact_63_nat_Odistinct_I1_J,axiom,
! [X25: nat] :
( ( zero_zero @ nat )
!= ( suc @ X25 ) ) ).
% nat.distinct(1)
thf(fact_64_old_Onat_Odistinct_I2_J,axiom,
! [Nat3: nat] :
( ( suc @ Nat3 )
!= ( zero_zero @ nat ) ) ).
% old.nat.distinct(2)
thf(fact_65_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( ( zero_zero @ nat )
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_66_nat_OdiscI,axiom,
! [Nat: nat,X25: nat] :
( ( Nat
= ( suc @ X25 ) )
=> ( Nat
!= ( zero_zero @ nat ) ) ) ).
% nat.discI
thf(fact_67_nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ( P @ ( zero_zero @ nat ) )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) ).
% nat_induct
thf(fact_68_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X5: nat] : ( P @ X5 @ ( zero_zero @ nat ) )
=> ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
=> ( ! [X5: nat,Y3: nat] :
( ( P @ X5 @ Y3 )
=> ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) ).
% diff_induct
thf(fact_69_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ ( zero_zero @ nat ) ) ) ) ).
% zero_induct
thf(fact_70_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= ( zero_zero @ nat ) ) ).
% Suc_neq_Zero
thf(fact_71_Zero__neq__Suc,axiom,
! [M: nat] :
( ( zero_zero @ nat )
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_72_Zero__not__Suc,axiom,
! [M: nat] :
( ( zero_zero @ nat )
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_73_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y
!= ( zero_zero @ nat ) )
=> ~ ! [Nat4: nat] :
( Y
!= ( suc @ Nat4 ) ) ) ).
% old.nat.exhaust
thf(fact_74_old_Onat_Oinducts,axiom,
! [P: nat > $o,Nat: nat] :
( ( P @ ( zero_zero @ nat ) )
=> ( ! [Nat4: nat] :
( ( P @ Nat4 )
=> ( P @ ( suc @ Nat4 ) ) )
=> ( P @ Nat ) ) ) ).
% old.nat.inducts
thf(fact_75_not0__implies__Suc,axiom,
! [N: nat] :
( ( N
!= ( zero_zero @ nat ) )
=> ? [M2: nat] :
( N
= ( suc @ M2 ) ) ) ).
% not0_implies_Suc
thf(fact_76_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
= N ) ).
% plus_nat.add_0
thf(fact_77_add__eq__self__zero,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus @ nat @ M @ N )
= M )
=> ( N
= ( zero_zero @ nat ) ) ) ).
% add_eq_self_zero
thf(fact_78_size__bool,axiom,
( ( size_size @ $o )
= ( ^ [B3: $o] : ( zero_zero @ nat ) ) ) ).
% size_bool
thf(fact_79_sum_Osize__neq,axiom,
! [A: $tType,B: $tType,X4: sum_sum @ A @ B] :
( ( size_size @ ( sum_sum @ A @ B ) @ X4 )
!= ( zero_zero @ nat ) ) ).
% sum.size_neq
thf(fact_80_prod_Osize__neq,axiom,
! [A: $tType,B: $tType,X4: product_prod @ A @ B] :
( ( size_size @ ( product_prod @ A @ B ) @ X4 )
!= ( zero_zero @ nat ) ) ).
% prod.size_neq
thf(fact_81_size__bool__def,axiom,
( size_bool
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% size_bool_def
thf(fact_82_dependent__nat__choice,axiom,
! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
( ? [X13: A] : ( P @ ( zero_zero @ nat ) @ X13 )
=> ( ! [X5: A,N2: nat] :
( ( P @ N2 @ X5 )
=> ? [Y4: A] :
( ( P @ ( suc @ N2 ) @ Y4 )
& ( Q @ N2 @ X5 @ Y4 ) ) )
=> ? [F3: nat > A] :
! [N3: nat] :
( ( P @ N3 @ ( F3 @ N3 ) )
& ( Q @ N3 @ ( F3 @ N3 ) @ ( F3 @ ( suc @ N3 ) ) ) ) ) ) ).
% dependent_nat_choice
thf(fact_83_size__natural__overloaded__def,axiom,
( ( size_size @ code_natural )
= ( code_rec_natural @ nat @ ( zero_zero @ nat )
@ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% size_natural_overloaded_def
thf(fact_84_semiring__normalization__rules_I6_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% semiring_normalization_rules(6)
thf(fact_85_semiring__normalization__rules_I5_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% semiring_normalization_rules(5)
thf(fact_86_add__0__iff,axiom,
! [A: $tType] :
( ( semiri456707255roduct @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A] :
( ( B2
= ( plus_plus @ A @ B2 @ A2 ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% add_0_iff
thf(fact_87_natural_Osize_I1_J,axiom,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ) ).
% natural.size(1)
thf(fact_88_natural_Osize_I4_J,axiom,
! [Natural: code_natural] :
( ( size_size @ code_natural @ ( code_Suc @ Natural ) )
= ( plus_plus @ nat @ ( size_size @ code_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% natural.size(4)
thf(fact_89_size__natural__def,axiom,
( code_size_natural
= ( code_rec_natural @ nat @ ( zero_zero @ nat )
@ ^ [X: code_natural,Y5: nat] : ( plus_plus @ nat @ Y5 @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% size_natural_def
thf(fact_90_option_Osize__neq,axiom,
! [A: $tType,X4: option @ A] :
( ( size_size @ ( option @ A ) @ X4 )
!= ( zero_zero @ nat ) ) ).
% option.size_neq
thf(fact_91_natural_Oinject,axiom,
! [Natural: code_natural,Natural2: code_natural] :
( ( ( code_Suc @ Natural )
= ( code_Suc @ Natural2 ) )
= ( Natural = Natural2 ) ) ).
% natural.inject
thf(fact_92_natural_Osimps_I6_J,axiom,
! [T: $tType,F1: T,F2: code_natural > T > T] :
( ( code_rec_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
= F1 ) ).
% natural.simps(6)
thf(fact_93_natural_Osimps_I7_J,axiom,
! [T: $tType,F1: T,F2: code_natural > T > T,Natural: code_natural] :
( ( code_rec_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
= ( F2 @ Natural @ ( code_rec_natural @ T @ F1 @ F2 @ Natural ) ) ) ).
% natural.simps(7)
thf(fact_94_natural_Osize_I2_J,axiom,
! [Natural: code_natural] :
( ( code_size_natural @ ( code_Suc @ Natural ) )
= ( plus_plus @ nat @ ( code_size_natural @ Natural ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% natural.size(2)
thf(fact_95_natural_Oinducts,axiom,
! [P: code_natural > $o,Natural: code_natural] :
( ( P @ ( zero_zero @ code_natural ) )
=> ( ! [Natural3: code_natural] :
( ( P @ Natural3 )
=> ( P @ ( code_Suc @ Natural3 ) ) )
=> ( P @ Natural ) ) ) ).
% natural.inducts
thf(fact_96_natural_Oexhaust,axiom,
! [Y: code_natural] :
( ( Y
!= ( zero_zero @ code_natural ) )
=> ~ ! [Natural3: code_natural] :
( Y
!= ( code_Suc @ Natural3 ) ) ) ).
% natural.exhaust
thf(fact_97_natural_Odistinct_I1_J,axiom,
! [Natural2: code_natural] :
( ( zero_zero @ code_natural )
!= ( code_Suc @ Natural2 ) ) ).
% natural.distinct(1)
thf(fact_98_natural_Odistinct_I2_J,axiom,
! [Natural4: code_natural] :
( ( code_Suc @ Natural4 )
!= ( zero_zero @ code_natural ) ) ).
% natural.distinct(2)
thf(fact_99_size__bool__overloaded__def,axiom,
( ( size_size @ $o )
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% size_bool_overloaded_def
thf(fact_100_semiring__normalization__rules_I20_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A,D: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ A @ C2 @ D ) )
= ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ).
% semiring_normalization_rules(20)
thf(fact_101_semiring__normalization__rules_I21_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% semiring_normalization_rules(21)
thf(fact_102_semiring__normalization__rules_I22_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A,C2: A,D: A] :
( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
= ( plus_plus @ A @ C2 @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% semiring_normalization_rules(22)
thf(fact_103_semiring__normalization__rules_I23_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% semiring_normalization_rules(23)
thf(fact_104_semiring__normalization__rules_I24_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ( ( plus_plus @ A )
= ( ^ [A4: A,C3: A] : ( plus_plus @ A @ C3 @ A4 ) ) ) ) ).
% semiring_normalization_rules(24)
thf(fact_105_semiring__normalization__rules_I25_J,axiom,
! [A: $tType] :
( ( comm_semiring_1 @ A @ ( type2 @ A ) )
=> ! [A2: A,C2: A,D: A] :
( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C2 @ D ) )
= ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ D ) ) ) ).
% semiring_normalization_rules(25)
thf(fact_106_old_Obool_Osimps_I5_J,axiom,
! [T: $tType,F1: T,F2: T] :
( ( product_rec_bool @ T @ F1 @ F2 @ $true )
= F1 ) ).
% old.bool.simps(5)
thf(fact_107_old_Obool_Osimps_I6_J,axiom,
! [T: $tType,F1: T,F2: T] :
( ( product_rec_bool @ T @ F1 @ F2 @ $false )
= F2 ) ).
% old.bool.simps(6)
thf(fact_108_natural_Osimps_I5_J,axiom,
! [T: $tType,F1: T,F2: code_natural > T,Natural: code_natural] :
( ( code_case_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
= ( F2 @ Natural ) ) ).
% natural.simps(5)
thf(fact_109_random__aux__set_Oinduct,axiom,
! [B: $tType] :
( ( quickcheck_random @ B @ ( type2 @ B ) )
=> ! [P: code_natural > code_natural > $o,A0: code_natural,A1: code_natural] :
( ! [X1: code_natural] : ( P @ ( zero_zero @ code_natural ) @ X1 )
=> ( ! [I2: code_natural,J2: code_natural] :
( ! [X6: product_prod @ B @ ( product_unit > code_term )] : ( P @ I2 @ J2 )
=> ( P @ ( code_Suc @ I2 ) @ J2 ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% random_aux_set.induct
thf(fact_110_random__aux__rec,axiom,
! [A: $tType,Random_aux: code_natural > A,Rhs: code_natural > A,K: code_natural] :
( ( ( Random_aux @ ( zero_zero @ code_natural ) )
= ( Rhs @ ( zero_zero @ code_natural ) ) )
=> ( ! [K2: code_natural] :
( ( Random_aux @ ( code_Suc @ K2 ) )
= ( Rhs @ ( code_Suc @ K2 ) ) )
=> ( ( Random_aux @ K )
= ( Rhs @ K ) ) ) ) ).
% random_aux_rec
thf(fact_111_natural_Osimps_I4_J,axiom,
! [T: $tType,F1: T,F2: code_natural > T] :
( ( code_case_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
= F1 ) ).
% natural.simps(4)
thf(fact_112_case__natural__def,axiom,
! [T: $tType] :
( ( code_case_natural @ T )
= ( ^ [F12: T,F22: code_natural > T] :
( code_rec_natural @ T @ F12
@ ^ [X12: code_natural,X24: T] : ( F22 @ X12 ) ) ) ) ).
% case_natural_def
thf(fact_113_option_Osize_I3_J,axiom,
! [A: $tType] :
( ( size_size @ ( option @ A ) @ ( none @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size(3)
thf(fact_114_option_Osize_I4_J,axiom,
! [A: $tType,X25: A] :
( ( size_size @ ( option @ A ) @ ( some @ A @ X25 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size(4)
thf(fact_115_sum_Osize_I3_J,axiom,
! [A: $tType,B: $tType,X14: A] :
( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ X14 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% sum.size(3)
thf(fact_116_sum_Osize_I4_J,axiom,
! [B: $tType,A: $tType,X25: B] :
( ( size_size @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ X25 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% sum.size(4)
thf(fact_117_typerep_Osize__neq,axiom,
! [X4: typerep] :
( ( size_size @ typerep @ X4 )
!= ( zero_zero @ nat ) ) ).
% typerep.size_neq
thf(fact_118_option_Oinject,axiom,
! [A: $tType,X25: A,Y2: A] :
( ( ( some @ A @ X25 )
= ( some @ A @ Y2 ) )
= ( X25 = Y2 ) ) ).
% option.inject
thf(fact_119_not__None__eq,axiom,
! [A: $tType,X4: option @ A] :
( ( X4
!= ( none @ A ) )
= ( ? [Y5: A] :
( X4
= ( some @ A @ Y5 ) ) ) ) ).
% not_None_eq
thf(fact_120_not__Some__eq,axiom,
! [A: $tType,X4: option @ A] :
( ( ! [Y5: A] :
( X4
!= ( some @ A @ Y5 ) ) )
= ( X4
= ( none @ A ) ) ) ).
% not_Some_eq
thf(fact_121_Inl__Inr__False,axiom,
! [A: $tType,B: $tType,X4: A,Y: B] :
( ( sum_Inl @ A @ B @ X4 )
!= ( sum_Inr @ B @ A @ Y ) ) ).
% Inl_Inr_False
thf(fact_122_Inr__Inl__False,axiom,
! [B: $tType,A: $tType,X4: B,Y: A] :
( ( sum_Inr @ B @ A @ X4 )
!= ( sum_Inl @ A @ B @ Y ) ) ).
% Inr_Inl_False
thf(fact_123_obj__sumE__f,axiom,
! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
( ! [X5: A] :
( ( S
= ( F @ ( sum_Inl @ A @ C @ X5 ) ) )
=> P )
=> ( ! [X5: C] :
( ( S
= ( F @ ( sum_Inr @ C @ A @ X5 ) ) )
=> P )
=> ! [X6: sum_sum @ A @ C] :
( ( S
= ( F @ X6 ) )
=> P ) ) ) ).
% obj_sumE_f
thf(fact_124_option_Odistinct_I1_J,axiom,
! [A: $tType,X25: A] :
( ( none @ A )
!= ( some @ A @ X25 ) ) ).
% option.distinct(1)
thf(fact_125_option_OdiscI,axiom,
! [A: $tType,Option: option @ A,X25: A] :
( ( Option
= ( some @ A @ X25 ) )
=> ( Option
!= ( none @ A ) ) ) ).
% option.discI
thf(fact_126_option_Oexhaust,axiom,
! [A: $tType,Y: option @ A] :
( ( Y
!= ( none @ A ) )
=> ~ ! [X2: A] :
( Y
!= ( some @ A @ X2 ) ) ) ).
% option.exhaust
thf(fact_127_option_Oinducts,axiom,
! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
( ( P @ ( none @ A ) )
=> ( ! [X5: A] : ( P @ ( some @ A @ X5 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_128_split__option__ex,axiom,
! [A: $tType] :
( ( ^ [P2: ( option @ A ) > $o] :
? [X7: option @ A] : ( P2 @ X7 ) )
= ( ^ [P3: ( option @ A ) > $o] :
( ( P3 @ ( none @ A ) )
| ? [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% split_option_ex
thf(fact_129_split__option__all,axiom,
! [A: $tType] :
( ( ^ [P2: ( option @ A ) > $o] :
! [X7: option @ A] : ( P2 @ X7 ) )
= ( ^ [P3: ( option @ A ) > $o] :
( ( P3 @ ( none @ A ) )
& ! [X: A] : ( P3 @ ( some @ A @ X ) ) ) ) ) ).
% split_option_all
thf(fact_130_combine__options__cases,axiom,
! [A: $tType,B: $tType,X4: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
( ( ( X4
= ( none @ A ) )
=> ( P @ X4 @ Y ) )
=> ( ( ( Y
= ( none @ B ) )
=> ( P @ X4 @ Y ) )
=> ( ! [A5: A,B4: B] :
( ( X4
= ( some @ A @ A5 ) )
=> ( ( Y
= ( some @ B @ B4 ) )
=> ( P @ X4 @ Y ) ) )
=> ( P @ X4 @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_131_sum_Osize__gen_I1_J,axiom,
! [B: $tType,A: $tType,Xa: A > nat,X4: B > nat,X14: A] :
( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inl @ A @ B @ X14 ) )
= ( plus_plus @ nat @ ( Xa @ X14 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% sum.size_gen(1)
thf(fact_132_sum_Osize__gen_I2_J,axiom,
! [A: $tType,B: $tType,Xa: A > nat,X4: B > nat,X25: B] :
( ( basic_BNF_size_sum @ A @ B @ Xa @ X4 @ ( sum_Inr @ B @ A @ X25 ) )
= ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% sum.size_gen(2)
thf(fact_133_option_Osize__gen_I2_J,axiom,
! [A: $tType,X4: A > nat,X25: A] :
( ( size_option @ A @ X4 @ ( some @ A @ X25 ) )
= ( plus_plus @ nat @ ( X4 @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% option.size_gen(2)
thf(fact_134_option_Osize__gen_I1_J,axiom,
! [A: $tType,X4: A > nat] :
( ( size_option @ A @ X4 @ ( none @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size_gen(1)
thf(fact_135_typerep_Osize_I2_J,axiom,
! [X14: literal,X25: list @ typerep] :
( ( size_size @ typerep @ ( typerep3 @ X14 @ X25 ) )
= ( plus_plus @ nat @ ( size_list @ typerep @ ( size_size @ typerep ) @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% typerep.size(2)
thf(fact_136_tuple__isomorphism_Osize__neq,axiom,
! [A: $tType,B: $tType,C: $tType,X4: tuple_isomorphism @ A @ B @ C] :
( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ X4 )
!= ( zero_zero @ nat ) ) ).
% tuple_isomorphism.size_neq
thf(fact_137_size__literal__def,axiom,
( ( size_size @ literal )
= ( ^ [S2: literal] : ( zero_zero @ nat ) ) ) ).
% size_literal_def
thf(fact_138_size__unit__overloaded__def,axiom,
( ( size_size @ product_unit )
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% size_unit_overloaded_def
thf(fact_139_typerep_Osize__gen,axiom,
! [X14: literal,X25: list @ typerep] :
( ( size_typerep @ ( typerep3 @ X14 @ X25 ) )
= ( plus_plus @ nat @ ( size_list @ typerep @ size_typerep @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% typerep.size_gen
thf(fact_140_size__unit__def,axiom,
( product_size_unit
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% size_unit_def
thf(fact_141_tuple__isomorphism_Osize_I2_J,axiom,
! [B: $tType,C: $tType,A: $tType,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% tuple_isomorphism.size(2)
thf(fact_142_unit_Osize_I2_J,axiom,
( ( size_size @ product_unit @ product_Unity )
= ( zero_zero @ nat ) ) ).
% unit.size(2)
thf(fact_143_unit__abs__eta__conv,axiom,
! [A: $tType,F: product_unit > A] :
( ( ^ [U: product_unit] : ( F @ product_Unity ) )
= F ) ).
% unit_abs_eta_conv
thf(fact_144_old_Ounit_Orec,axiom,
! [T: $tType,F1: T] :
( ( product_rec_unit @ T @ F1 @ product_Unity )
= F1 ) ).
% old.unit.rec
thf(fact_145_unit_Osize_I1_J,axiom,
( ( product_size_unit @ product_Unity )
= ( zero_zero @ nat ) ) ).
% unit.size(1)
thf(fact_146_eq__sym__Unity__conv,axiom,
! [X4: $o] :
( ( X4
= ( product_Unity = product_Unity ) )
= X4 ) ).
% eq_sym_Unity_conv
thf(fact_147_unit__all__impI,axiom,
! [P: product_unit > $o,Q: product_unit > $o] :
( ( ( P @ product_Unity )
=> ( Q @ product_Unity ) )
=> ! [X6: product_unit] :
( ( P @ X6 )
=> ( Q @ X6 ) ) ) ).
% unit_all_impI
thf(fact_148_old_Ounit_Oinducts,axiom,
! [P: product_unit > $o,Unit: product_unit] :
( ( P @ product_Unity )
=> ( P @ Unit ) ) ).
% old.unit.inducts
thf(fact_149_old_Ounit_Oexhaust,axiom,
! [Y: product_unit] : Y = product_Unity ).
% old.unit.exhaust
thf(fact_150_tuple__isomorphism_Osize__gen,axiom,
! [B: $tType,C: $tType,A: $tType,Xb: A > nat,Xa: B > nat,X4: C > nat,X14: A > ( product_prod @ B @ C ),X25: ( product_prod @ B @ C ) > A] :
( ( tuple_1907371454rphism @ A @ B @ C @ Xb @ Xa @ X4 @ ( tuple_742722141rphism @ A @ B @ C @ X14 @ X25 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% tuple_isomorphism.size_gen
thf(fact_151_default__unit__def,axiom,
( ( default_default @ product_unit )
= product_Unity ) ).
% default_unit_def
thf(fact_152_list_Osize__gen_I2_J,axiom,
! [A: $tType,X4: A > nat,X21: A,X22: list @ A] :
( ( size_list @ A @ X4 @ ( cons @ A @ X21 @ X22 ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( X4 @ X21 ) @ ( size_list @ A @ X4 @ X22 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% list.size_gen(2)
thf(fact_153_length__Suc__conv,axiom,
! [A: $tType,Xs: list @ A,N: nat] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( suc @ N ) )
= ( ? [Y5: A,Ys: list @ A] :
( ( Xs
= ( cons @ A @ Y5 @ Ys ) )
& ( ( size_size @ ( list @ A ) @ Ys )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_154_Suc__length__conv,axiom,
! [A: $tType,N: nat,Xs: list @ A] :
( ( ( suc @ N )
= ( size_size @ ( list @ A ) @ Xs ) )
= ( ? [Y5: A,Ys: list @ A] :
( ( Xs
= ( cons @ A @ Y5 @ Ys ) )
& ( ( size_size @ ( list @ A ) @ Ys )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_155_list_Osize_I4_J,axiom,
! [A: $tType,X21: A,X22: list @ A] :
( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X22 ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X22 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% list.size(4)
thf(fact_156_length__Cons,axiom,
! [A: $tType,X4: A,Xs: list @ A] :
( ( size_size @ ( list @ A ) @ ( cons @ A @ X4 @ Xs ) )
= ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% length_Cons
thf(fact_157_gen__length__code_I2_J,axiom,
! [B: $tType,N: nat,X4: B,Xs: list @ B] :
( ( gen_length @ B @ N @ ( cons @ B @ X4 @ Xs ) )
= ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% gen_length_code(2)
thf(fact_158_linordered__field__class_Osign__simps_I26_J,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% linordered_field_class.sign_simps(26)
thf(fact_159_length__code,axiom,
! [A: $tType] :
( ( size_size @ ( list @ A ) )
= ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% length_code
thf(fact_160_gen__length__def,axiom,
! [A: $tType] :
( ( gen_length @ A )
= ( ^ [N4: nat,Xs2: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs2 ) ) ) ) ).
% gen_length_def
thf(fact_161_linordered__field__class_Osign__simps_I28_J,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A,C2: A] :
( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% linordered_field_class.sign_simps(28)
thf(fact_162_linordered__field__class_Osign__simps_I27_J,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ( ( plus_plus @ A )
= ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% linordered_field_class.sign_simps(27)
thf(fact_163_length__splice,axiom,
! [A: $tType,Xs: list @ A,Ys2: list @ A] :
( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys2 ) ) ) ).
% length_splice
thf(fact_164_Shift__def,axiom,
! [A: $tType] :
( ( bNF_Greatest_Shift @ A )
= ( ^ [Kl: set @ ( list @ A ),K3: A] :
( collect @ ( list @ A )
@ ^ [Kl2: list @ A] : ( member @ ( list @ A ) @ ( cons @ A @ K3 @ Kl2 ) @ Kl ) ) ) ) ).
% Shift_def
thf(fact_165_is__num__normalize_I1_J,axiom,
! [A: $tType] :
( ( neg_numeral @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% is_num_normalize(1)
thf(fact_166_option_Ocollapse,axiom,
! [A: $tType,Option: option @ A] :
( ( Option
!= ( none @ A ) )
=> ( ( some @ A @ ( the @ A @ Option ) )
= Option ) ) ).
% option.collapse
thf(fact_167_old_Ounit_Ocase,axiom,
! [A: $tType,F: A] :
( ( product_case_unit @ A @ F @ product_Unity )
= F ) ).
% old.unit.case
thf(fact_168_case__optionE,axiom,
! [A: $tType,P: $o,Q: A > $o,X4: option @ A] :
( ( case_option @ $o @ A @ P @ Q @ X4 )
=> ( ( ( X4
= ( none @ A ) )
=> ~ P )
=> ~ ! [Y3: A] :
( ( X4
= ( some @ A @ Y3 ) )
=> ~ ( Q @ Y3 ) ) ) ) ).
% case_optionE
thf(fact_169_option_Odisc__eq__case_I1_J,axiom,
! [A: $tType,Option: option @ A] :
( ( Option
= ( none @ A ) )
= ( case_option @ $o @ A @ $true
@ ^ [Uu: A] : $false
@ Option ) ) ).
% option.disc_eq_case(1)
thf(fact_170_option_Odisc__eq__case_I2_J,axiom,
! [A: $tType,Option: option @ A] :
( ( Option
!= ( none @ A ) )
= ( case_option @ $o @ A @ $false
@ ^ [Uu: A] : $true
@ Option ) ) ).
% option.disc_eq_case(2)
thf(fact_171_option_Osimps_I4_J,axiom,
! [A: $tType,B: $tType,F1: B,F2: A > B] :
( ( case_option @ B @ A @ F1 @ F2 @ ( none @ A ) )
= F1 ) ).
% option.simps(4)
thf(fact_172_option_Osimps_I5_J,axiom,
! [B: $tType,A: $tType,F1: B,F2: A > B,X25: A] :
( ( case_option @ B @ A @ F1 @ F2 @ ( some @ A @ X25 ) )
= ( F2 @ X25 ) ) ).
% option.simps(5)
thf(fact_173_option_Ocase__distrib,axiom,
! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F2: A > B,Option: option @ A] :
( ( H @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
= ( case_option @ C @ A @ ( H @ F1 )
@ ^ [X: A] : ( H @ ( F2 @ X ) )
@ Option ) ) ).
% option.case_distrib
thf(fact_174_option_Osplit__sel,axiom,
! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
= ( ( ( Option
= ( none @ A ) )
=> ( P @ F1 ) )
& ( ( Option
= ( some @ A @ ( the @ A @ Option ) ) )
=> ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ).
% option.split_sel
thf(fact_175_option_Ocase__eq__if,axiom,
! [A: $tType,B: $tType] :
( ( case_option @ B @ A )
= ( ^ [F12: B,F22: A > B,Option2: option @ A] :
( if @ B
@ ( Option2
= ( none @ A ) )
@ F12
@ ( F22 @ ( the @ A @ Option2 ) ) ) ) ) ).
% option.case_eq_if
thf(fact_176_option_Osplit__sel__asm,axiom,
! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > B,Option: option @ A] :
( ( P @ ( case_option @ B @ A @ F1 @ F2 @ Option ) )
= ( ~ ( ( ( Option
= ( none @ A ) )
& ~ ( P @ F1 ) )
| ( ( Option
= ( some @ A @ ( the @ A @ Option ) ) )
& ~ ( P @ ( F2 @ ( the @ A @ Option ) ) ) ) ) ) ) ).
% option.split_sel_asm
thf(fact_177_case__unit__Unity,axiom,
! [A: $tType] :
( ( product_case_unit @ A )
= ( ^ [F4: A,U: product_unit] : F4 ) ) ).
% case_unit_Unity
thf(fact_178_unit_Ocase__distrib,axiom,
! [A: $tType,B: $tType,H: A > B,F: A,Unit: product_unit] :
( ( H @ ( product_case_unit @ A @ F @ Unit ) )
= ( product_case_unit @ B @ ( H @ F ) @ Unit ) ) ).
% unit.case_distrib
thf(fact_179_option_Osel,axiom,
! [A: $tType,X25: A] :
( ( the @ A @ ( some @ A @ X25 ) )
= X25 ) ).
% option.sel
thf(fact_180_option_Oexpand,axiom,
! [A: $tType,Option: option @ A,Option3: option @ A] :
( ( ( Option
= ( none @ A ) )
= ( Option3
= ( none @ A ) ) )
=> ( ( ( Option
!= ( none @ A ) )
=> ( ( Option3
!= ( none @ A ) )
=> ( ( the @ A @ Option )
= ( the @ A @ Option3 ) ) ) )
=> ( Option = Option3 ) ) ) ).
% option.expand
thf(fact_181_option_Oexhaust__sel,axiom,
! [A: $tType,Option: option @ A] :
( ( Option
!= ( none @ A ) )
=> ( Option
= ( some @ A @ ( the @ A @ Option ) ) ) ) ).
% option.exhaust_sel
thf(fact_182_disjE__realizer2,axiom,
! [B: $tType,A: $tType,P: $o,Q: A > $o,X4: option @ A,R: B > $o,F: B,G: A > B] :
( ( case_option @ $o @ A @ P @ Q @ X4 )
=> ( ( P
=> ( R @ F ) )
=> ( ! [Q2: A] :
( ( Q @ Q2 )
=> ( R @ ( G @ Q2 ) ) )
=> ( R @ ( case_option @ B @ A @ F @ G @ X4 ) ) ) ) ) ).
% disjE_realizer2
thf(fact_183_option_Othe__def,axiom,
! [A: $tType] :
( ( the @ A )
= ( case_option @ A @ A @ ( undefined @ A )
@ ^ [X24: A] : X24 ) ) ).
% option.the_def
thf(fact_184_num_Osize_I5_J,axiom,
! [X25: num] :
( ( size_size @ num @ ( bit0 @ X25 ) )
= ( plus_plus @ nat @ ( size_size @ num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% num.size(5)
thf(fact_185_num_Osize__gen_I2_J,axiom,
! [X25: num] :
( ( size_num @ ( bit0 @ X25 ) )
= ( plus_plus @ nat @ ( size_num @ X25 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% num.size_gen(2)
thf(fact_186_num_Osize_I6_J,axiom,
! [X33: num] :
( ( size_size @ num @ ( bit1 @ X33 ) )
= ( plus_plus @ nat @ ( size_size @ num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% num.size(6)
thf(fact_187_num_Osize__gen_I3_J,axiom,
! [X33: num] :
( ( size_num @ ( bit1 @ X33 ) )
= ( plus_plus @ nat @ ( size_num @ X33 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% num.size_gen(3)
thf(fact_188_nat__of__num__code_I3_J,axiom,
! [N: num] :
( ( nat_of_num @ ( bit1 @ N ) )
= ( suc @ ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% nat_of_num_code(3)
thf(fact_189_nat__of__num_Osimps_I3_J,axiom,
! [X4: num] :
( ( nat_of_num @ ( bit1 @ X4 ) )
= ( suc @ ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ) ).
% nat_of_num.simps(3)
thf(fact_190_nat__of__num__add,axiom,
! [X4: num,Y: num] :
( ( nat_of_num @ ( plus_plus @ num @ X4 @ Y ) )
= ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ Y ) ) ) ).
% nat_of_num_add
thf(fact_191_nat__of__num__neq__0,axiom,
! [X4: num] :
( ( nat_of_num @ X4 )
!= ( zero_zero @ nat ) ) ).
% nat_of_num_neq_0
thf(fact_192_nat__of__num_Osimps_I2_J,axiom,
! [X4: num] :
( ( nat_of_num @ ( bit0 @ X4 ) )
= ( plus_plus @ nat @ ( nat_of_num @ X4 ) @ ( nat_of_num @ X4 ) ) ) ).
% nat_of_num.simps(2)
thf(fact_193_nat__of__num__code_I2_J,axiom,
! [N: num] :
( ( nat_of_num @ ( bit0 @ N ) )
= ( plus_plus @ nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% nat_of_num_code(2)
thf(fact_194_nat__of__num__inc,axiom,
! [X4: num] :
( ( nat_of_num @ ( inc @ X4 ) )
= ( suc @ ( nat_of_num @ X4 ) ) ) ).
% nat_of_num_inc
thf(fact_195_nat__of__num_Osimps_I1_J,axiom,
( ( nat_of_num @ one2 )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% nat_of_num.simps(1)
thf(fact_196_num_Osize__gen_I1_J,axiom,
( ( size_num @ one2 )
= ( zero_zero @ nat ) ) ).
% num.size_gen(1)
thf(fact_197_num_Osize_I4_J,axiom,
( ( size_size @ num @ one2 )
= ( zero_zero @ nat ) ) ).
% num.size(4)
thf(fact_198_add__2__eq__Suc,axiom,
! [N: nat] :
( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N )
= ( suc @ ( suc @ N ) ) ) ).
% add_2_eq_Suc
thf(fact_199_add__2__eq__Suc_H,axiom,
! [N: nat] :
( ( plus_plus @ nat @ N @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( suc @ ( suc @ N ) ) ) ).
% add_2_eq_Suc'
thf(fact_200_numeral__plus__numeral,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [M: num,N: num] :
( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
= ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% numeral_plus_numeral
thf(fact_201_add__numeral__left,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [V: num,W: num,Z: A] :
( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
= ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% add_numeral_left
thf(fact_202_Suc__numeral,axiom,
! [N: num] :
( ( suc @ ( numeral_numeral @ nat @ N ) )
= ( numeral_numeral @ nat @ ( plus_plus @ num @ N @ one2 ) ) ) ).
% Suc_numeral
thf(fact_203_numeral__Bit0,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( numeral_numeral @ A @ ( bit0 @ N ) )
= ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% numeral_Bit0
thf(fact_204_numeral__code_I2_J,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( numeral_numeral @ A @ ( bit0 @ N ) )
= ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% numeral_code(2)
thf(fact_205_zero__neq__numeral,axiom,
! [A: $tType] :
( ( semiring_char_0 @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( zero_zero @ A )
!= ( numeral_numeral @ A @ N ) ) ) ).
% zero_neq_numeral
thf(fact_206_eval__nat__numeral_I3_J,axiom,
! [N: num] :
( ( numeral_numeral @ nat @ ( bit1 @ N ) )
= ( suc @ ( numeral_numeral @ nat @ ( bit0 @ N ) ) ) ) ).
% eval_nat_numeral(3)
thf(fact_207_numeral__1__eq__Suc__0,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% numeral_1_eq_Suc_0
thf(fact_208_numeral__2__eq__2,axiom,
( ( numeral_numeral @ nat @ ( bit0 @ one2 ) )
= ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% numeral_2_eq_2
thf(fact_209_numeral__3__eq__3,axiom,
( ( numeral_numeral @ nat @ ( bit1 @ one2 ) )
= ( suc @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% numeral_3_eq_3
thf(fact_210_Suc3__eq__add__3,axiom,
! [N: nat] :
( ( suc @ ( suc @ ( suc @ N ) ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ).
% Suc3_eq_add_3
thf(fact_211_Suc__nat__number__of__add,axiom,
! [V: num,N: nat] :
( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V ) @ N ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V @ one2 ) ) @ N ) ) ).
% Suc_nat_number_of_add
thf(fact_212_zero__not__eq__two,axiom,
! [A: $tType] :
( ( semiring_div_parity @ A @ ( type2 @ A ) )
=> ( ( zero_zero @ A )
!= ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% zero_not_eq_two
thf(fact_213_one__plus__numeral,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
= ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% one_plus_numeral
thf(fact_214_Suc__1,axiom,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% Suc_1
thf(fact_215_one__add__one,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
= ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% one_add_one
thf(fact_216_numeral__plus__one,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
= ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% numeral_plus_one
thf(fact_217_one__plus__numeral__commute,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [X4: num] :
( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X4 ) )
= ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% one_plus_numeral_commute
thf(fact_218_One__nat__def,axiom,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% One_nat_def
thf(fact_219_one__reorient,axiom,
! [A: $tType] :
( ( one @ A @ ( type2 @ A ) )
=> ! [X4: A] :
( ( ( one_one @ A )
= X4 )
= ( X4
= ( one_one @ A ) ) ) ) ).
% one_reorient
thf(fact_220_Suc__eq__plus1,axiom,
( suc
= ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% Suc_eq_plus1
thf(fact_221_Suc__eq__plus1__left,axiom,
( suc
= ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% Suc_eq_plus1_left
thf(fact_222_numeral__Bit1,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( numeral_numeral @ A @ ( bit1 @ N ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% numeral_Bit1
thf(fact_223_numeral__inc,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [X4: num] :
( ( numeral_numeral @ A @ ( inc @ X4 ) )
= ( plus_plus @ A @ ( numeral_numeral @ A @ X4 ) @ ( one_one @ A ) ) ) ) ).
% numeral_inc
thf(fact_224_numeral__code_I3_J,axiom,
! [A: $tType] :
( ( numeral @ A @ ( type2 @ A ) )
=> ! [N: num] :
( ( numeral_numeral @ A @ ( bit1 @ N ) )
= ( plus_plus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) @ ( one_one @ A ) ) ) ) ).
% numeral_code(3)
thf(fact_225_nat__1__add__1,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% nat_1_add_1
thf(fact_226_zero__neq__one,axiom,
! [A: $tType] :
( ( zero_neq_one @ A @ ( type2 @ A ) )
=> ( ( zero_zero @ A )
!= ( one_one @ A ) ) ) ).
% zero_neq_one
thf(fact_227_dbl__inc__simps_I2_J,axiom,
! [A: $tType] :
( ( neg_numeral @ A @ ( type2 @ A ) )
=> ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
= ( one_one @ A ) ) ) ).
% dbl_inc_simps(2)
thf(fact_228_one__natural_Orsp,axiom,
( ( one_one @ nat )
= ( one_one @ nat ) ) ).
% one_natural.rsp
thf(fact_229_dbl__inc__def,axiom,
! [A: $tType] :
( ( neg_numeral @ A @ ( type2 @ A ) )
=> ( ( neg_numeral_dbl_inc @ A )
= ( ^ [X: A] : ( plus_plus @ A @ ( plus_plus @ A @ X @ X ) @ ( one_one @ A ) ) ) ) ) ).
% dbl_inc_def
thf(fact_230_Suc__div__eq__add3__div__numeral,axiom,
! [M: nat,V: num] :
( ( divide_divide @ nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral @ nat @ V ) )
= ( divide_divide @ nat @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ M ) @ ( numeral_numeral @ nat @ V ) ) ) ).
% Suc_div_eq_add3_div_numeral
thf(fact_231_div__Suc__eq__div__add3,axiom,
! [M: nat,N: nat] :
( ( divide_divide @ nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
= ( divide_divide @ nat @ M @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) @ N ) ) ) ).
% div_Suc_eq_div_add3
thf(fact_232_divide__zero,axiom,
! [A: $tType] :
( ( semidom_divide @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ) ).
% divide_zero
thf(fact_233_divide__zero__left,axiom,
! [A: $tType] :
( ( semidom_divide @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
= ( zero_zero @ A ) ) ) ).
% divide_zero_left
thf(fact_234_divide__eq__0__iff,axiom,
! [A: $tType] :
( ( field @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( ( divide_divide @ A @ A2 @ B2 )
= ( zero_zero @ A ) )
= ( ( A2
= ( zero_zero @ A ) )
| ( B2
= ( zero_zero @ A ) ) ) ) ) ).
% divide_eq_0_iff
thf(fact_235_divide__cancel__left,axiom,
! [A: $tType] :
( ( field @ A @ ( type2 @ A ) )
=> ! [C2: A,A2: A,B2: A] :
( ( ( divide_divide @ A @ C2 @ A2 )
= ( divide_divide @ A @ C2 @ B2 ) )
= ( ( C2
= ( zero_zero @ A ) )
| ( A2 = B2 ) ) ) ) ).
% divide_cancel_left
thf(fact_236_divide__cancel__right,axiom,
! [A: $tType] :
( ( field @ A @ ( type2 @ A ) )
=> ! [A2: A,C2: A,B2: A] :
( ( ( divide_divide @ A @ A2 @ C2 )
= ( divide_divide @ A @ B2 @ C2 ) )
= ( ( C2
= ( zero_zero @ A ) )
| ( A2 = B2 ) ) ) ) ).
% divide_cancel_right
thf(fact_237_division__ring__divide__zero,axiom,
! [A: $tType] :
( ( division_ring @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ) ).
% division_ring_divide_zero
thf(fact_238_div__0,axiom,
! [A: $tType] :
( ( semiring_div @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
= ( zero_zero @ A ) ) ) ).
% div_0
thf(fact_239_div__by__0,axiom,
! [A: $tType] :
( ( semiring_div @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
= ( zero_zero @ A ) ) ) ).
% div_by_0
thf(fact_240_div__self,axiom,
! [A: $tType] :
( ( semidom_divide @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( A2
!= ( zero_zero @ A ) )
=> ( ( divide_divide @ A @ A2 @ A2 )
= ( one_one @ A ) ) ) ) ).
% div_self
thf(fact_241_divide__eq__1__iff,axiom,
! [A: $tType] :
( ( field @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( ( divide_divide @ A @ A2 @ B2 )
= ( one_one @ A ) )
= ( ( B2
!= ( zero_zero @ A ) )
& ( A2 = B2 ) ) ) ) ).
% divide_eq_1_iff
thf(fact_242_one__eq__divide__iff,axiom,
! [A: $tType] :
( ( field @ A @ ( type2 @ A ) )
=> ! [A2: A,B2: A] :
( ( ( one_one @ A )
= ( divide_divide @ A @ A2 @ B2 ) )
= ( ( B2
!= ( zero_zero @ A ) )
& ( A2 = B2 ) ) ) ) ).
% one_eq_divide_iff
thf(fact_243_divide__self,axiom,
! [A: $tType] :
( ( division_ring @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( A2
!= ( zero_zero @ A ) )
=> ( ( divide_divide @ A @ A2 @ A2 )
= ( one_one @ A ) ) ) ) ).
% divide_self
thf(fact_244_divide__self__if,axiom,
! [A: $tType] :
( ( division_ring @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( ( A2
= ( zero_zero @ A ) )
=> ( ( divide_divide @ A @ A2 @ A2 )
= ( zero_zero @ A ) ) )
& ( ( A2
!= ( zero_zero @ A ) )
=> ( ( divide_divide @ A @ A2 @ A2 )
= ( one_one @ A ) ) ) ) ) ).
% divide_self_if
thf(fact_245_divide__eq__eq__1,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A] :
( ( ( divide_divide @ A @ B2 @ A2 )
= ( one_one @ A ) )
= ( ( A2
!= ( zero_zero @ A ) )
& ( A2 = B2 ) ) ) ) ).
% divide_eq_eq_1
thf(fact_246_eq__divide__eq__1,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A] :
( ( ( one_one @ A )
= ( divide_divide @ A @ B2 @ A2 ) )
= ( ( A2
!= ( zero_zero @ A ) )
& ( A2 = B2 ) ) ) ) ).
% eq_divide_eq_1
thf(fact_247_one__divide__eq__0__iff,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( ( divide_divide @ A @ ( one_one @ A ) @ A2 )
= ( zero_zero @ A ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% one_divide_eq_0_iff
thf(fact_248_zero__eq__1__divide__iff,axiom,
! [A: $tType] :
( ( linordered_field @ A @ ( type2 @ A ) )
=> ! [A2: A] :
( ( ( zero_zero @ A )
= ( divide_divide @ A @ ( one_one @ A ) @ A2 ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% zero_eq_1_divide_iff
thf(fact_249_div__1,axiom,
! [M: nat] :
( ( divide_divide @ nat @ M @ ( suc @ ( zero_zero @ nat ) ) )
= M ) ).
% div_1
thf(fact_250_div__add__self2,axiom,
! [A: $tType] :
( ( semiring_div @ A @ ( type2 @ A ) )
=> ! [B2: A,A2: A] :
( ( B2
!= ( zero_zero @ A ) )
=> ( ( divide_divide @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
= ( plus_plus @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ).
% div_add_self2
%----Type constructors (115)
thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Code__Evaluation_Oterm__of,axiom,
code_term_of @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___HOL_Oequal,axiom,
cl_HOL_Oequal @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1,axiom,
! [A6: $tType,A7: $tType,A8: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) )
& ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
=> ( code_term_of @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2,axiom,
! [A6: $tType,A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3,axiom,
code_term_of @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4,axiom,
cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5,axiom,
code_term_of @ code_term @ ( type2 @ code_term ) ).
thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6,axiom,
cl_HOL_Oequal @ code_term @ ( type2 @ code_term ) ).
thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7,axiom,
code_term_of @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Product__Type_Ounit___HOL_Oequal_8,axiom,
cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( code_term_of @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
thf(tcon_Product__Type_Oprod___HOL_Oequal_10,axiom,
! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_11,axiom,
code_term_of @ typerep @ ( type2 @ typerep ) ).
thf(tcon_Typerep_Otyperep___HOL_Oequal_12,axiom,
cl_HOL_Oequal @ typerep @ ( type2 @ typerep ) ).
thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_13,axiom,
code_term_of @ literal @ ( type2 @ literal ) ).
thf(tcon_String_Oliteral___HOL_Oequal_14,axiom,
cl_HOL_Oequal @ literal @ ( type2 @ literal ) ).
thf(tcon_Simpl__Heap_Oref___Code__Evaluation_Oterm__of_15,axiom,
code_term_of @ simpl_ref @ ( type2 @ simpl_ref ) ).
thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_16,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( code_term_of @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
thf(tcon_Option_Ooption___HOL_Oequal_17,axiom,
! [A6: $tType] : ( cl_HOL_Oequal @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_18,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( code_term_of @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
thf(tcon_Sum__Type_Osum___HOL_Oequal_19,axiom,
! [A6: $tType,A7: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
thf(tcon_List_Olist___Code__Evaluation_Oterm__of_20,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( code_term_of @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
thf(tcon_List_Olist___HOL_Oequal_21,axiom,
! [A6: $tType] : ( cl_HOL_Oequal @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_22,axiom,
code_term_of @ $o @ ( type2 @ $o ) ).
thf(tcon_HOL_Obool___HOL_Oequal_23,axiom,
cl_HOL_Oequal @ $o @ ( type2 @ $o ) ).
thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_24,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( code_term_of @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
thf(tcon_Set_Oset___HOL_Oequal_25,axiom,
! [A6: $tType] :
( ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
=> ( cl_HOL_Oequal @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
thf(tcon_Num_Onum___Code__Evaluation_Oterm__of_26,axiom,
code_term_of @ num @ ( type2 @ num ) ).
thf(tcon_Num_Onum___HOL_Oequal_27,axiom,
cl_HOL_Oequal @ num @ ( type2 @ num ) ).
thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_28,axiom,
code_term_of @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___HOL_Oequal_29,axiom,
cl_HOL_Oequal @ nat @ ( type2 @ nat ) ).
thf(tcon_fun___Code__Evaluation_Oterm__of_30,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( code_term_of @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
thf(tcon_fun___HOL_Oequal_31,axiom,
! [A6: $tType,A7: $tType] :
( ( ( enum @ A6 @ ( type2 @ A6 ) )
& ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) ) )
=> ( cl_HOL_Oequal @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
thf(tcon_fun___Typerep_Otyperep,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( typerep2 @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
thf(tcon_fun___Enum_Oenum,axiom,
! [A6: $tType,A7: $tType] :
( ( ( enum @ A6 @ ( type2 @ A6 ) )
& ( enum @ A7 @ ( type2 @ A7 ) ) )
=> ( enum @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
thf(tcon_Nat_Onat___Typerep_Otyperep_32,axiom,
typerep2 @ nat @ ( type2 @ nat ) ).
thf(tcon_Num_Onum___Typerep_Otyperep_33,axiom,
typerep2 @ num @ ( type2 @ num ) ).
thf(tcon_Set_Oset___Typerep_Otyperep_34,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( typerep2 @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
thf(tcon_Set_Oset___Enum_Oenum_35,axiom,
! [A6: $tType] :
( ( enum @ A6 @ ( type2 @ A6 ) )
=> ( enum @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
thf(tcon_HOL_Obool___Typerep_Otyperep_36,axiom,
typerep2 @ $o @ ( type2 @ $o ) ).
thf(tcon_HOL_Obool___Enum_Oenum_37,axiom,
enum @ $o @ ( type2 @ $o ) ).
thf(tcon_List_Olist___Typerep_Otyperep_38,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( typerep2 @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
thf(tcon_Sum__Type_Osum___Typerep_Otyperep_39,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( typerep2 @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
thf(tcon_Sum__Type_Osum___Enum_Oenum_40,axiom,
! [A6: $tType,A7: $tType] :
( ( ( enum @ A6 @ ( type2 @ A6 ) )
& ( enum @ A7 @ ( type2 @ A7 ) ) )
=> ( enum @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
thf(tcon_Option_Ooption___Typerep_Otyperep_41,axiom,
! [A6: $tType] :
( ( typerep2 @ A6 @ ( type2 @ A6 ) )
=> ( typerep2 @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
thf(tcon_Option_Ooption___Enum_Oenum_42,axiom,
! [A6: $tType] :
( ( enum @ A6 @ ( type2 @ A6 ) )
=> ( enum @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
thf(tcon_Simpl__Heap_Oref___Typerep_Otyperep_43,axiom,
typerep2 @ simpl_ref @ ( type2 @ simpl_ref ) ).
thf(tcon_String_Oliteral___Typerep_Otyperep_44,axiom,
typerep2 @ literal @ ( type2 @ literal ) ).
thf(tcon_Typerep_Otyperep___Typerep_Otyperep_45,axiom,
typerep2 @ typerep @ ( type2 @ typerep ) ).
thf(tcon_Product__Type_Oprod___Typerep_Otyperep_46,axiom,
! [A6: $tType,A7: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) ) )
=> ( typerep2 @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
thf(tcon_Product__Type_Oprod___Enum_Oenum_47,axiom,
! [A6: $tType,A7: $tType] :
( ( ( enum @ A6 @ ( type2 @ A6 ) )
& ( enum @ A7 @ ( type2 @ A7 ) ) )
=> ( enum @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
thf(tcon_Product__Type_Ounit___Typerep_Otyperep_48,axiom,
typerep2 @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Product__Type_Ounit___Enum_Oenum_49,axiom,
enum @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_50,axiom,
typerep2 @ code_term @ ( type2 @ code_term ) ).
thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_51,axiom,
typerep2 @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_52,axiom,
! [A6: $tType,A7: $tType,A8: $tType] :
( ( ( typerep2 @ A6 @ ( type2 @ A6 ) )
& ( typerep2 @ A7 @ ( type2 @ A7 ) )
& ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
=> ( typerep2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Typerep_Otyperep_53,axiom,
typerep2 @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
thf(tcon_fun___Quickcheck__Random_Orandom,axiom,
! [A6: $tType,A7: $tType] :
( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
& ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
& ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
=> ( quickcheck_random @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
semiri456707255roduct @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
canoni770627133id_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Divides_Osemiring__div__parity,axiom,
semiring_div_parity @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_54,axiom,
quickcheck_random @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Rings_Osemidom__divide,axiom,
semidom_divide @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
semigroup_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Divides_Osemiring__div,axiom,
semiring_div @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
semiring_char_0 @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
zero_neq_one @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
monoid_add @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Num_Onumeral,axiom,
numeral @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Ozero,axiom,
zero @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Groups_Oone,axiom,
one @ nat @ ( type2 @ nat ) ).
thf(tcon_Nat_Onat___Nat_Osize,axiom,
size @ nat @ ( type2 @ nat ) ).
thf(tcon_Num_Onum___Quickcheck__Random_Orandom_55,axiom,
quickcheck_random @ num @ ( type2 @ num ) ).
thf(tcon_Num_Onum___Nat_Osize_56,axiom,
size @ num @ ( type2 @ num ) ).
thf(tcon_Set_Oset___Quickcheck__Random_Orandom_57,axiom,
! [A6: $tType] :
( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
=> ( quickcheck_random @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ) ).
thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_58,axiom,
quickcheck_random @ $o @ ( type2 @ $o ) ).
thf(tcon_HOL_Obool___Nat_Osize_59,axiom,
size @ $o @ ( type2 @ $o ) ).
thf(tcon_List_Olist___Quickcheck__Random_Orandom_60,axiom,
! [A6: $tType] :
( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
=> ( quickcheck_random @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ) ).
thf(tcon_List_Olist___Nat_Osize_61,axiom,
! [A6: $tType] : ( size @ ( list @ A6 ) @ ( type2 @ ( list @ A6 ) ) ) ).
thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_62,axiom,
! [A6: $tType,A7: $tType] :
( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
& ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
=> ( quickcheck_random @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ) ).
thf(tcon_Sum__Type_Osum___Nat_Osize_63,axiom,
! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) @ ( type2 @ ( sum_sum @ A6 @ A7 ) ) ) ).
thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_64,axiom,
! [A6: $tType] :
( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
=> ( quickcheck_random @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ) ).
thf(tcon_Option_Ooption___Nat_Osize_65,axiom,
! [A6: $tType] : ( size @ ( option @ A6 ) @ ( type2 @ ( option @ A6 ) ) ) ).
thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_66,axiom,
quickcheck_random @ literal @ ( type2 @ literal ) ).
thf(tcon_String_Oliteral___Nat_Osize_67,axiom,
size @ literal @ ( type2 @ literal ) ).
thf(tcon_Typerep_Otyperep___Nat_Osize_68,axiom,
size @ typerep @ ( type2 @ typerep ) ).
thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_69,axiom,
! [A6: $tType,A7: $tType] :
( ( ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
& ( quickcheck_random @ A7 @ ( type2 @ A7 ) ) )
=> ( quickcheck_random @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ) ).
thf(tcon_Product__Type_Oprod___Nat_Osize_70,axiom,
! [A6: $tType,A7: $tType] : ( size @ ( product_prod @ A6 @ A7 ) @ ( type2 @ ( product_prod @ A6 @ A7 ) ) ) ).
thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_71,axiom,
quickcheck_random @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Product__Type_Ounit___Nat_Osize_72,axiom,
size @ product_unit @ ( type2 @ product_unit ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_73,axiom,
ordere779506340up_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_74,axiom,
cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_75,axiom,
cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_76,axiom,
quickcheck_random @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_77,axiom,
ab_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_78,axiom,
comm_monoid_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_79,axiom,
comm_semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Rings_Osemidom__divide_80,axiom,
semidom_divide @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_81,axiom,
semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Divides_Osemiring__div_82,axiom,
semiring_div @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_83,axiom,
zero_neq_one @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_84,axiom,
monoid_add @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Num_Onumeral_85,axiom,
numeral @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Ozero_86,axiom,
zero @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Groups_Oone_87,axiom,
one @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Code__Numeral_Onatural___Nat_Osize_88,axiom,
size @ code_natural @ ( type2 @ code_natural ) ).
thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_89,axiom,
! [A6: $tType,A7: $tType,A8: $tType] :
( ( ( code_term_of @ A6 @ ( type2 @ A6 ) )
& ( cl_HOL_Oequal @ A6 @ ( type2 @ A6 ) )
& ( quickcheck_random @ A6 @ ( type2 @ A6 ) )
& ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
& ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
=> ( quickcheck_random @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ) ).
thf(tcon_Record_Otuple__isomorphism___Nat_Osize_90,axiom,
! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) @ ( type2 @ ( tuple_isomorphism @ A6 @ A7 @ A8 ) ) ) ).
thf(tcon_BinDag__Mirabelle__rybootvolr_Odag___Nat_Osize_91,axiom,
size @ binDag_Mirabelle_dag @ ( type2 @ binDag_Mirabelle_dag ) ).
%----Helper facts (3)
thf(help_If_3_1_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_T,axiom,
! [A: $tType,X4: A,Y: A] :
( ( if @ A @ $false @ X4 @ Y )
= Y ) ).
thf(help_If_1_1_T,axiom,
! [A: $tType,X4: A,Y: A] :
( ( if @ A @ $true @ X4 @ Y )
= X4 ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
( ( binDag476092410e_Node @ lt @ a @ rt )
!= lt ) ).
%------------------------------------------------------------------------------