%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT137^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:44:54 AM UTC 2026
% Result : Theorem 2.77s 1.60s
% Output : Refutation 2.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT137^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:09:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : DAT137^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.47 % Domain : Data Structures
% 0.20/0.47 % Problem : Coinductive list 4812
% 0.20/0.47 % Version : [Bla16] axioms : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.20/0.47 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.20/0.47 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bla16]
% 0.20/0.47 % Names : coinductive_list__4812.p [Bla16]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.33 v9.1.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.20/0.47 % Syntax : Number of formulae : 359 ( 118 unt; 68 typ; 0 def)
% 0.20/0.47 % Number of atoms : 647 ( 291 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 12 ( 2 avg)
% 0.20/0.47 % Number of connectives : 3388 ( 89 ~; 10 |; 22 &;2975 @)
% 0.20/0.47 % ( 0 <=>; 292 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 23 ( 6 avg)
% 0.20/0.47 % Number of types : 4 ( 3 usr)
% 0.20/0.47 % Number of type conns : 125 ( 125 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 68 ( 65 usr; 5 con; 0-4 aty)
% 0.20/0.47 % Number of variables : 837 ( 14 ^; 746 !; 24 ?; 837 :)
% 0.20/0.47 % ( 53 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.47 % SPC : TH1_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.20/0.47 % 2016-07-13 15:09:14.032
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 %----Could-be-implicit typings (6)
% 0.20/0.47 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.20/0.47 coindu1593790203_llist: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Extended__Nat_Oenat,type,
% 0.20/0.47 extended_enat: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_List_Olist,type,
% 0.20/0.47 list: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Num_Onum,type,
% 0.20/0.47 num: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Nat_Onat,type,
% 0.20/0.47 nat: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_itself,type,
% 0.20/0.47 itself: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 %----Explicit typings (62)
% 0.20/0.47 thf(sy_cl_HOL_Otype,type,
% 0.20/0.47 type:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oone,type,
% 0.20/0.47 one:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Num_Onumeral,type,
% 0.20/0.47 numeral:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Rings_Oring__1,type,
% 0.20/0.47 ring_1:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Ouminus,type,
% 0.20/0.47 uminus:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.47 ord:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Nat_Oring__char__0,type,
% 0.20/0.47 ring_char_0:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Num_Oneg__numeral,type,
% 0.20/0.47 neg_numeral:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.20/0.47 order:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.20/0.47 group_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.47 linorder:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oab__group__add,type,
% 0.20/0.47 ab_group_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.20/0.47 semiring_char_0:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.20/0.47 semigroup_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.20/0.47 comm_semiring_1:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.20/0.47 linordered_idom:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Fields_Olinordered__field,type,
% 0.20/0.47 linordered_field:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.20/0.47 ab_semigroup_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.20/0.47 linordered_semidom:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.20/0.47 cancel_semigroup_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.20/0.47 ordered_ab_group_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.20/0.47 ordere779506340up_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.20/0.47 ordere236663937imp_le:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.20/0.47 ordere223160158up_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.20/0.47 strict2144017051up_add:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.20/0.47 condit1656338222tinuum:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 0.20/0.47 coindu493225792length:
% 0.20/0.47 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux,type,
% 0.20/0.47 coindu1542816657of_aux:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.20/0.47 coindu1121789889_LCons:
% 0.20/0.47 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.20/0.47 coindu1598213697e_LNil:
% 0.20/0.47 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of,type,
% 0.20/0.47 coindu1079202755ist_of:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.20/0.47 coindu567634248member:
% 0.20/0.47 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.20/0.47 one_one:
% 0.20/0.47 !>[A: $tType] : A ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.20/0.47 plus_plus:
% 0.20/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.20/0.47 uminus_uminus:
% 0.20/0.47 !>[A: $tType] : ( A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_If,type,
% 0.20/0.47 if:
% 0.20/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Ocount__list,type,
% 0.20/0.47 count_list:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Ogen__length,type,
% 0.20/0.47 gen_length:
% 0.20/0.47 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Olist_OCons,type,
% 0.20/0.47 cons:
% 0.20/0.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Olist_ONil,type,
% 0.20/0.47 nil:
% 0.20/0.47 !>[A: $tType] : ( list @ A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Omember,type,
% 0.20/0.47 member:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Onth,type,
% 0.20/0.47 nth:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.20/0.47 ord_lexordp_eq:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Oproduct__lists,type,
% 0.20/0.47 product_lists:
% 0.20/0.47 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Osublists,type,
% 0.20/0.47 sublists:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_List_Oupt,type,
% 0.20/0.47 upt: nat > nat > ( list @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Nat_OSuc,type,
% 0.20/0.47 suc: nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.20/0.47 nat_triangle: nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_OBitM,type,
% 0.20/0.47 bitM: num > num ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Oinc,type,
% 0.20/0.47 inc: num > num ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.20/0.47 neg_numeral_dbl:
% 0.20/0.47 !>[A: $tType] : ( A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 0.20/0.47 neg_numeral_dbl_dec:
% 0.20/0.47 !>[A: $tType] : ( A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Oneg__numeral__class_Osub,type,
% 0.20/0.47 neg_numeral_sub:
% 0.20/0.47 !>[A: $tType] : ( num > num > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Onum_OBit0,type,
% 0.20/0.47 bit0: num > num ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Onum_OOne,type,
% 0.20/0.47 one2: num ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.20/0.47 numeral_numeral:
% 0.20/0.47 !>[A: $tType] : ( num > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Num_Oring__1__class_Oiszero,type,
% 0.20/0.47 ring_1_iszero:
% 0.20/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.20/0.47 ord_less:
% 0.20/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Pure_Otype,type,
% 0.20/0.47 type2:
% 0.20/0.47 !>[A: $tType] : ( itself @ A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sublist_Oprefixes,type,
% 0.20/0.47 prefixes:
% 0.20/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_ma____,type,
% 0.20/0.47 ma: nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_na____,type,
% 0.20/0.47 na: nat ).
% 0.20/0.47
% 0.20/0.47 %----Relevant facts (251)
% 0.20/0.47 thf(fact_0_llist__of__inject,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.47 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.20/0.47 = ( coindu1079202755ist_of @ A @ Ys ) )
% 0.20/0.47 = ( Xs = Ys ) ) ).
% 0.20/0.47
% 0.20/0.47 % llist_of_inject
% 0.20/0.47 thf(fact_1_add__Suc__right,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 0.20/0.47 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_Suc_right
% 0.20/0.47 thf(fact_2_upt__conv__Cons__Cons,axiom,
% 0.20/0.47 ! [M: nat,N: nat,Ns: list @ nat,Q: nat] :
% 0.20/0.47 ( ( ( cons @ nat @ M @ ( cons @ nat @ N @ Ns ) )
% 0.20/0.47 = ( upt @ M @ Q ) )
% 0.20/0.47 = ( ( cons @ nat @ N @ Ns )
% 0.20/0.47 = ( upt @ ( suc @ M ) @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % upt_conv_Cons_Cons
% 0.20/0.47 thf(fact_3_nat_Oinject,axiom,
% 0.20/0.47 ! [X2: nat,Y2: nat] :
% 0.20/0.47 ( ( ( suc @ X2 )
% 0.20/0.47 = ( suc @ Y2 ) )
% 0.20/0.47 = ( X2 = Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat.inject
% 0.20/0.47 thf(fact_4_old_Onat_Oinject,axiom,
% 0.20/0.47 ! [Nat: nat,Nat2: nat] :
% 0.20/0.47 ( ( ( suc @ Nat )
% 0.20/0.47 = ( suc @ Nat2 ) )
% 0.20/0.47 = ( Nat = Nat2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.nat.inject
% 0.20/0.47 thf(fact_5_add__left__cancel,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.47 = ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_left_cancel
% 0.20/0.47 thf(fact_6_add__right__cancel,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.47 = ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_right_cancel
% 0.20/0.47 thf(fact_7_list_Oinject,axiom,
% 0.20/0.47 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.20/0.47 ( ( ( cons @ A @ X21 @ X22 )
% 0.20/0.47 = ( cons @ A @ Y21 @ Y22 ) )
% 0.20/0.47 = ( ( X21 = Y21 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % list.inject
% 0.20/0.47 thf(fact_8_add__Suc__shift,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.20/0.47 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_Suc_shift
% 0.20/0.47 thf(fact_9_add__Suc,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.20/0.47 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_Suc
% 0.20/0.47 thf(fact_10__092_060open_062_092_060And_062xs_Ax_O_ALCons_Ax_A_Illist__of_Axs_J_A_061_Allist__of_A_Ix_A_D_Axs_J_092_060close_062,axiom,
% 0.20/0.47 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.47 ( ( coindu1121789889_LCons @ A @ X @ ( coindu1079202755ist_of @ A @ Xs ) )
% 0.20/0.47 = ( coindu1079202755ist_of @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<And>xs x. LCons x (llist_of xs) = llist_of (x # xs)\<close>
% 0.20/0.47 thf(fact_11_nat__add__left__cancel,axiom,
% 0.20/0.47 ! [K: nat,M: nat,N: nat] :
% 0.20/0.47 ( ( ( plus_plus @ nat @ K @ M )
% 0.20/0.47 = ( plus_plus @ nat @ K @ N ) )
% 0.20/0.47 = ( M = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_add_left_cancel
% 0.20/0.47 thf(fact_12_llist_Oinject,axiom,
% 0.20/0.47 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.20/0.47 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.20/0.47 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.20/0.47 = ( ( X21 = Y21 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % llist.inject
% 0.20/0.47 thf(fact_13_llist__of__eq__LCons__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.20/0.47 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.20/0.47 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.20/0.47 = ( ? [Xs2: list @ A] :
% 0.20/0.47 ( ( Xs
% 0.20/0.47 = ( cons @ A @ Y @ Xs2 ) )
% 0.20/0.47 & ( Ys
% 0.20/0.47 = ( coindu1079202755ist_of @ A @ Xs2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % llist_of_eq_LCons_conv
% 0.20/0.47 thf(fact_14_not__Cons__self2,axiom,
% 0.20/0.47 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.47 ( ( cons @ A @ X @ Xs )
% 0.20/0.47 != Xs ) ).
% 0.20/0.47
% 0.20/0.47 % not_Cons_self2
% 0.20/0.47 thf(fact_15_add__right__imp__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.47 => ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_right_imp_eq
% 0.20/0.47 thf(fact_16_add__left__imp__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.47 => ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_left_imp_eq
% 0.20/0.47 thf(fact_17_add_Oleft__commute,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A,C: A] :
% 0.20/0.47 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.left_commute
% 0.20/0.47 thf(fact_18_add_Ocommute,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( plus_plus @ A )
% 0.20/0.47 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.commute
% 0.20/0.47 thf(fact_19_add_Oright__cancel,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.47 = ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.right_cancel
% 0.20/0.47 thf(fact_20_add_Oleft__cancel,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.47 = ( B = C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.left_cancel
% 0.20/0.47 thf(fact_21_add_Oassoc,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.assoc
% 0.20/0.47 thf(fact_22_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.20/0.47 ( ( ( I = J )
% 0.20/0.47 & ( K = L ) )
% 0.20/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.20/0.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_mono_thms_linordered_semiring(4)
% 0.20/0.47 thf(fact_23_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.20/0.47 thf(fact_24_n__not__Suc__n,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ( N
% 0.20/0.47 != ( suc @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % n_not_Suc_n
% 0.20/0.47 thf(fact_25_Suc__inject,axiom,
% 0.20/0.47 ! [X: nat,Y: nat] :
% 0.20/0.47 ( ( ( suc @ X )
% 0.20/0.47 = ( suc @ Y ) )
% 0.20/0.47 => ( X = Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % Suc_inject
% 0.20/0.47 thf(fact_26_nat__add__right__cancel,axiom,
% 0.20/0.47 ! [M: nat,K: nat,N: nat] :
% 0.20/0.47 ( ( ( plus_plus @ nat @ M @ K )
% 0.20/0.47 = ( plus_plus @ nat @ N @ K ) )
% 0.20/0.47 = ( M = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_add_right_cancel
% 0.20/0.47 thf(fact_27_list__of__aux__code_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.20/0.47 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.20/0.47 = ( coindu1542816657of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 0.20/0.47
% 0.20/0.47 % list_of_aux_code(2)
% 0.20/0.47 thf(fact_28_gen__length__code_I2_J,axiom,
% 0.20/0.47 ! [B3: $tType,N: nat,X: B3,Xs: list @ B3] :
% 0.20/0.47 ( ( gen_length @ B3 @ N @ ( cons @ B3 @ X @ Xs ) )
% 0.20/0.47 = ( gen_length @ B3 @ ( suc @ N ) @ Xs ) ) ).
% 0.20/0.47
% 0.20/0.47 % gen_length_code(2)
% 0.20/0.47 thf(fact_29_upt__conv__Cons,axiom,
% 0.20/0.47 ! [I: nat,J: nat] :
% 0.20/0.47 ( ( ord_less @ nat @ I @ J )
% 0.20/0.47 => ( ( upt @ I @ J )
% 0.20/0.47 = ( cons @ nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % upt_conv_Cons
% 0.20/0.47 thf(fact_30_lmember__code_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.20/0.47 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.20/0.47 = ( ( X = Y )
% 0.20/0.47 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lmember_code(2)
% 0.20/0.47 thf(fact_31_semiring__normalization__rules_I20_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) )
% 0.20/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(20)
% 0.32/0.47 thf(fact_32_semiring__normalization__rules_I21_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.32/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(21)
% 0.32/0.47 thf(fact_33_semiring__normalization__rules_I22_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,C: A,D: A] :
% 0.32/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 0.32/0.47 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(22)
% 0.32/0.47 thf(fact_34_semiring__normalization__rules_I23_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.32/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(23)
% 0.32/0.47 thf(fact_35_semiring__normalization__rules_I24_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( plus_plus @ A )
% 0.32/0.47 = ( ^ [A3: A,C2: A] : ( plus_plus @ A @ C2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(24)
% 0.32/0.47 thf(fact_36_semiring__normalization__rules_I25_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,C: A,D: A] :
% 0.32/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 0.32/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ D ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_normalization_rules(25)
% 0.32/0.47 thf(fact_37_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.32/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linordered_field_class.sign_simps(26)
% 0.32/0.47 thf(fact_38_add__less__cancel__left,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [C: A,A2: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.32/0.47 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_cancel_left
% 0.32/0.47 thf(fact_39_add__less__cancel__right,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,C: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.32/0.47 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_cancel_right
% 0.32/0.47 thf(fact_40_lessI,axiom,
% 0.32/0.47 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % lessI
% 0.32/0.47 thf(fact_41_Suc__mono,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_mono
% 0.32/0.47 thf(fact_42_Suc__less__eq,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.47 = ( ord_less @ nat @ M @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_less_eq
% 0.32/0.47 thf(fact_43_nat__add__left__cancel__less,axiom,
% 0.32/0.47 ! [K: nat,M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.32/0.47 = ( ord_less @ nat @ M @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % nat_add_left_cancel_less
% 0.32/0.47 thf(fact_44_nat__neq__iff,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( M != N )
% 0.32/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nat_neq_iff
% 0.32/0.47 thf(fact_45_less__not__refl,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.32/0.47
% 0.32/0.47 % less_not_refl
% 0.32/0.47 thf(fact_46_less__not__refl2,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ N @ M )
% 0.32/0.47 => ( M != N ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_not_refl2
% 0.32/0.47 thf(fact_47_less__not__refl3,axiom,
% 0.32/0.47 ! [S: nat,T: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ S @ T )
% 0.32/0.47 => ( S != T ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_not_refl3
% 0.32/0.47 thf(fact_48_measure__induct,axiom,
% 0.32/0.47 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ! [Y3: A] :
% 0.32/0.47 ( ( ord_less @ nat @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.32/0.47 => ( P @ Y3 ) )
% 0.32/0.47 => ( P @ X3 ) )
% 0.32/0.47 => ( P @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % measure_induct
% 0.32/0.47 thf(fact_49_less__irrefl__nat,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.32/0.47
% 0.32/0.47 % less_irrefl_nat
% 0.32/0.47 thf(fact_50_nat__less__induct,axiom,
% 0.32/0.47 ! [P: nat > $o,N: nat] :
% 0.32/0.47 ( ! [N2: nat] :
% 0.32/0.47 ( ! [M2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M2 @ N2 )
% 0.32/0.47 => ( P @ M2 ) )
% 0.32/0.47 => ( P @ N2 ) )
% 0.32/0.47 => ( P @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % nat_less_induct
% 0.32/0.47 thf(fact_51_infinite__descent,axiom,
% 0.32/0.47 ! [P: nat > $o,N: nat] :
% 0.32/0.47 ( ! [N2: nat] :
% 0.32/0.47 ( ~ ( P @ N2 )
% 0.32/0.47 => ? [M2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M2 @ N2 )
% 0.32/0.47 & ~ ( P @ M2 ) ) )
% 0.32/0.47 => ( P @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % infinite_descent
% 0.32/0.47 thf(fact_52_linorder__neqE__nat,axiom,
% 0.32/0.47 ! [X: nat,Y: nat] :
% 0.32/0.47 ( ( X != Y )
% 0.32/0.47 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.32/0.47 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linorder_neqE_nat
% 0.32/0.47 thf(fact_53_measure__induct__rule,axiom,
% 0.32/0.47 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ! [Y3: A] :
% 0.32/0.47 ( ( ord_less @ nat @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.32/0.47 => ( P @ Y3 ) )
% 0.32/0.47 => ( P @ X3 ) )
% 0.32/0.47 => ( P @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % measure_induct_rule
% 0.32/0.47 thf(fact_54_infinite__descent__measure,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ~ ( P @ X3 )
% 0.32/0.47 => ? [Y3: A] :
% 0.32/0.47 ( ( ord_less @ nat @ ( V @ Y3 ) @ ( V @ X3 ) )
% 0.32/0.47 & ~ ( P @ Y3 ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % infinite_descent_measure
% 0.32/0.47 thf(fact_55_linordered__field__no__ub,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X4: A] :
% 0.32/0.47 ? [X1: A] : ( ord_less @ A @ X4 @ X1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % linordered_field_no_ub
% 0.32/0.47 thf(fact_56_linordered__field__no__lb,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X4: A] :
% 0.32/0.47 ? [Y4: A] : ( ord_less @ A @ Y4 @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % linordered_field_no_lb
% 0.32/0.47 thf(fact_57_lift__Suc__mono__less__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [F: nat > A,N: nat,M: nat] :
% 0.32/0.47 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.47 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.47 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lift_Suc_mono_less_iff
% 0.32/0.47 thf(fact_58_lift__Suc__mono__less,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [F: nat > A,N: nat,N3: nat] :
% 0.32/0.47 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.47 => ( ( ord_less @ nat @ N @ N3 )
% 0.32/0.47 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lift_Suc_mono_less
% 0.32/0.47 thf(fact_59_add__mono__thms__linordered__field_I5_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.32/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.32/0.47 & ( ord_less @ A @ K @ L ) )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_mono_thms_linordered_field(5)
% 0.32/0.47 thf(fact_60_add__mono__thms__linordered__field_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.32/0.47 ( ( ( I = J )
% 0.32/0.47 & ( ord_less @ A @ K @ L ) )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_mono_thms_linordered_field(2)
% 0.32/0.47 thf(fact_61_add__mono__thms__linordered__field_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.32/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.32/0.47 & ( K = L ) )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_mono_thms_linordered_field(1)
% 0.32/0.47 thf(fact_62_add__strict__mono,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.32/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.32/0.47 => ( ( ord_less @ A @ C @ D )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_strict_mono
% 0.32/0.47 thf(fact_63_add__strict__left__mono,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_strict_left_mono
% 0.32/0.47 thf(fact_64_add__strict__right__mono,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.32/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_strict_right_mono
% 0.32/0.47 thf(fact_65_add__less__imp__less__left,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [C: A,A2: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.32/0.47 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_imp_less_left
% 0.32/0.47 thf(fact_66_add__less__imp__less__right,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,C: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.32/0.47 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_imp_less_right
% 0.32/0.47 thf(fact_67_lessE,axiom,
% 0.32/0.47 ! [I: nat,K: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ K )
% 0.32/0.47 => ( ( K
% 0.32/0.47 != ( suc @ I ) )
% 0.32/0.47 => ~ ! [J2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J2 )
% 0.32/0.47 => ( K
% 0.32/0.47 != ( suc @ J2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lessE
% 0.32/0.47 thf(fact_68_Suc__lessD,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.32/0.47 => ( ord_less @ nat @ M @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_lessD
% 0.32/0.47 thf(fact_69_Suc__lessE,axiom,
% 0.32/0.47 ! [I: nat,K: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.32/0.47 => ~ ! [J2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J2 )
% 0.32/0.47 => ( K
% 0.32/0.47 != ( suc @ J2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_lessE
% 0.32/0.47 thf(fact_70_Suc__lessI,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 => ( ( ( suc @ M )
% 0.32/0.47 != N )
% 0.32/0.47 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_lessI
% 0.32/0.47 thf(fact_71_less__SucE,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.32/0.47 => ( ~ ( ord_less @ nat @ M @ N )
% 0.32/0.47 => ( M = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_SucE
% 0.32/0.47 thf(fact_72_less__SucI,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_SucI
% 0.32/0.47 thf(fact_73_less__Suc__eq,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.32/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 | ( M = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_Suc_eq
% 0.32/0.47 thf(fact_74_not__less__eq,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.32/0.47 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_less_eq
% 0.32/0.47 thf(fact_75_Suc__less__eq2,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.32/0.47 = ( ? [M3: nat] :
% 0.32/0.47 ( ( M
% 0.32/0.47 = ( suc @ M3 ) )
% 0.32/0.47 & ( ord_less @ nat @ N @ M3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_less_eq2
% 0.32/0.47 thf(fact_76_less__antisym,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ~ ( ord_less @ nat @ N @ M )
% 0.32/0.47 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.32/0.47 => ( M = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_antisym
% 0.32/0.47 thf(fact_77_Suc__less__SucD,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.47 => ( ord_less @ nat @ M @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_less_SucD
% 0.32/0.47 thf(fact_78_less__trans__Suc,axiom,
% 0.32/0.47 ! [I: nat,J: nat,K: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ( ord_less @ nat @ J @ K )
% 0.32/0.47 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_trans_Suc
% 0.32/0.47 thf(fact_79_less__Suc__induct,axiom,
% 0.32/0.47 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.32/0.47 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I2 @ J2 )
% 0.32/0.47 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.32/0.47 => ( ( P @ I2 @ J2 )
% 0.32/0.47 => ( ( P @ J2 @ K2 )
% 0.32/0.47 => ( P @ I2 @ K2 ) ) ) ) )
% 0.32/0.47 => ( P @ I @ J ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_Suc_induct
% 0.32/0.47 thf(fact_80_strict__inc__induct,axiom,
% 0.32/0.47 ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ! [I2: nat] :
% 0.32/0.47 ( ( J
% 0.32/0.47 = ( suc @ I2 ) )
% 0.32/0.47 => ( P @ I2 ) )
% 0.32/0.47 => ( ! [I2: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I2 @ J )
% 0.32/0.47 => ( ( P @ ( suc @ I2 ) )
% 0.32/0.47 => ( P @ I2 ) ) )
% 0.32/0.47 => ( P @ I ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % strict_inc_induct
% 0.32/0.47 thf(fact_81_not__less__less__Suc__eq,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ~ ( ord_less @ nat @ N @ M )
% 0.32/0.47 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.32/0.47 = ( N = M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_less_less_Suc_eq
% 0.32/0.47 thf(fact_82_add__lessD1,axiom,
% 0.32/0.47 ! [I: nat,J: nat,K: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.32/0.47 => ( ord_less @ nat @ I @ K ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_lessD1
% 0.32/0.47 thf(fact_83_add__less__mono,axiom,
% 0.32/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ( ord_less @ nat @ K @ L )
% 0.32/0.47 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_mono
% 0.32/0.47 thf(fact_84_not__add__less1,axiom,
% 0.32/0.47 ! [I: nat,J: nat] :
% 0.32/0.47 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.32/0.47
% 0.32/0.47 % not_add_less1
% 0.32/0.47 thf(fact_85_not__add__less2,axiom,
% 0.32/0.47 ! [J: nat,I: nat] :
% 0.32/0.47 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.32/0.47
% 0.32/0.47 % not_add_less2
% 0.32/0.47 thf(fact_86_add__less__mono1,axiom,
% 0.32/0.47 ! [I: nat,J: nat,K: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_less_mono1
% 0.32/0.47 thf(fact_87_trans__less__add1,axiom,
% 0.32/0.47 ! [I: nat,J: nat,M: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % trans_less_add1
% 0.32/0.47 thf(fact_88_trans__less__add2,axiom,
% 0.32/0.47 ! [I: nat,J: nat,M: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % trans_less_add2
% 0.32/0.47 thf(fact_89_less__add__eq__less,axiom,
% 0.32/0.47 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ K @ L )
% 0.32/0.47 => ( ( ( plus_plus @ nat @ M @ L )
% 0.32/0.47 = ( plus_plus @ nat @ K @ N ) )
% 0.32/0.47 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_add_eq_less
% 0.32/0.47 thf(fact_90_less__add__Suc1,axiom,
% 0.32/0.47 ! [I: nat,M: nat] : ( ord_less @ nat @ I @ ( suc @ ( plus_plus @ nat @ I @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_add_Suc1
% 0.32/0.47 thf(fact_91_less__add__Suc2,axiom,
% 0.32/0.47 ! [I: nat,M: nat] : ( ord_less @ nat @ I @ ( suc @ ( plus_plus @ nat @ M @ I ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_add_Suc2
% 0.32/0.47 thf(fact_92_less__iff__Suc__add,axiom,
% 0.32/0.47 ( ( ord_less @ nat )
% 0.32/0.47 = ( ^ [M4: nat,N4: nat] :
% 0.32/0.47 ? [K3: nat] :
% 0.32/0.47 ( N4
% 0.32/0.47 = ( suc @ ( plus_plus @ nat @ M4 @ K3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_iff_Suc_add
% 0.32/0.47 thf(fact_93_less__imp__Suc__add,axiom,
% 0.32/0.47 ! [M: nat,N: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ M @ N )
% 0.32/0.47 => ? [K2: nat] :
% 0.32/0.47 ( N
% 0.32/0.47 = ( suc @ ( plus_plus @ nat @ M @ K2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_Suc_add
% 0.32/0.47 thf(fact_94_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [B: A,A2: A,C: A] :
% 0.32/0.47 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.32/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linordered_field_class.sign_simps(28)
% 0.32/0.47 thf(fact_95_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( plus_plus @ A )
% 0.32/0.47 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linordered_field_class.sign_simps(27)
% 0.32/0.47 thf(fact_96_upt__eq__Cons__conv,axiom,
% 0.32/0.47 ! [I: nat,J: nat,X: nat,Xs: list @ nat] :
% 0.32/0.47 ( ( ( upt @ I @ J )
% 0.32/0.47 = ( cons @ nat @ X @ Xs ) )
% 0.32/0.47 = ( ( ord_less @ nat @ I @ J )
% 0.32/0.47 & ( I = X )
% 0.32/0.47 & ( ( upt @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) @ J )
% 0.32/0.47 = Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % upt_eq_Cons_conv
% 0.32/0.47 thf(fact_97_upt__rec,axiom,
% 0.32/0.47 ( upt
% 0.32/0.47 = ( ^ [I3: nat,J3: nat] : ( if @ ( list @ nat ) @ ( ord_less @ nat @ I3 @ J3 ) @ ( cons @ nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ ( nil @ nat ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % upt_rec
% 0.32/0.47 thf(fact_98_nth__upt,axiom,
% 0.32/0.47 ! [I: nat,K: nat,J: nat] :
% 0.32/0.47 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ J )
% 0.32/0.47 => ( ( nth @ nat @ ( upt @ I @ J ) @ K )
% 0.32/0.47 = ( plus_plus @ nat @ I @ K ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nth_upt
% 0.32/0.47 thf(fact_99_lexordp__eq__simps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.32/0.47 = ( ( ord_less @ A @ X @ Y )
% 0.32/0.47 | ( ~ ( ord_less @ A @ Y @ X )
% 0.32/0.47 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(4)
% 0.32/0.47 thf(fact_100_is__num__normalize_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A,C: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.32/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % is_num_normalize(1)
% 0.32/0.47 thf(fact_101_member__rec_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Xs: list @ A,Y: A] :
% 0.32/0.47 ( ( member @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 0.32/0.47 = ( ( X = Y )
% 0.32/0.47 | ( member @ A @ Xs @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % member_rec(1)
% 0.32/0.47 thf(fact_102_ex__gt__or__lt,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A] :
% 0.32/0.47 ? [B4: A] :
% 0.32/0.47 ( ( ord_less @ A @ A2 @ B4 )
% 0.32/0.47 | ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ex_gt_or_lt
% 0.32/0.47 thf(fact_103_linorder__neqE__linordered__idom,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A,Y: A] :
% 0.32/0.47 ( ( X != Y )
% 0.32/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.32/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linorder_neqE_linordered_idom
% 0.32/0.47 thf(fact_104_lexordp__eq__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(1)
% 0.32/0.47 thf(fact_105_lexordp__eq__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Xs: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(2)
% 0.32/0.47 thf(fact_106_nth__Cons__Suc,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Xs: list @ A,N: nat] :
% 0.32/0.47 ( ( nth @ A @ ( cons @ A @ X @ Xs ) @ ( suc @ N ) )
% 0.32/0.47 = ( nth @ A @ Xs @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % nth_Cons_Suc
% 0.32/0.47 thf(fact_107_lexordp__eq__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A,Xs: list @ A] :
% 0.32/0.47 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(3)
% 0.32/0.47 thf(fact_108_less__numeral__extra_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_numeral_extra(4)
% 0.32/0.47 thf(fact_109_transpose_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,X: list @ ( list @ A )] :
% 0.32/0.47 ( ( X
% 0.32/0.47 != ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ( ! [Xss: list @ ( list @ A )] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.32/0.47 => ~ ! [X3: A,Xs3: list @ A,Xss: list @ ( list @ A )] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs3 ) @ Xss ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % transpose.cases
% 0.32/0.47 thf(fact_110_lexordp__eq__antisym,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Xs: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 0.32/0.47 => ( Xs = Ys ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_antisym
% 0.32/0.47 thf(fact_111_lexordp__eq__linear,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Xs: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.32/0.47 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_linear
% 0.32/0.47 thf(fact_112_lexordp__eq__trans,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 0.32/0.47 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_trans
% 0.32/0.47 thf(fact_113_lexordp__eq__refl,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_refl
% 0.32/0.47 thf(fact_114_lexordp__eq_ONil,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.Nil
% 0.32/0.47 thf(fact_115_one__reorient,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( one @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A] :
% 0.32/0.47 ( ( ( one_one @ A )
% 0.32/0.47 = X )
% 0.32/0.47 = ( X
% 0.32/0.47 = ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_reorient
% 0.32/0.47 thf(fact_116_member__rec_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Y: A] :
% 0.32/0.47 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 0.32/0.47
% 0.32/0.47 % member_rec(2)
% 0.32/0.47 thf(fact_117_lexordp__eq_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X12: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ X12 @ X2 )
% 0.32/0.47 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.32/0.47 => ( ! [X3: A,Y4: A,Xs3: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 0.32/0.47 => ( ! [X3: A,Y4: A,Xs3: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ~ ( ord_less @ A @ X3 @ Y4 )
% 0.32/0.47 => ( ~ ( ord_less @ A @ Y4 @ X3 )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Xs3 @ Ys2 )
% 0.32/0.47 => ( ( P @ Xs3 @ Ys2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) ) ) )
% 0.32/0.47 => ( P @ X12 @ X2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.inducts
% 0.32/0.47 thf(fact_118_lexordp__eq_Osimps,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A )
% 0.32/0.47 = ( ^ [A1: list @ A,A22: list @ A] :
% 0.32/0.47 ( ? [Ys3: list @ A] :
% 0.32/0.47 ( ( A1
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( A22 = Ys3 ) )
% 0.32/0.47 | ? [X5: A,Y5: A,Xs4: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ( A1
% 0.32/0.47 = ( cons @ A @ X5 @ Xs4 ) )
% 0.32/0.47 & ( A22
% 0.32/0.47 = ( cons @ A @ Y5 @ Ys3 ) )
% 0.32/0.47 & ( ord_less @ A @ X5 @ Y5 ) )
% 0.32/0.47 | ? [X5: A,Y5: A,Xs4: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ( A1
% 0.32/0.47 = ( cons @ A @ X5 @ Xs4 ) )
% 0.32/0.47 & ( A22
% 0.32/0.47 = ( cons @ A @ Y5 @ Ys3 ) )
% 0.32/0.47 & ~ ( ord_less @ A @ X5 @ Y5 )
% 0.32/0.47 & ~ ( ord_less @ A @ Y5 @ X5 )
% 0.32/0.47 & ( ord_lexordp_eq @ A @ Xs4 @ Ys3 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.simps
% 0.32/0.47 thf(fact_119_lexordp__eq_Ocases,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A12: list @ A,A23: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ A12 @ A23 )
% 0.32/0.47 => ( ( ( A12
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ! [Ys2: list @ A] : ( A23 != Ys2 ) )
% 0.32/0.47 => ( ! [X3: A] :
% 0.32/0.47 ( ? [Xs3: list @ A] :
% 0.32/0.47 ( A12
% 0.32/0.47 = ( cons @ A @ X3 @ Xs3 ) )
% 0.32/0.47 => ! [Y4: A] :
% 0.32/0.47 ( ? [Ys2: list @ A] :
% 0.32/0.47 ( A23
% 0.32/0.47 = ( cons @ A @ Y4 @ Ys2 ) )
% 0.32/0.47 => ~ ( ord_less @ A @ X3 @ Y4 ) ) )
% 0.32/0.47 => ~ ! [X3: A,Y4: A,Xs3: list @ A] :
% 0.32/0.47 ( ( A12
% 0.32/0.47 = ( cons @ A @ X3 @ Xs3 ) )
% 0.32/0.47 => ! [Ys2: list @ A] :
% 0.32/0.47 ( ( A23
% 0.32/0.47 = ( cons @ A @ Y4 @ Ys2 ) )
% 0.32/0.47 => ( ~ ( ord_less @ A @ X3 @ Y4 )
% 0.32/0.47 => ( ~ ( ord_less @ A @ Y4 @ X3 )
% 0.32/0.47 => ~ ( ord_lexordp_eq @ A @ Xs3 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.cases
% 0.32/0.47 thf(fact_120_map__tailrec__rev_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,B3: $tType,P: ( A > B3 ) > ( list @ A ) > ( list @ B3 ) > $o,A0: A > B3,A12: list @ A,A23: list @ B3] :
% 0.32/0.47 ( ! [F2: A > B3,X1: list @ B3] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 0.32/0.47 => ( ! [F2: A > B3,A4: A,As: list @ A,Bs: list @ B3] :
% 0.32/0.47 ( ( P @ F2 @ As @ ( cons @ B3 @ ( F2 @ A4 ) @ Bs ) )
% 0.32/0.47 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.32/0.47 => ( P @ A0 @ A12 @ A23 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_rev.induct
% 0.32/0.47 thf(fact_121_list__nonempty__induct,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: list @ A] :
% 0.32/0.47 ( ( Xs3
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( P @ Xs3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_nonempty_induct
% 0.32/0.47 thf(fact_122_remdups__adj_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X3: A,Y4: A,Xs3: list @ A] :
% 0.32/0.47 ( ( ( X3 = Y4 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) )
% 0.32/0.47 => ( ( ( X3 != Y4 )
% 0.32/0.47 => ( P @ ( cons @ A @ Y4 @ Xs3 ) ) )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y4 @ Xs3 ) ) ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.induct
% 0.32/0.47 thf(fact_123_remdups__adj_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,X: list @ A] :
% 0.32/0.47 ( ( X
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X3: A] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 => ~ ! [X3: A,Y4: A,Xs3: list @ A] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ A @ X3 @ ( cons @ A @ Y4 @ Xs3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.cases
% 0.32/0.47 thf(fact_124_splice_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A12: list @ A] :
% 0.32/0.47 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.32/0.47 => ( ! [V2: A,Va: list @ A] : ( P @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: list @ A,Y4: A,Ys2: list @ A] :
% 0.32/0.47 ( ( P @ Xs3 @ Ys2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 0.32/0.47 => ( P @ A0 @ A12 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % splice.induct
% 0.32/0.47 thf(fact_125_list__induct2_H,axiom,
% 0.32/0.47 ! [A: $tType,B3: $tType,P: ( list @ A ) > ( list @ B3 ) > $o,Xs: list @ A,Ys: list @ B3] :
% 0.32/0.47 ( ( P @ ( nil @ A ) @ ( nil @ B3 ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: list @ A] : ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( nil @ B3 ) )
% 0.32/0.47 => ( ! [Y4: B3,Ys2: list @ B3] : ( P @ ( nil @ A ) @ ( cons @ B3 @ Y4 @ Ys2 ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: list @ A,Y4: B3,Ys2: list @ B3] :
% 0.32/0.47 ( ( P @ Xs3 @ Ys2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ B3 @ Y4 @ Ys2 ) ) )
% 0.32/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_induct2'
% 0.32/0.47 thf(fact_126_neq__Nil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 = ( ? [Y5: A,Ys3: list @ A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neq_Nil_conv
% 0.32/0.47 thf(fact_127_list_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X1: A,X23: list @ A] :
% 0.32/0.47 ( ( P @ X23 )
% 0.32/0.47 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.32/0.47 => ( P @ List ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.inducts
% 0.32/0.47 thf(fact_128_list_Oexhaust,axiom,
% 0.32/0.47 ! [A: $tType,Y: list @ A] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ~ ! [X212: A,X222: list @ A] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.exhaust
% 0.32/0.47 thf(fact_129_list_OdiscI,axiom,
% 0.32/0.47 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.32/0.47 ( ( List
% 0.32/0.47 = ( cons @ A @ X21 @ X22 ) )
% 0.32/0.47 => ( List
% 0.32/0.47 != ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.discI
% 0.32/0.47 thf(fact_130_list_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X22: list @ A] :
% 0.32/0.47 ( ( nil @ A )
% 0.32/0.47 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.distinct(1)
% 0.32/0.47 thf(fact_131_less__add__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_add_one
% 0.32/0.47 thf(fact_132_gen__length__code_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,N: nat] :
% 0.32/0.47 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 0.32/0.47 = N ) ).
% 0.32/0.47
% 0.32/0.47 % gen_length_code(1)
% 0.32/0.47 thf(fact_133_Suc__eq__plus1__left,axiom,
% 0.32/0.47 ( suc
% 0.32/0.47 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_eq_plus1_left
% 0.32/0.47 thf(fact_134_Suc__eq__plus1,axiom,
% 0.32/0.47 ( suc
% 0.32/0.47 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_eq_plus1
% 0.32/0.47 thf(fact_135_lexordp__eq_OCons,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ( ord_less @ A @ X @ Y )
% 0.32/0.47 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.Cons
% 0.32/0.47 thf(fact_136_lexordp__eq_OCons__eq,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ~ ( ord_less @ A @ X @ Y )
% 0.32/0.47 => ( ~ ( ord_less @ A @ Y @ X )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.32/0.47 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.Cons_eq
% 0.32/0.47 thf(fact_137_fold__atLeastAtMost__nat_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A12: nat,A23: nat,A32: A] :
% 0.32/0.47 ( ! [F2: nat > A > A,A4: nat,B4: nat,Acc: A] :
% 0.32/0.47 ( ( ~ ( ord_less @ nat @ B4 @ A4 )
% 0.32/0.47 => ( P @ F2 @ ( plus_plus @ nat @ A4 @ ( one_one @ nat ) ) @ B4 @ ( F2 @ A4 @ Acc ) ) )
% 0.32/0.47 => ( P @ F2 @ A4 @ B4 @ Acc ) )
% 0.32/0.47 => ( P @ A0 @ A12 @ A23 @ A32 ) ) ).
% 0.32/0.47
% 0.32/0.47 % fold_atLeastAtMost_nat.induct
% 0.32/0.47 thf(fact_138_list__encode_Oinduct,axiom,
% 0.32/0.47 ! [P: ( list @ nat ) > $o,A0: list @ nat] :
% 0.32/0.47 ( ( P @ ( nil @ nat ) )
% 0.32/0.47 => ( ! [X3: nat,Xs3: list @ nat] :
% 0.32/0.47 ( ( P @ Xs3 )
% 0.32/0.47 => ( P @ ( cons @ nat @ X3 @ Xs3 ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_encode.induct
% 0.32/0.47 thf(fact_139_list__encode_Ocases,axiom,
% 0.32/0.47 ! [X: list @ nat] :
% 0.32/0.47 ( ( X
% 0.32/0.47 != ( nil @ nat ) )
% 0.32/0.47 => ~ ! [X3: nat,Xs3: list @ nat] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ nat @ X3 @ Xs3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_encode.cases
% 0.32/0.47 thf(fact_140_gen__llength__code_I2_J,axiom,
% 0.32/0.47 ! [B3: $tType,N: nat,X: B3,Xs: coindu1593790203_llist @ B3] :
% 0.32/0.47 ( ( coindu493225792length @ B3 @ N @ ( coindu1121789889_LCons @ B3 @ X @ Xs ) )
% 0.32/0.47 = ( coindu493225792length @ B3 @ ( plus_plus @ nat @ N @ ( one_one @ nat ) ) @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % gen_llength_code(2)
% 0.32/0.47 thf(fact_141_upt__rec__numeral,axiom,
% 0.32/0.47 ! [M: num,N: num] :
% 0.32/0.47 ( ( ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 0.32/0.47 => ( ( upt @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 0.32/0.47 = ( cons @ nat @ ( numeral_numeral @ nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral @ nat @ M ) ) @ ( numeral_numeral @ nat @ N ) ) ) ) )
% 0.32/0.47 & ( ~ ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 0.32/0.47 => ( ( upt @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 0.32/0.47 = ( nil @ nat ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % upt_rec_numeral
% 0.32/0.47 thf(fact_142_numeral__eq__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( ( numeral_numeral @ A @ M )
% 0.32/0.47 = ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( M = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_eq_iff
% 0.32/0.47 thf(fact_143_numeral__less__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( ord_less @ num @ M @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_less_iff
% 0.32/0.47 thf(fact_144_add__numeral__left,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [V3: num,W: num,Z: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V3 ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.32/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V3 @ W ) ) @ Z ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_numeral_left
% 0.32/0.47 thf(fact_145_numeral__plus__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_plus_numeral
% 0.32/0.47 thf(fact_146_not__numeral__less__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ~ ( ord_less @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_numeral_less_one
% 0.32/0.47 thf(fact_147_one__plus__numeral__commute,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X ) )
% 0.32/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_plus_numeral_commute
% 0.32/0.47 thf(fact_148_sublists_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( sublists @ A @ ( nil @ A ) )
% 0.32/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sublists.simps(1)
% 0.32/0.47 thf(fact_149_triangle__Suc,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( nat_triangle @ ( suc @ N ) )
% 0.32/0.47 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % triangle_Suc
% 0.32/0.47 thf(fact_150_longest__common__prefix_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A12: list @ A] :
% 0.32/0.47 ( ! [X3: A,Xs3: list @ A,Y4: A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( X3 = Y4 )
% 0.32/0.47 => ( P @ Xs3 @ Ys2 ) )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 0.32/0.47 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.32/0.47 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 0.32/0.47 => ( P @ A0 @ A12 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % longest_common_prefix.induct
% 0.32/0.47 thf(fact_151_prefixes_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,X: list @ A] :
% 0.32/0.47 ( ( X
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ~ ! [X3: A,Xs3: list @ A] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( cons @ A @ X3 @ Xs3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prefixes.cases
% 0.32/0.47 thf(fact_152_prefixes_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X3: A,Xs3: list @ A] :
% 0.32/0.47 ( ( P @ Xs3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prefixes.induct
% 0.32/0.47 thf(fact_153_enat__ord__number_I2_J,axiom,
% 0.32/0.47 ! [M: num,N: num] :
% 0.32/0.47 ( ( ord_less @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( numeral_numeral @ extended_enat @ N ) )
% 0.32/0.47 = ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % enat_ord_number(2)
% 0.32/0.47 thf(fact_154_product__lists_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.32/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % product_lists.simps(1)
% 0.32/0.47 thf(fact_155__092_060open_062LNil_A_061_Allist__of_A_091_093_092_060close_062,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( coindu1598213697e_LNil @ A )
% 0.32/0.47 = ( coindu1079202755ist_of @ A @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<open>LNil = llist_of []\<close>
% 0.32/0.47 thf(fact_156_enat__less__induct,axiom,
% 0.32/0.47 ! [P: extended_enat > $o,N: extended_enat] :
% 0.32/0.47 ( ! [N2: extended_enat] :
% 0.32/0.47 ( ! [M2: extended_enat] :
% 0.32/0.47 ( ( ord_less @ extended_enat @ M2 @ N2 )
% 0.32/0.47 => ( P @ M2 ) )
% 0.32/0.47 => ( P @ N2 ) )
% 0.32/0.47 => ( P @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % enat_less_induct
% 0.32/0.47 thf(fact_157_llist_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.32/0.47 ( ( coindu1598213697e_LNil @ A )
% 0.32/0.47 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist.distinct(1)
% 0.32/0.47 thf(fact_158_llist_Oexhaust,axiom,
% 0.32/0.47 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 != ( coindu1598213697e_LNil @ A ) )
% 0.32/0.47 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist.exhaust
% 0.32/0.47 thf(fact_159_neq__LNil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( coindu1598213697e_LNil @ A ) )
% 0.32/0.47 = ( ? [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neq_LNil_conv
% 0.32/0.47 thf(fact_160_lmember__code_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X: A] :
% 0.32/0.47 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % lmember_code(1)
% 0.32/0.47 thf(fact_161_llist__of__eq__LNil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.32/0.47 = ( coindu1598213697e_LNil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % llist_of_eq_LNil_conv
% 0.32/0.47 thf(fact_162_count__list_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Y: A,Xs: list @ A] :
% 0.32/0.47 ( ( ( X = Y )
% 0.32/0.47 => ( ( count_list @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 0.32/0.47 = ( plus_plus @ nat @ ( count_list @ A @ Xs @ Y ) @ ( one_one @ nat ) ) ) )
% 0.32/0.47 & ( ( X != Y )
% 0.32/0.47 => ( ( count_list @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 0.32/0.47 = ( count_list @ A @ Xs @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % count_list.simps(2)
% 0.32/0.47 thf(fact_163_one__less__numeral__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( ord_less @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( ord_less @ num @ one2 @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_less_numeral_iff
% 0.32/0.47 thf(fact_164_one__plus__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_plus_numeral
% 0.32/0.47 thf(fact_165_one__eq__numeral__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( ( one_one @ A )
% 0.32/0.47 = ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( one2 = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_eq_numeral_iff
% 0.32/0.47 thf(fact_166_numeral__eq__one__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( ( numeral_numeral @ A @ N )
% 0.32/0.47 = ( one_one @ A ) )
% 0.32/0.47 = ( N = one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_eq_one_iff
% 0.32/0.47 thf(fact_167_Suc__numeral,axiom,
% 0.32/0.47 ! [N: num] :
% 0.32/0.47 ( ( suc @ ( numeral_numeral @ nat @ N ) )
% 0.32/0.47 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N @ one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_numeral
% 0.32/0.47 thf(fact_168_numeral__plus__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_plus_one
% 0.32/0.47 thf(fact_169_add__One__commute,axiom,
% 0.32/0.47 ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ num @ one2 @ N )
% 0.32/0.47 = ( plus_plus @ num @ N @ one2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_One_commute
% 0.32/0.47 thf(fact_170_numeral__One,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( numeral_numeral @ A @ one2 )
% 0.32/0.47 = ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_One
% 0.32/0.47 thf(fact_171_numerals_I1_J,axiom,
% 0.32/0.47 ( ( numeral_numeral @ nat @ one2 )
% 0.32/0.47 = ( one_one @ nat ) ) ).
% 0.32/0.47
% 0.32/0.47 % numerals(1)
% 0.32/0.47 thf(fact_172_Suc__nat__number__of__add,axiom,
% 0.32/0.47 ! [V3: num,N: nat] :
% 0.32/0.47 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V3 ) @ N ) )
% 0.32/0.47 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V3 @ one2 ) ) @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_nat_number_of_add
% 0.32/0.47 thf(fact_173_semiring__norm_I75_J,axiom,
% 0.32/0.47 ! [M: num] :
% 0.32/0.47 ~ ( ord_less @ num @ M @ one2 ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(75)
% 0.32/0.47 thf(fact_174_prefixes_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( prefixes @ A @ ( nil @ A ) )
% 0.32/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prefixes.simps(1)
% 0.32/0.47 thf(fact_175_Suc__1,axiom,
% 0.32/0.47 ( ( suc @ ( one_one @ nat ) )
% 0.32/0.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Suc_1
% 0.32/0.47 thf(fact_176_num_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X2: num,Y2: num] :
% 0.32/0.47 ( ( ( bit0 @ X2 )
% 0.32/0.47 = ( bit0 @ Y2 ) )
% 0.32/0.47 = ( X2 = Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % num.inject(1)
% 0.32/0.47 thf(fact_177_semiring__norm_I6_J,axiom,
% 0.32/0.47 ! [M: num,N: num] :
% 0.32/0.47 ( ( plus_plus @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/0.47 = ( bit0 @ ( plus_plus @ num @ M @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(6)
% 0.32/0.47 thf(fact_178_semiring__norm_I78_J,axiom,
% 0.32/0.47 ! [M: num,N: num] :
% 0.32/0.47 ( ( ord_less @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/0.47 = ( ord_less @ num @ M @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(78)
% 0.32/0.47 thf(fact_179_semiring__norm_I2_J,axiom,
% 0.32/0.47 ( ( plus_plus @ num @ one2 @ one2 )
% 0.32/0.47 = ( bit0 @ one2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(2)
% 0.32/0.47 thf(fact_180_semiring__norm_I76_J,axiom,
% 0.32/0.47 ! [N: num] : ( ord_less @ num @ one2 @ ( bit0 @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(76)
% 0.32/0.47 thf(fact_181_one__add__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_add_one
% 0.32/0.47 thf(fact_182_add__2__eq__Suc,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N )
% 0.32/0.47 = ( suc @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_2_eq_Suc
% 0.32/0.47 thf(fact_183_add__2__eq__Suc_H,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( plus_plus @ nat @ N @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 0.32/0.47 = ( suc @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_2_eq_Suc'
% 0.32/0.47 thf(fact_184_num_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X2: num] :
% 0.32/0.47 ( one2
% 0.32/0.47 != ( bit0 @ X2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % num.distinct(1)
% 0.32/0.47 thf(fact_185_numeral__Bit0,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 0.32/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_Bit0
% 0.32/0.47 thf(fact_186_nat__1__add__1,axiom,
% 0.32/0.47 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 0.32/0.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nat_1_add_1
% 0.32/0.47 thf(fact_187_dbl__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_simps(3)
% 0.32/0.47 thf(fact_188_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(9)
% 0.32/0.47 thf(fact_189_dbl__simps_I5_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [K: num] :
% 0.32/0.47 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_simps(5)
% 0.32/0.47 thf(fact_190_neg__equal__iff__equal,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.32/0.47 = ( uminus_uminus @ A @ B ) )
% 0.32/0.47 = ( A2 = B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_equal_iff_equal
% 0.32/0.47 thf(fact_191_add_Oinverse__inverse,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A] :
% 0.32/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 0.32/0.47 = A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % add.inverse_inverse
% 0.32/0.47 thf(fact_192_neg__less__iff__less,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [B: A,A2: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) )
% 0.32/0.47 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_less_iff_less
% 0.32/0.47 thf(fact_193_neg__numeral__eq__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( M = N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_eq_iff
% 0.32/0.47 thf(fact_194_minus__add__distrib,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 0.32/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % minus_add_distrib
% 0.32/0.47 thf(fact_195_minus__add__cancel,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ ( plus_plus @ A @ A2 @ B ) )
% 0.32/0.47 = B ) ) ).
% 0.32/0.47
% 0.32/0.47 % minus_add_cancel
% 0.32/0.47 thf(fact_196_add__minus__cancel,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ B ) )
% 0.32/0.47 = B ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_minus_cancel
% 0.32/0.47 thf(fact_197_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_simps(3)
% 0.32/0.47 thf(fact_198_dbl__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [K: num] :
% 0.32/0.47 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_simps(1)
% 0.32/0.47 thf(fact_199_neg__one__eq__numeral__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( N = one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_one_eq_numeral_iff
% 0.32/0.47 thf(fact_200_numeral__eq__neg__one__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( N = one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_eq_neg_one_iff
% 0.32/0.47 thf(fact_201_semiring__norm_I168_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [V3: num,W: num,Y: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V3 ) ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 0.32/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V3 @ W ) ) ) @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(168)
% 0.32/0.47 thf(fact_202_neg__numeral__less__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( ord_less @ num @ N @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_less_iff
% 0.32/0.47 thf(fact_203_neg__numeral__less__neg__one__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( M != one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_less_neg_one_iff
% 0.32/0.47 thf(fact_204_dbl__simps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_simps(4)
% 0.32/0.47 thf(fact_205_not__numeral__less__neg__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ~ ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_numeral_less_neg_numeral
% 0.32/0.47 thf(fact_206_neg__numeral__less__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_less_numeral
% 0.32/0.47 thf(fact_207_less__minus__one__simps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_minus_one_simps(4)
% 0.32/0.47 thf(fact_208_less__minus__one__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_minus_one_simps(2)
% 0.32/0.47 thf(fact_209_numeral__neq__neg__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( numeral_numeral @ A @ N )
% 0.32/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_neq_neg_one
% 0.32/0.47 thf(fact_210_one__neq__neg__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( one_one @ A )
% 0.32/0.47 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_neq_neg_numeral
% 0.32/0.47 thf(fact_211_neg__numeral__neq__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.32/0.47 != ( numeral_numeral @ A @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_neq_numeral
% 0.32/0.47 thf(fact_212_numeral__neq__neg__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( numeral_numeral @ A @ M )
% 0.32/0.47 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_neq_neg_numeral
% 0.32/0.47 thf(fact_213_less__minus__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 0.32/0.47 = ( ord_less @ A @ B @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_minus_iff
% 0.32/0.47 thf(fact_214_minus__less__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 0.32/0.47 = ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % minus_less_iff
% 0.32/0.47 thf(fact_215_one__neq__neg__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( one_one @ A )
% 0.32/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_neq_neg_one
% 0.32/0.47 thf(fact_216_minus__equation__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.32/0.47 = B )
% 0.32/0.47 = ( ( uminus_uminus @ A @ B )
% 0.32/0.47 = A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % minus_equation_iff
% 0.32/0.47 thf(fact_217_equation__minus__iff,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( uminus_uminus @ A @ B ) )
% 0.32/0.47 = ( B
% 0.32/0.47 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % equation_minus_iff
% 0.32/0.47 thf(fact_218_is__num__normalize_I8_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 0.32/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % is_num_normalize(8)
% 0.32/0.47 thf(fact_219_add_Oinverse__distrib__swap,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [A2: A,B: A] :
% 0.32/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 0.32/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add.inverse_distrib_swap
% 0.32/0.47 thf(fact_220_dbl__def,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( neg_numeral_dbl @ A )
% 0.32/0.47 = ( ^ [X5: A] : ( plus_plus @ A @ X5 @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_def
% 0.32/0.47 thf(fact_221_uminus__numeral__One,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ one2 ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % uminus_numeral_One
% 0.32/0.47 thf(fact_222_neg__numeral__less__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_numeral_less_one
% 0.32/0.47 thf(fact_223_neg__one__less__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( numeral_numeral @ A @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neg_one_less_numeral
% 0.32/0.47 thf(fact_224_not__numeral__less__neg__one,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ~ ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_numeral_less_neg_one
% 0.32/0.47 thf(fact_225_not__one__less__neg__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_one_less_neg_numeral
% 0.32/0.47 thf(fact_226_not__neg__one__less__neg__numeral,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ~ ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_neg_one_less_neg_numeral
% 0.32/0.47 thf(fact_227_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ N ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(5)
% 0.32/0.47 thf(fact_228_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(6)
% 0.32/0.47 thf(fact_229_num__induct,axiom,
% 0.32/0.47 ! [P: num > $o,X: num] :
% 0.32/0.47 ( ( P @ one2 )
% 0.32/0.47 => ( ! [X3: num] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 => ( P @ ( inc @ X3 ) ) )
% 0.32/0.47 => ( P @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % num_induct
% 0.32/0.47 thf(fact_230_add__inc,axiom,
% 0.32/0.47 ! [X: num,Y: num] :
% 0.32/0.47 ( ( plus_plus @ num @ X @ ( inc @ Y ) )
% 0.32/0.47 = ( inc @ ( plus_plus @ num @ X @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_inc
% 0.32/0.47 thf(fact_231_inc_Osimps_I1_J,axiom,
% 0.32/0.47 ( ( inc @ one2 )
% 0.32/0.47 = ( bit0 @ one2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % inc.simps(1)
% 0.32/0.47 thf(fact_232_add__One,axiom,
% 0.32/0.47 ! [X: num] :
% 0.32/0.47 ( ( plus_plus @ num @ X @ one2 )
% 0.32/0.47 = ( inc @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_One
% 0.32/0.47 thf(fact_233_numeral__inc,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [X: num] :
% 0.32/0.47 ( ( numeral_numeral @ A @ ( inc @ X ) )
% 0.32/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % numeral_inc
% 0.32/0.47 thf(fact_234_add__neg__numeral__special_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ N @ one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(4)
% 0.32/0.47 thf(fact_235_add__neg__numeral__special_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ M @ one2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(3)
% 0.32/0.47 thf(fact_236_sub__num__simps_I6_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [K: num,L: num] :
% 0.32/0.47 ( ( neg_numeral_sub @ A @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.32/0.47 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K @ L ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sub_num_simps(6)
% 0.32/0.47 thf(fact_237_semiring__norm_I166_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [V3: num,W: num,Y: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V3 ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 0.32/0.47 = ( plus_plus @ A @ ( neg_numeral_sub @ A @ V3 @ W ) @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(166)
% 0.32/0.47 thf(fact_238_semiring__norm_I167_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [V3: num,W: num,Y: A] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V3 ) ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Y ) )
% 0.32/0.47 = ( plus_plus @ A @ ( neg_numeral_sub @ A @ W @ V3 ) @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semiring_norm(167)
% 0.32/0.47 thf(fact_239_add__neg__numeral__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ M @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_simps(1)
% 0.32/0.47 thf(fact_240_add__neg__numeral__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num,N: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ N @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_simps(2)
% 0.32/0.47 thf(fact_241_add__neg__numeral__special_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ one2 @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(1)
% 0.32/0.47 thf(fact_242_add__neg__numeral__special_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [M: num] :
% 0.32/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( one_one @ A ) )
% 0.32/0.47 = ( neg_numeral_sub @ A @ one2 @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % add_neg_numeral_special(2)
% 0.32/0.47 thf(fact_243_sub__num__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [L: num] :
% 0.32/0.47 ( ( neg_numeral_sub @ A @ one2 @ ( bit0 @ L ) )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bitM @ L ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sub_num_simps(2)
% 0.32/0.47 thf(fact_244_sub__num__simps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [K: num] :
% 0.32/0.47 ( ( neg_numeral_sub @ A @ ( bit0 @ K ) @ one2 )
% 0.32/0.47 = ( numeral_numeral @ A @ ( bitM @ K ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sub_num_simps(4)
% 0.32/0.47 thf(fact_245_eval__nat__numeral_I2_J,axiom,
% 0.32/0.47 ! [N: num] :
% 0.32/0.47 ( ( numeral_numeral @ nat @ ( bit0 @ N ) )
% 0.32/0.47 = ( suc @ ( numeral_numeral @ nat @ ( bitM @ N ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eval_nat_numeral(2)
% 0.32/0.47 thf(fact_246_one__plus__BitM,axiom,
% 0.32/0.47 ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ num @ one2 @ ( bitM @ N ) )
% 0.32/0.47 = ( bit0 @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % one_plus_BitM
% 0.32/0.47 thf(fact_247_BitM__plus__one,axiom,
% 0.32/0.47 ! [N: num] :
% 0.32/0.47 ( ( plus_plus @ num @ ( bitM @ N ) @ one2 )
% 0.32/0.47 = ( bit0 @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 % BitM_plus_one
% 0.32/0.47 thf(fact_248_dbl__dec__simps_I5_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [K: num] :
% 0.32/0.47 ( ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K ) )
% 0.32/0.47 = ( numeral_numeral @ A @ ( bitM @ K ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_dec_simps(5)
% 0.32/0.47 thf(fact_249_eq__numeral__iff__iszero_I8_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/0.47 => ! [Y: num] :
% 0.32/0.47 ( ( ( one_one @ A )
% 0.32/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ Y ) ) )
% 0.32/0.47 = ( ring_1_iszero @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ Y ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_numeral_iff_iszero(8)
% 0.32/0.47 thf(fact_250_dbl__dec__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/0.47 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 0.32/0.47 = ( one_one @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dbl_dec_simps(3)
% 0.32/0.47
% 0.32/0.47 %----Type constructors (36)
% 0.32/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/0.47 ! [A5: $tType,A6: $tType] :
% 0.32/0.47 ( ( order @ A6 @ ( type2 @ A6 ) )
% 0.32/0.47 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.47 ! [A5: $tType,A6: $tType] :
% 0.32/0.47 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 0.32/0.47 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.32/0.47 ! [A5: $tType,A6: $tType] :
% 0.32/0.47 ( ( uminus @ A6 @ ( type2 @ A6 ) )
% 0.32/0.47 => ( uminus @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.32/0.47 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.32/0.47 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.32/0.47 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.32/0.47 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.32/0.47 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.32/0.47 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.32/0.47 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.32/0.47 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.32/0.47 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.32/0.47 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/0.47 linorder @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.32/0.47 order @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Orderings_Oord_2,axiom,
% 0.32/0.47 ord @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.32/0.47 numeral @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.32/0.47 one @ nat @ ( type2 @ nat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Num_Onum___Orderings_Olinorder_3,axiom,
% 0.32/0.47 linorder @ num @ ( type2 @ num ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Num_Onum___Orderings_Oorder_4,axiom,
% 0.32/0.47 order @ num @ ( type2 @ num ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Num_Onum___Orderings_Oord_5,axiom,
% 0.32/0.47 ord @ num @ ( type2 @ num ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_6,axiom,
% 0.32/0.47 linorder @ $o @ ( type2 @ $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_7,axiom,
% 0.32/0.47 order @ $o @ ( type2 @ $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Orderings_Oord_8,axiom,
% 0.32/0.47 ord @ $o @ ( type2 @ $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Groups_Ouminus_9,axiom,
% 0.32/0.47 uminus @ $o @ ( type2 @ $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_10,axiom,
% 0.32/0.47 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11,axiom,
% 0.32/0.47 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12,axiom,
% 0.32/0.47 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_13,axiom,
% 0.32/0.47 comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_14,axiom,
% 0.32/0.47 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_15,axiom,
% 0.32/0.47 semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_16,axiom,
% 0.32/0.47 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_17,axiom,
% 0.32/0.47 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_18,axiom,
% 0.32/0.47 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_19,axiom,
% 0.32/0.47 numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Oone_20,axiom,
% 0.32/0.47 one @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/0.47
% 0.32/0.47 %----Helper facts (3)
% 0.32/0.47 thf(help_If_3_1_T,axiom,
% 0.32/0.47 ! [P: $o] :
% 0.32/0.47 ( ( P = $true )
% 0.32/0.47 | ( P = $false ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.32/0.47 = Y ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.32/0.47 = X ) ).
% 0.32/0.47
% 0.32/0.47 %----Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 ( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
% 0.32/0.47 = ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 2.46/1.49 ---- Embedded in THF ---
% 2.46/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.49 %%% Generated on Tue Feb 24 06:09:15 EST 2026
% 2.46/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.49 %%% Logic specification used:
% 2.46/1.49 %%% thf(spec, logic, $$dhol).
% 2.46/1.49
% 2.46/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2DTF16466.p
% 2.46/1.49 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 2.46/1.49 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 2.46/1.49 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.46/1.49 thf(ty_t_Num_Onum, type, num: $tType).
% 2.46/1.49 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.46/1.49 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.46/1.49 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Num_Onumeral, type, numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength, type, coindu493225792length: (!> [A:$tType]: ((nat > ((coindu1593790203_llist @ A) > extended_enat))))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux, type, coindu1542816657of_aux: (!> [A:$tType]: (((list @ A) > ((coindu1593790203_llist @ A) > (list @ A)))))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of, type, coindu1079202755ist_of: (!> [A:$tType]: (((list @ A) > (coindu1593790203_llist @ A))))).
% 2.46/1.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 2.46/1.49 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.46/1.49 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.46/1.49 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.46/1.49 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.46/1.49 thf(sy_c_List_Ocount__list, type, count_list: (!> [A:$tType]: (((list @ A) > (A > nat))))).
% 2.46/1.49 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 2.46/1.49 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.46/1.49 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.46/1.49 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 2.46/1.49 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 2.46/1.49 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.46/1.49 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.46/1.49 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.46/1.49 thf(sy_c_List_Oupt, type, upt: (nat > (nat > (list @ nat)))).
% 2.46/1.49 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.46/1.49 thf(sy_c_Nat__Bijection_Otriangle, type, nat_triangle: (nat > nat)).
% 2.46/1.49 thf(sy_c_Num_OBitM, type, bitM: (num > num)).
% 2.46/1.49 thf(sy_c_Num_Oinc, type, inc: (num > num)).
% 2.46/1.49 thf(sy_c_Num_Oneg__numeral__class_Odbl, type, neg_numeral_dbl: (!> [A:$tType]: ((A > A)))).
% 2.46/1.49 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec, type, neg_numeral_dbl_dec: (!> [A:$tType]: ((A > A)))).
% 2.46/1.49 thf(sy_c_Num_Oneg__numeral__class_Osub, type, neg_numeral_sub: (!> [A:$tType]: ((num > (num > A))))).
% 2.46/1.49 thf(sy_c_Num_Onum_OBit0, type, bit0: (num > num)).
% 2.46/1.49 thf(sy_c_Num_Onum_OOne, type, one2: num).
% 2.46/1.49 thf(sy_c_Num_Onumeral__class_Onumeral, type, numeral_numeral: (!> [A:$tType]: ((num > A)))).
% 2.46/1.49 thf(sy_c_Num_Oring__1__class_Oiszero, type, ring_1_iszero: (!> [A:$tType]: ((A > $o)))).
% 2.46/1.49 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.46/1.49 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.46/1.49 thf(sy_c_Sublist_Oprefixes, type, prefixes: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.46/1.49 thf(sy_v_ma____, type, ma: nat).
% 2.46/1.49 thf(sy_v_na____, type, na: nat).
% 2.46/1.49 thf(fact_0_llist__of__inject, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = ((coindu1079202755ist_of @ A) @ Ys)) = (Xs = Ys))))).
% 2.46/1.49 thf(fact_1_add__Suc__right, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ M) @ (suc @ N)) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.46/1.49 thf(fact_2_upt__conv__Cons__Cons, axiom, (! [M:nat,N:nat,Ns:(list @ nat),Q:nat]: ((((((cons @ nat) @ M) @ (((cons @ nat) @ N) @ Ns)) = ((upt @ M) @ Q)) = ((((cons @ nat) @ N) @ Ns) = ((upt @ (suc @ M)) @ Q)))))).
% 2.46/1.49 thf(fact_3_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 2.46/1.49 thf(fact_4_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.46/1.49 thf(fact_5_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.46/1.49 thf(fact_6_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.46/1.49 thf(fact_7_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.46/1.49 thf(fact_8_add__Suc__shift, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (((plus_plus @ nat) @ M) @ (suc @ N)))))).
% 2.46/1.49 thf(fact_9_add__Suc, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.46/1.49 thf(fact_10__092_060open_062_092_060And_062xs_Ax_O_ALCons_Ax_A_Illist__of_Axs_J_A_061_Allist__of_A_Ix_A_D_Axs_J_092_060close_062, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((coindu1121789889_LCons @ A) @ X) @ ((coindu1079202755ist_of @ A) @ Xs)) = ((coindu1079202755ist_of @ A) @ (((cons @ A) @ X) @ Xs)))))).
% 2.46/1.49 thf(fact_11_nat__add__left__cancel, axiom, (! [K:nat,M:nat,N:nat]: ((((((plus_plus @ nat) @ K) @ M) = (((plus_plus @ nat) @ K) @ N)) = (M = N))))).
% 2.46/1.49 thf(fact_12_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.46/1.49 thf(fact_13_llist__of__eq__LCons__conv, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (? [Xs2:(list @ A)]: (((Xs = (((cons @ A) @ Y) @ Xs2)) & (Ys = ((coindu1079202755ist_of @ A) @ Xs2))))))))).
% 2.46/1.49 thf(fact_14_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.46/1.49 thf(fact_15_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B = C)))))))).
% 2.46/1.49 thf(fact_16_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) => (B = C)))))))).
% 2.46/1.49 thf(fact_17_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_18_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,B2:A]: ((((plus_plus @ A) @ B2) @ A3)))))))).
% 2.46/1.49 thf(fact_19_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.46/1.49 thf(fact_20_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.46/1.49 thf(fact_21_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_22_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.46/1.49 thf(fact_23_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_24_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.46/1.49 thf(fact_25_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.46/1.49 thf(fact_26_nat__add__right__cancel, axiom, (! [M:nat,K:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ K) = (((plus_plus @ nat) @ N) @ K)) = (M = N))))).
% 2.46/1.49 thf(fact_27_list__of__aux__code_I2_J, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1542816657of_aux @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((coindu1542816657of_aux @ A) @ (((cons @ A) @ Y) @ Xs)) @ Ys))))).
% 2.46/1.49 thf(fact_28_gen__length__code_I2_J, axiom, (! [B3:$tType,N:nat,X:B3,Xs:(list @ B3)]: (((((gen_length @ B3) @ N) @ (((cons @ B3) @ X) @ Xs)) = (((gen_length @ B3) @ (suc @ N)) @ Xs))))).
% 2.46/1.49 thf(fact_29_upt__conv__Cons, axiom, (! [I:nat,J:nat]: (((((ord_less @ nat) @ I) @ J) => (((upt @ I) @ J) = (((cons @ nat) @ I) @ ((upt @ (suc @ I)) @ J))))))).
% 2.46/1.49 thf(fact_30_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 2.46/1.49 thf(fact_31_semiring__normalization__rules_I20_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D))))))))).
% 2.46/1.49 thf(fact_32_semiring__normalization__rules_I21_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_33_semiring__normalization__rules_I22_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ C) @ (((plus_plus @ A) @ A2) @ D))))))))).
% 2.46/1.49 thf(fact_34_semiring__normalization__rules_I23_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B)))))))).
% 2.46/1.49 thf(fact_35_semiring__normalization__rules_I24_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,C2:A]: ((((plus_plus @ A) @ C2) @ A3)))))))).
% 2.46/1.49 thf(fact_36_semiring__normalization__rules_I25_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ D)))))))).
% 2.46/1.49 thf(fact_37_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_38_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.46/1.49 thf(fact_39_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.46/1.49 thf(fact_40_lessI, axiom, (! [N:nat]: ((((ord_less @ nat) @ N) @ (suc @ N))))).
% 2.46/1.49 thf(fact_41_Suc__mono, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N)))))).
% 2.46/1.49 thf(fact_42_Suc__less__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.49 thf(fact_43_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.49 thf(fact_44_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.46/1.49 thf(fact_45_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.46/1.49 thf(fact_46_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.46/1.49 thf(fact_47_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.46/1.49 thf(fact_48_measure__induct, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ nat) @ (F @ Y3)) @ (F @ X3)) => (P @ Y3)))) => (P @ X3)))) => (P @ A2))))).
% 2.46/1.49 thf(fact_49_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.46/1.49 thf(fact_50_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.46/1.49 thf(fact_51_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.46/1.49 thf(fact_52_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 2.46/1.49 thf(fact_53_measure__induct__rule, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ nat) @ (F @ Y3)) @ (F @ X3)) => (P @ Y3)))) => (P @ X3)))) => (P @ A2))))).
% 2.46/1.49 thf(fact_54_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X:A]: (((! [X3:A]: (((~ ((P @ X3))) => (? [Y3:A]: (((((ord_less @ nat) @ (V @ Y3)) @ (V @ X3)) & (~ ((P @ Y3))))))))) => (P @ X))))).
% 2.46/1.49 thf(fact_55_linordered__field__no__ub, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X4:A]: ((? [X1:A]: ((((ord_less @ A) @ X4) @ X1))))))))).
% 2.46/1.49 thf(fact_56_linordered__field__no__lb, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X4:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X4))))))))).
% 2.46/1.49 thf(fact_57_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ A) @ (F @ N)) @ (F @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 2.46/1.49 thf(fact_58_lift__Suc__mono__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N3) => (((ord_less @ A) @ (F @ N)) @ (F @ N3)))))))))).
% 2.46/1.49 thf(fact_59_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.46/1.49 thf(fact_60_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.46/1.49 thf(fact_61_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.46/1.49 thf(fact_62_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.46/1.49 thf(fact_63_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B))))))))).
% 2.46/1.49 thf(fact_64_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_65_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.46/1.49 thf(fact_66_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.46/1.49 thf(fact_67_lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ I) @ K) => ((K != (suc @ I)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2)))))))))))).
% 2.46/1.49 thf(fact_68_Suc__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.49 thf(fact_69_Suc__lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2))))))))))).
% 2.46/1.49 thf(fact_70_Suc__lessI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((suc @ M) != N) => (((ord_less @ nat) @ (suc @ M)) @ N)))))).
% 2.46/1.49 thf(fact_71_less__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less @ nat) @ M) @ N))) => (M = N)))))).
% 2.46/1.49 thf(fact_72_less__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.46/1.49 thf(fact_73_less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((((ord_less @ nat) @ M) @ N) | (M = N)))))).
% 2.46/1.49 thf(fact_74_not__less__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less @ nat) @ M) @ N))) = (((ord_less @ nat) @ N) @ (suc @ M)))))).
% 2.46/1.49 thf(fact_75_Suc__less__eq2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N)) @ M) = (? [M3:nat]: (((M = (suc @ M3)) & (((ord_less @ nat) @ N) @ M3)))))))).
% 2.46/1.49 thf(fact_76_less__antisym, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) => (M = N)))))).
% 2.46/1.49 thf(fact_77_Suc__less__SucD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) => (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.49 thf(fact_78_less__trans__Suc, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I)) @ K)))))).
% 2.46/1.49 thf(fact_79_less__Suc__induct, axiom, (! [I:nat,J:nat,P:(nat > (nat > $o))]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((P @ I2) @ (suc @ I2)))) => ((! [I2:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P @ I2) @ J2) => (((P @ J2) @ K2) => ((P @ I2) @ K2))))))) => ((P @ I) @ J))))))).
% 2.46/1.49 thf(fact_80_strict__inc__induct, axiom, (! [I:nat,J:nat,P:(nat > $o)]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((J = (suc @ I2)) => (P @ I2)))) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((P @ (suc @ I2)) => (P @ I2))))) => (P @ I))))))).
% 2.46/1.49 thf(fact_81_not__less__less__Suc__eq, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.46/1.49 thf(fact_82_add__lessD1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K) => (((ord_less @ nat) @ I) @ K))))).
% 2.46/1.49 thf(fact_83_add__less__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K) @ L) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.46/1.49 thf(fact_84_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.46/1.49 thf(fact_85_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.46/1.49 thf(fact_86_add__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.46/1.49 thf(fact_87_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.46/1.49 thf(fact_88_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.46/1.49 thf(fact_89_less__add__eq__less, axiom, (! [K:nat,L:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K) @ L) => (((((plus_plus @ nat) @ M) @ L) = (((plus_plus @ nat) @ K) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 2.46/1.49 thf(fact_90_less__add__Suc1, axiom, (! [I:nat,M:nat]: ((((ord_less @ nat) @ I) @ (suc @ (((plus_plus @ nat) @ I) @ M)))))).
% 2.46/1.49 thf(fact_91_less__add__Suc2, axiom, (! [I:nat,M:nat]: ((((ord_less @ nat) @ I) @ (suc @ (((plus_plus @ nat) @ M) @ I)))))).
% 2.46/1.49 thf(fact_92_less__iff__Suc__add, axiom, ((ord_less @ nat) = (^ [M4:nat,N4:nat]: ((? [K3:nat]: ((N4 = (suc @ (((plus_plus @ nat) @ M4) @ K3))))))))).
% 2.46/1.49 thf(fact_93_less__imp__Suc__add, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (? [K2:nat]: ((N = (suc @ (((plus_plus @ nat) @ M) @ K2))))))))).
% 2.46/1.49 thf(fact_94_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_95_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,B2:A]: ((((plus_plus @ A) @ B2) @ A3)))))))).
% 2.46/1.49 thf(fact_96_upt__eq__Cons__conv, axiom, (! [I:nat,J:nat,X:nat,Xs:(list @ nat)]: (((((upt @ I) @ J) = (((cons @ nat) @ X) @ Xs)) = ((((ord_less @ nat) @ I) @ J) & ((I = X) & (((upt @ (((plus_plus @ nat) @ I) @ (one_one @ nat))) @ J) = Xs))))))).
% 2.46/1.49 thf(fact_97_upt__rec, axiom, (upt = (^ [I3:nat,J3:nat]: (((((if @ (list @ nat)) @ (((ord_less @ nat) @ I3) @ J3)) @ (((cons @ nat) @ I3) @ ((upt @ (suc @ I3)) @ J3))) @ (nil @ nat)))))).
% 2.46/1.49 thf(fact_98_nth__upt, axiom, (! [I:nat,K:nat,J:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ J) => ((((nth @ nat) @ ((upt @ I) @ J)) @ K) = (((plus_plus @ nat) @ I) @ K)))))).
% 2.46/1.49 thf(fact_99_lexordp__eq__simps_I4_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = ((((ord_less @ A) @ X) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X))) & (((ord_lexordp_eq @ A) @ Xs) @ Ys)))))))))).
% 2.46/1.49 thf(fact_100_is__num__normalize_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.46/1.49 thf(fact_101_member__rec_I1_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A]: (((((member @ A) @ (((cons @ A) @ X) @ Xs)) @ Y) = ((X = Y) | (((member @ A) @ Xs) @ Y)))))).
% 2.46/1.49 thf(fact_102_ex__gt__or__lt, axiom, (! [A:$tType]: ((((condit1656338222tinuum @ A) @ (type2 @ A)) => (! [A2:A]: ((? [B4:A]: (((((ord_less @ A) @ A2) @ B4) | (((ord_less @ A) @ B4) @ A2)))))))))).
% 2.46/1.49 thf(fact_103_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.46/1.49 thf(fact_104_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 2.46/1.49 thf(fact_105_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 2.46/1.49 thf(fact_106_nth__Cons__Suc, axiom, (! [A:$tType,X:A,Xs:(list @ A),N:nat]: (((((nth @ A) @ (((cons @ A) @ X) @ Xs)) @ (suc @ N)) = (((nth @ A) @ Xs) @ N))))).
% 2.46/1.49 thf(fact_107_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A)))))))))).
% 2.46/1.49 thf(fact_108_less__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.46/1.49 thf(fact_109_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X3:A,Xs3:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X3) @ Xs3)) @ Xss))))))))))).
% 2.46/1.49 thf(fact_110_lexordp__eq__antisym, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Xs) => (Xs = Ys))))))))).
% 2.46/1.49 thf(fact_111_lexordp__eq__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) | (((ord_lexordp_eq @ A) @ Ys) @ Xs)))))))).
% 2.46/1.49 thf(fact_112_lexordp__eq__trans, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Zs) => (((ord_lexordp_eq @ A) @ Xs) @ Zs))))))))).
% 2.46/1.49 thf(fact_113_lexordp__eq__refl, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 2.46/1.49 thf(fact_114_lexordp__eq_ONil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 2.46/1.49 thf(fact_115_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.46/1.49 thf(fact_116_member__rec_I2_J, axiom, (! [A:$tType,Y:A]: ((~ ((((member @ A) @ (nil @ A)) @ Y)))))).
% 2.46/1.49 thf(fact_117_lexordp__eq_Oinducts, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X12:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X12) @ X2) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [X3:A,Y4:A,Xs3:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X3) @ Y4) => ((P @ (((cons @ A) @ X3) @ Xs3)) @ (((cons @ A) @ Y4) @ Ys2))))) => ((! [X3:A,Y4:A,Xs3:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X3) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X3))) => ((((ord_lexordp_eq @ A) @ Xs3) @ Ys2) => (((P @ Xs3) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs3)) @ (((cons @ A) @ Y4) @ Ys2)))))))) => ((P @ X12) @ X2))))))))))).
% 2.46/1.49 thf(fact_118_lexordp__eq_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((ord_lexordp_eq @ A) = (^ [A1:(list @ A),A22:(list @ A)]: (((? [Ys3:(list @ A)]: (((A1 = (nil @ A)) & (A22 = Ys3)))) | ((? [X5:A,Y5:A,Xs4:(list @ A),Ys3:(list @ A)]: (((A1 = (((cons @ A) @ X5) @ Xs4)) & ((A22 = (((cons @ A) @ Y5) @ Ys3)) & (((ord_less @ A) @ X5) @ Y5))))) | (? [X5:A,Y5:A,Xs4:(list @ A),Ys3:(list @ A)]: (((A1 = (((cons @ A) @ X5) @ Xs4)) & ((A22 = (((cons @ A) @ Y5) @ Ys3)) & ((~ ((((ord_less @ A) @ X5) @ Y5))) & ((~ ((((ord_less @ A) @ Y5) @ X5))) & (((ord_lexordp_eq @ A) @ Xs4) @ Ys3)))))))))))))))).
% 2.46/1.49 thf(fact_119_lexordp__eq_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A12:(list @ A),A23:(list @ A)]: (((((ord_lexordp_eq @ A) @ A12) @ A23) => (((A12 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A23 != Ys2)))) => ((! [X3:A]: (((? [Xs3:(list @ A)]: ((A12 = (((cons @ A) @ X3) @ Xs3)))) => (! [Y4:A]: (((? [Ys2:(list @ A)]: ((A23 = (((cons @ A) @ Y4) @ Ys2)))) => (~ ((((ord_less @ A) @ X3) @ Y4))))))))) => (~ ((! [X3:A,Y4:A,Xs3:(list @ A)]: (((A12 = (((cons @ A) @ X3) @ Xs3)) => (! [Ys2:(list @ A)]: (((A23 = (((cons @ A) @ Y4) @ Ys2)) => ((~ ((((ord_less @ A) @ X3) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X3))) => (~ ((((ord_lexordp_eq @ A) @ Xs3) @ Ys2)))))))))))))))))))))).
% 2.46/1.49 thf(fact_120_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B3:$tType,P:((A > B3) > ((list @ A) > ((list @ B3) > $o))),A0:(A > B3),A12:(list @ A),A23:(list @ B3)]: (((! [F2:(A > B3),X1:(list @ B3)]: ((((P @ F2) @ (nil @ A)) @ X1))) => ((! [F2:(A > B3),A4:A,As:(list @ A),Bs:(list @ B3)]: (((((P @ F2) @ As) @ (((cons @ B3) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A12) @ A23)))))).
% 2.46/1.49 thf(fact_121_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs3:(list @ A)]: (((Xs3 != (nil @ A)) => ((P @ Xs3) => (P @ (((cons @ A) @ X3) @ Xs3)))))) => (P @ Xs))))))).
% 2.46/1.49 thf(fact_122_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y4:A,Xs3:(list @ A)]: ((((X3 = Y4) => (P @ (((cons @ A) @ X3) @ Xs3))) => (((X3 != Y4) => (P @ (((cons @ A) @ Y4) @ Xs3))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y4) @ Xs3))))))) => (P @ A0))))))).
% 2.46/1.49 thf(fact_123_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X3:A]: ((X != (((cons @ A) @ X3) @ (nil @ A))))) => (~ ((! [X3:A,Y4:A,Xs3:(list @ A)]: ((X != (((cons @ A) @ X3) @ (((cons @ A) @ Y4) @ Xs3)))))))))))).
% 2.46/1.49 thf(fact_124_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A12:(list @ A)]: (((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [V2:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V2) @ Va)) @ (nil @ A)))) => ((! [X3:A,Xs3:(list @ A),Y4:A,Ys2:(list @ A)]: ((((P @ Xs3) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs3)) @ (((cons @ A) @ Y4) @ Ys2))))) => ((P @ A0) @ A12))))))).
% 2.46/1.49 thf(fact_125_list__induct2_H, axiom, (! [A:$tType,B3:$tType,P:((list @ A) > ((list @ B3) > $o)),Xs:(list @ A),Ys:(list @ B3)]: ((((P @ (nil @ A)) @ (nil @ B3)) => ((! [X3:A,Xs3:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs3)) @ (nil @ B3)))) => ((! [Y4:B3,Ys2:(list @ B3)]: (((P @ (nil @ A)) @ (((cons @ B3) @ Y4) @ Ys2)))) => ((! [X3:A,Xs3:(list @ A),Y4:B3,Ys2:(list @ B3)]: ((((P @ Xs3) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs3)) @ (((cons @ B3) @ Y4) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.46/1.49 thf(fact_126_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y5:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y5) @ Ys3)))))))).
% 2.46/1.49 thf(fact_127_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.46/1.49 thf(fact_128_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.46/1.49 thf(fact_129_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.46/1.49 thf(fact_130_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.46/1.49 thf(fact_131_less__add__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 2.46/1.49 thf(fact_132_gen__length__code_I1_J, axiom, (! [A:$tType,N:nat]: (((((gen_length @ A) @ N) @ (nil @ A)) = N)))).
% 2.46/1.49 thf(fact_133_Suc__eq__plus1__left, axiom, (suc = ((plus_plus @ nat) @ (one_one @ nat)))).
% 2.46/1.49 thf(fact_134_Suc__eq__plus1, axiom, (suc = (^ [N4:nat]: ((((plus_plus @ nat) @ N4) @ (one_one @ nat)))))).
% 2.46/1.49 thf(fact_135_lexordp__eq_OCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((((ord_less @ A) @ X) @ Y) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))).
% 2.46/1.49 thf(fact_136_lexordp__eq_OCons__eq, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X))) => ((((ord_lexordp_eq @ A) @ Xs) @ Ys) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))))).
% 2.46/1.49 thf(fact_137_fold__atLeastAtMost__nat_Oinduct, axiom, (! [A:$tType,P:((nat > (A > A)) > (nat > (nat > (A > $o)))),A0:(nat > (A > A)),A12:nat,A23:nat,A32:A]: (((! [F2:(nat > (A > A)),A4:nat,B4:nat,Acc:A]: ((((~ ((((ord_less @ nat) @ B4) @ A4))) => ((((P @ F2) @ (((plus_plus @ nat) @ A4) @ (one_one @ nat))) @ B4) @ ((F2 @ A4) @ Acc))) => ((((P @ F2) @ A4) @ B4) @ Acc)))) => ((((P @ A0) @ A12) @ A23) @ A32))))).
% 2.46/1.49 thf(fact_138_list__encode_Oinduct, axiom, (! [P:((list @ nat) > $o),A0:(list @ nat)]: (((P @ (nil @ nat)) => ((! [X3:nat,Xs3:(list @ nat)]: (((P @ Xs3) => (P @ (((cons @ nat) @ X3) @ Xs3))))) => (P @ A0)))))).
% 2.46/1.49 thf(fact_139_list__encode_Ocases, axiom, (! [X:(list @ nat)]: (((X != (nil @ nat)) => (~ ((! [X3:nat,Xs3:(list @ nat)]: ((X != (((cons @ nat) @ X3) @ Xs3)))))))))).
% 2.46/1.49 thf(fact_140_gen__llength__code_I2_J, axiom, (! [B3:$tType,N:nat,X:B3,Xs:(coindu1593790203_llist @ B3)]: (((((coindu493225792length @ B3) @ N) @ (((coindu1121789889_LCons @ B3) @ X) @ Xs)) = (((coindu493225792length @ B3) @ (((plus_plus @ nat) @ N) @ (one_one @ nat))) @ Xs))))).
% 2.46/1.49 thf(fact_141_upt__rec__numeral, axiom, (! [M:num,N:num]: ((((((ord_less @ nat) @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)) => (((upt @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)) = (((cons @ nat) @ ((numeral_numeral @ nat) @ M)) @ ((upt @ (suc @ ((numeral_numeral @ nat) @ M))) @ ((numeral_numeral @ nat) @ N))))) & ((~ ((((ord_less @ nat) @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)))) => (((upt @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)) = (nil @ nat))))))).
% 2.46/1.49 thf(fact_142_numeral__eq__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((numeral_numeral @ A) @ M) = ((numeral_numeral @ A) @ N)) = (M = N)))))))).
% 2.46/1.49 thf(fact_143_numeral__less__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((ord_less @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = (((ord_less @ num) @ M) @ N)))))))).
% 2.46/1.49 thf(fact_144_add__numeral__left, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [V3:num,W:num,Z:A]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ V3)) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V3) @ W))) @ Z)))))))).
% 2.46/1.49 thf(fact_145_numeral__plus__numeral, axiom, (! [A:$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))))))))).
% 2.46/1.49 thf(fact_146_not__numeral__less__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:num]: ((~ ((((ord_less @ A) @ ((numeral_numeral @ A) @ N)) @ (one_one @ A)))))))))).
% 2.46/1.49 thf(fact_147_one__plus__numeral__commute, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [X:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ X)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X)) @ (one_one @ A))))))))).
% 2.46/1.49 thf(fact_148_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.46/1.49 thf(fact_149_triangle__Suc, axiom, (! [N:nat]: (((nat_triangle @ (suc @ N)) = (((plus_plus @ nat) @ (nat_triangle @ N)) @ (suc @ N)))))).
% 2.46/1.49 thf(fact_150_longest__common__prefix_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A12:(list @ A)]: (((! [X3:A,Xs3:(list @ A),Y4:A,Ys2:(list @ A)]: ((((X3 = Y4) => ((P @ Xs3) @ Ys2)) => ((P @ (((cons @ A) @ X3) @ Xs3)) @ (((cons @ A) @ Y4) @ Ys2))))) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [Uu:(list @ A)]: (((P @ Uu) @ (nil @ A)))) => ((P @ A0) @ A12))))))).
% 2.46/1.49 thf(fact_151_prefixes_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X3:A,Xs3:(list @ A)]: ((X != (((cons @ A) @ X3) @ Xs3)))))))))).
% 2.46/1.49 thf(fact_152_prefixes_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A,Xs3:(list @ A)]: (((P @ Xs3) => (P @ (((cons @ A) @ X3) @ Xs3))))) => (P @ A0)))))).
% 2.46/1.49 thf(fact_153_enat__ord__number_I2_J, axiom, (! [M:num,N:num]: (((((ord_less @ extended_enat) @ ((numeral_numeral @ extended_enat) @ M)) @ ((numeral_numeral @ extended_enat) @ N)) = (((ord_less @ nat) @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)))))).
% 2.46/1.49 thf(fact_154_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.46/1.49 thf(fact_155__092_060open_062LNil_A_061_Allist__of_A_091_093_092_060close_062, axiom, (! [A:$tType]: (((coindu1598213697e_LNil @ A) = ((coindu1079202755ist_of @ A) @ (nil @ A)))))).
% 2.46/1.49 thf(fact_156_enat__less__induct, axiom, (! [P:(extended_enat > $o),N:extended_enat]: (((! [N2:extended_enat]: (((! [M2:extended_enat]: (((((ord_less @ extended_enat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.46/1.49 thf(fact_157_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 2.46/1.49 thf(fact_158_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 2.46/1.49 thf(fact_159_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X5:A,Xs2:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))))))).
% 2.46/1.49 thf(fact_160_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 2.46/1.49 thf(fact_161_llist__of__eq__LNil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = (coindu1598213697e_LNil @ A)) = (Xs = (nil @ A)))))).
% 2.46/1.49 thf(fact_162_count__list_Osimps_I2_J, axiom, (! [A:$tType,X:A,Y:A,Xs:(list @ A)]: ((((X = Y) => ((((count_list @ A) @ (((cons @ A) @ X) @ Xs)) @ Y) = (((plus_plus @ nat) @ (((count_list @ A) @ Xs) @ Y)) @ (one_one @ nat)))) & ((X != Y) => ((((count_list @ A) @ (((cons @ A) @ X) @ Xs)) @ Y) = (((count_list @ A) @ Xs) @ Y))))))).
% 2.46/1.49 thf(fact_163_one__less__numeral__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:num]: (((((ord_less @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)) = (((ord_less @ num) @ one2) @ N)))))))).
% 2.46/1.49 thf(fact_164_one__plus__numeral, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ one2) @ N))))))))).
% 2.46/1.49 thf(fact_165_one__eq__numeral__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: ((((one_one @ A) = ((numeral_numeral @ A) @ N)) = (one2 = N)))))))).
% 2.46/1.49 thf(fact_166_numeral__eq__one__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((numeral_numeral @ A) @ N) = (one_one @ A)) = (N = one2)))))))).
% 2.46/1.49 thf(fact_167_Suc__numeral, axiom, (! [N:num]: (((suc @ ((numeral_numeral @ nat) @ N)) = ((numeral_numeral @ nat) @ (((plus_plus @ num) @ N) @ one2)))))).
% 2.46/1.49 thf(fact_168_numeral__plus__one, axiom, (! [A:$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))))))))).
% 2.46/1.49 thf(fact_169_add__One__commute, axiom, (! [N:num]: (((((plus_plus @ num) @ one2) @ N) = (((plus_plus @ num) @ N) @ one2))))).
% 2.46/1.49 thf(fact_170_numeral__One, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (((numeral_numeral @ A) @ one2) = (one_one @ A)))))).
% 2.46/1.49 thf(fact_171_numerals_I1_J, axiom, (((numeral_numeral @ nat) @ one2) = (one_one @ nat))).
% 2.46/1.49 thf(fact_172_Suc__nat__number__of__add, axiom, (! [V3:num,N:nat]: (((suc @ (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ V3)) @ N)) = (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (((plus_plus @ num) @ V3) @ one2))) @ N))))).
% 2.46/1.49 thf(fact_173_semiring__norm_I75_J, axiom, (! [M:num]: ((~ ((((ord_less @ num) @ M) @ one2)))))).
% 2.46/1.49 thf(fact_174_prefixes_Osimps_I1_J, axiom, (! [A:$tType]: ((((prefixes @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.46/1.49 thf(fact_175_Suc__1, axiom, ((suc @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.46/1.49 thf(fact_176_num_Oinject_I1_J, axiom, (! [X2:num,Y2:num]: ((((bit0 @ X2) = (bit0 @ Y2)) = (X2 = Y2))))).
% 2.46/1.49 thf(fact_177_semiring__norm_I6_J, axiom, (! [M:num,N:num]: (((((plus_plus @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (bit0 @ (((plus_plus @ num) @ M) @ N)))))).
% 2.46/1.49 thf(fact_178_semiring__norm_I78_J, axiom, (! [M:num,N:num]: (((((ord_less @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (((ord_less @ num) @ M) @ N))))).
% 2.46/1.49 thf(fact_179_semiring__norm_I2_J, axiom, ((((plus_plus @ num) @ one2) @ one2) = (bit0 @ one2))).
% 2.46/1.49 thf(fact_180_semiring__norm_I76_J, axiom, (! [N:num]: ((((ord_less @ num) @ one2) @ (bit0 @ N))))).
% 2.46/1.49 thf(fact_181_one__add__one, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => ((((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.46/1.49 thf(fact_182_add__2__eq__Suc, axiom, (! [N:nat]: (((((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ N) = (suc @ (suc @ N)))))).
% 2.46/1.49 thf(fact_183_add__2__eq__Suc_H, axiom, (! [N:nat]: (((((plus_plus @ nat) @ N) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) = (suc @ (suc @ N)))))).
% 2.46/1.49 thf(fact_184_num_Odistinct_I1_J, axiom, (! [X2:num]: ((one2 != (bit0 @ X2))))).
% 2.46/1.49 thf(fact_185_numeral__Bit0, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ (bit0 @ N)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))))))))).
% 2.46/1.49 thf(fact_186_nat__1__add__1, axiom, ((((plus_plus @ nat) @ (one_one @ nat)) @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.46/1.49 thf(fact_187_dbl__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.46/1.49 thf(fact_188_add__neg__numeral__special_I9_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((((plus_plus @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2)))))))).
% 2.46/1.49 thf(fact_189_dbl__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: ((((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K)) = ((numeral_numeral @ A) @ (bit0 @ K))))))))).
% 2.46/1.49 thf(fact_190_neg__equal__iff__equal, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((uminus_uminus @ A) @ A2) = ((uminus_uminus @ A) @ B)) = (A2 = B)))))))).
% 2.46/1.49 thf(fact_191_add_Oinverse__inverse, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A2)) = A2))))))).
% 2.46/1.49 thf(fact_192_neg__less__iff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.46/1.49 thf(fact_193_neg__numeral__eq__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (M = N)))))))).
% 2.46/1.49 thf(fact_194_minus__add__distrib, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A2) @ B)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ A2)) @ ((uminus_uminus @ A) @ B))))))))).
% 2.46/1.49 thf(fact_195_minus__add__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ A2)) @ (((plus_plus @ A) @ A2) @ B)) = B))))))).
% 2.46/1.49 thf(fact_196_add__minus__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ ((uminus_uminus @ A) @ A2)) @ B)) = B))))))).
% 2.46/1.49 thf(fact_197_add__neg__numeral__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = ((uminus_uminus @ A) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)))))))))).
% 2.46/1.49 thf(fact_198_dbl__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: ((((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ K))) = ((uminus_uminus @ A) @ ((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K)))))))))).
% 2.46/1.49 thf(fact_199_neg__one__eq__numeral__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((uminus_uminus @ A) @ (one_one @ A)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (N = one2)))))))).
% 2.46/1.49 thf(fact_200_numeral__eq__neg__one__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N)) = ((uminus_uminus @ A) @ (one_one @ A))) = (N = one2)))))))).
% 2.46/1.49 thf(fact_201_semiring__norm_I168_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [V3:num,W:num,Y:A]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ V3))) @ (((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ W))) @ Y)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V3) @ W)))) @ Y)))))))).
% 2.46/1.49 thf(fact_202_neg__numeral__less__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (((ord_less @ num) @ N) @ M)))))))).
% 2.46/1.49 thf(fact_203_neg__numeral__less__neg__one__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ (one_one @ A))) = (M != one2)))))))).
% 2.46/1.49 thf(fact_204_dbl__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2)))))))).
% 2.46/1.49 thf(fact_205_not__numeral__less__neg__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((~ ((((ord_less @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))))).
% 2.46/1.49 thf(fact_206_neg__numeral__less__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((ord_less @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((numeral_numeral @ A) @ N)))))))).
% 2.46/1.49 thf(fact_207_less__minus__one__simps_I4_J, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.46/1.49 thf(fact_208_less__minus__one__simps_I2_J, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ (one_one @ A)))))).
% 2.46/1.49 thf(fact_209_numeral__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ N) != ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.46/1.49 thf(fact_210_one__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((one_one @ A) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))).
% 2.46/1.49 thf(fact_211_neg__numeral__neq__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M)) != ((numeral_numeral @ A) @ N)))))))).
% 2.46/1.49 thf(fact_212_numeral__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((numeral_numeral @ A) @ M) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))).
% 2.46/1.49 thf(fact_213_less__minus__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ ((uminus_uminus @ A) @ B)) = (((ord_less @ A) @ B) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.46/1.49 thf(fact_214_minus__less__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ B) = (((ord_less @ A) @ ((uminus_uminus @ A) @ B)) @ A2)))))))).
% 2.46/1.49 thf(fact_215_one__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => ((one_one @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.46/1.49 thf(fact_216_minus__equation__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((uminus_uminus @ A) @ A2) = B) = (((uminus_uminus @ A) @ B) = A2)))))))).
% 2.46/1.49 thf(fact_217_equation__minus__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((A2 = ((uminus_uminus @ A) @ B)) = (B = ((uminus_uminus @ A) @ A2))))))))).
% 2.46/1.49 thf(fact_218_is__num__normalize_I8_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A2:A,B:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A2) @ B)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ B)) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.46/1.49 thf(fact_219_add_Oinverse__distrib__swap, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A2) @ B)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ B)) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.46/1.49 thf(fact_220_dbl__def, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((neg_numeral_dbl @ A) = (^ [X5:A]: ((((plus_plus @ A) @ X5) @ X5)))))))).
% 2.46/1.49 thf(fact_221_uminus__numeral__One, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ ((numeral_numeral @ A) @ one2)) = ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.46/1.49 thf(fact_222_neg__numeral__less__one, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: ((((ord_less @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ (one_one @ A)))))))).
% 2.46/1.49 thf(fact_223_neg__one__less__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: ((((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((numeral_numeral @ A) @ M)))))))).
% 2.46/1.49 thf(fact_224_not__numeral__less__neg__one, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: ((~ ((((ord_less @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))))).
% 2.46/1.49 thf(fact_225_not__one__less__neg__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: ((~ ((((ord_less @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))))))))))).
% 2.46/1.49 thf(fact_226_not__neg__one__less__neg__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: ((~ ((((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))))))))))).
% 2.46/1.49 thf(fact_227_add__neg__numeral__special_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [N:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (inc @ N)))))))))).
% 2.46/1.49 thf(fact_228_add__neg__numeral__special_I6_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (inc @ M)))))))))).
% 2.46/1.49 thf(fact_229_num__induct, axiom, (! [P:(num > $o),X:num]: (((P @ one2) => ((! [X3:num]: (((P @ X3) => (P @ (inc @ X3))))) => (P @ X)))))).
% 2.46/1.49 thf(fact_230_add__inc, axiom, (! [X:num,Y:num]: (((((plus_plus @ num) @ X) @ (inc @ Y)) = (inc @ (((plus_plus @ num) @ X) @ Y)))))).
% 2.46/1.49 thf(fact_231_inc_Osimps_I1_J, axiom, ((inc @ one2) = (bit0 @ one2))).
% 2.46/1.49 thf(fact_232_add__One, axiom, (! [X:num]: (((((plus_plus @ num) @ X) @ one2) = (inc @ X))))).
% 2.46/1.49 thf(fact_233_numeral__inc, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [X:num]: ((((numeral_numeral @ A) @ (inc @ X)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X)) @ (one_one @ A))))))))).
% 2.46/1.49 thf(fact_234_add__neg__numeral__special_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [N:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((numeral_numeral @ A) @ N)) = (((neg_numeral_sub @ A) @ N) @ one2)))))))).
% 2.46/1.49 thf(fact_235_add__neg__numeral__special_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ (one_one @ A))) = (((neg_numeral_sub @ A) @ M) @ one2)))))))).
% 2.46/1.49 thf(fact_236_sub__num__simps_I6_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num,L:num]: (((((neg_numeral_sub @ A) @ (bit0 @ K)) @ (bit0 @ L)) = ((neg_numeral_dbl @ A) @ (((neg_numeral_sub @ A) @ K) @ L))))))))).
% 2.46/1.49 thf(fact_237_semiring__norm_I166_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [V3:num,W:num,Y:A]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ V3)) @ (((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ W))) @ Y)) = (((plus_plus @ A) @ (((neg_numeral_sub @ A) @ V3) @ W)) @ Y)))))))).
% 2.46/1.49 thf(fact_238_semiring__norm_I167_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [V3:num,W:num,Y:A]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ V3))) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ W)) @ Y)) = (((plus_plus @ A) @ (((neg_numeral_sub @ A) @ W) @ V3)) @ Y)))))))).
% 2.46/1.49 thf(fact_239_add__neg__numeral__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (((neg_numeral_sub @ A) @ M) @ N)))))))).
% 2.46/1.49 thf(fact_240_add__neg__numeral__simps_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((numeral_numeral @ A) @ N)) = (((neg_numeral_sub @ A) @ N) @ M)))))))).
% 2.46/1.49 thf(fact_241_add__neg__numeral__special_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) = (((neg_numeral_sub @ A) @ one2) @ M)))))))).
% 2.46/1.49 thf(fact_242_add__neg__numeral__special_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ (one_one @ A)) = (((neg_numeral_sub @ A) @ one2) @ M)))))))).
% 2.46/1.49 thf(fact_243_sub__num__simps_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [L:num]: (((((neg_numeral_sub @ A) @ one2) @ (bit0 @ L)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bitM @ L)))))))))).
% 2.46/1.49 thf(fact_244_sub__num__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: (((((neg_numeral_sub @ A) @ (bit0 @ K)) @ one2) = ((numeral_numeral @ A) @ (bitM @ K))))))))).
% 2.46/1.49 thf(fact_245_eval__nat__numeral_I2_J, axiom, (! [N:num]: ((((numeral_numeral @ nat) @ (bit0 @ N)) = (suc @ ((numeral_numeral @ nat) @ (bitM @ N))))))).
% 2.46/1.49 thf(fact_246_one__plus__BitM, axiom, (! [N:num]: (((((plus_plus @ num) @ one2) @ (bitM @ N)) = (bit0 @ N))))).
% 2.46/1.49 thf(fact_247_BitM__plus__one, axiom, (! [N:num]: (((((plus_plus @ num) @ (bitM @ N)) @ one2) = (bit0 @ N))))).
% 2.46/1.49 thf(fact_248_dbl__dec__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: ((((neg_numeral_dbl_dec @ A) @ ((numeral_numeral @ A) @ K)) = ((numeral_numeral @ A) @ (bitM @ K))))))))).
% 2.46/1.49 thf(fact_249_eq__numeral__iff__iszero_I8_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [Y:num]: ((((one_one @ A) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ Y))) = ((ring_1_iszero @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ one2) @ Y)))))))))).
% 2.46/1.49 thf(fact_250_dbl__dec__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_dec @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 2.46/1.49 thf(tcon_fun___Orderings_Oorder, axiom, (! [A5:$tType,A6:$tType]: ((((order @ A6) @ (type2 @ A6)) => ((order @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.46/1.49 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A6:$tType]: ((((ord @ A6) @ (type2 @ A6)) => ((ord @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.46/1.49 thf(tcon_fun___Groups_Ouminus, axiom, (! [A5:$tType,A6:$tType]: ((((uminus @ A6) @ (type2 @ A6)) => ((uminus @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, ((ordere223160158up_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Nat_Osemiring__char__0, axiom, ((semiring_char_0 @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Orderings_Oorder_1, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Orderings_Oord_2, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Num_Onumeral, axiom, ((numeral @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.46/1.49 thf(tcon_Num_Onum___Orderings_Olinorder_3, axiom, ((linorder @ num) @ (type2 @ num))).
% 2.46/1.49 thf(tcon_Num_Onum___Orderings_Oorder_4, axiom, ((order @ num) @ (type2 @ num))).
% 2.46/1.49 thf(tcon_Num_Onum___Orderings_Oord_5, axiom, ((ord @ num) @ (type2 @ num))).
% 2.46/1.49 thf(tcon_HOL_Obool___Orderings_Olinorder_6, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.46/1.49 thf(tcon_HOL_Obool___Orderings_Oorder_7, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.46/1.49 thf(tcon_HOL_Obool___Orderings_Oord_8, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.46/1.49 thf(tcon_HOL_Obool___Groups_Ouminus_9, axiom, ((uminus @ $o) @ (type2 @ $o))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_10, axiom, ((strict2144017051up_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11, axiom, ((ordere779506340up_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12, axiom, ((ab_semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_13, axiom, ((comm_semiring_1 @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_14, axiom, ((semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_15, axiom, ((semiring_char_0 @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_16, axiom, ((linorder @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_17, axiom, ((order @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_18, axiom, ((ord @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_19, axiom, ((numeral @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(tcon_Extended__Nat_Oenat___Groups_Oone_20, axiom, ((one @ extended_enat) @ (type2 @ extended_enat))).
% 2.46/1.49 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.46/1.49 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.46/1.49 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.46/1.49 thf(conj_0, conjecture, (((coindu1079202755ist_of @ nat) @ (((cons @ nat) @ ma) @ ((upt @ (suc @ ma)) @ (((plus_plus @ nat) @ na) @ (suc @ ma))))) = ((coindu1079202755ist_of @ nat) @ ((upt @ ma) @ (((plus_plus @ nat) @ (suc @ na)) @ ma))))).
% 2.46/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2DTF16466.p
% 2.46/1.49 ------------------------
% 2.74/1.52 ---- Cleaned THF ---
% 2.74/1.52 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 2.74/1.52 coindu1593790203_llist: $tType > $tType ).
% 2.74/1.52
% 2.74/1.52 thf(ty_t_Extended__Nat_Oenat,type,
% 2.74/1.52 extended_enat: $tType ).
% 2.74/1.52
% 2.74/1.52 thf(ty_t_List_Olist,type,
% 2.74/1.52 list: $tType > $tType ).
% 2.74/1.52
% 2.74/1.52 thf(ty_t_Num_Onum,type,
% 2.74/1.52 num: $tType ).
% 2.74/1.52
% 2.74/1.52 thf(ty_t_Nat_Onat,type,
% 2.74/1.52 nat: $tType ).
% 2.74/1.52
% 2.74/1.52 thf(ty_t_itself,type,
% 2.74/1.52 itself: $tType > $tType ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_HOL_Otype,type,
% 2.74/1.52 type:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oone,type,
% 2.74/1.52 one:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Num_Onumeral,type,
% 2.74/1.52 numeral:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Rings_Oring__1,type,
% 2.74/1.52 ring_1:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Ouminus,type,
% 2.74/1.52 uminus:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Orderings_Oord,type,
% 2.74/1.52 ord:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Nat_Oring__char__0,type,
% 2.74/1.52 ring_char_0:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Num_Oneg__numeral,type,
% 2.74/1.52 neg_numeral:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Orderings_Oorder,type,
% 2.74/1.52 order:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Ogroup__add,type,
% 2.74/1.52 group_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 2.74/1.52 linorder:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oab__group__add,type,
% 2.74/1.52 ab_group_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Nat_Osemiring__char__0,type,
% 2.74/1.52 semiring_char_0:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.74/1.52 semigroup_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.74/1.52 comm_semiring_1:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.74/1.52 linordered_idom:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Fields_Olinordered__field,type,
% 2.74/1.52 linordered_field:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.74/1.52 ab_semigroup_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.74/1.52 linordered_semidom:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.74/1.52 cancel_semigroup_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.74/1.52 ordered_ab_group_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.74/1.52 ordere779506340up_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.74/1.52 ordere236663937imp_le:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.74/1.52 ordere223160158up_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.74/1.52 strict2144017051up_add:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 2.74/1.52 condit1656338222tinuum:
% 2.74/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 2.74/1.52 coindu493225792length:
% 2.74/1.52 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux,type,
% 2.74/1.52 coindu1542816657of_aux:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 2.74/1.52 coindu1121789889_LCons:
% 2.74/1.52 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 2.74/1.52 coindu1598213697e_LNil:
% 2.74/1.52 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of,type,
% 2.74/1.52 coindu1079202755ist_of:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 2.74/1.52 coindu567634248member:
% 2.74/1.52 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.74/1.52 one_one:
% 2.74/1.52 !>[A: $tType] : A ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.74/1.52 plus_plus:
% 2.74/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.74/1.52 uminus_uminus:
% 2.74/1.52 !>[A: $tType] : ( A > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_If,type,
% 2.74/1.52 if:
% 2.74/1.52 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Ocount__list,type,
% 2.74/1.52 count_list:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Ogen__length,type,
% 2.74/1.52 gen_length:
% 2.74/1.52 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Olist_OCons,type,
% 2.74/1.52 cons:
% 2.74/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Olist_ONil,type,
% 2.74/1.52 nil:
% 2.74/1.52 !>[A: $tType] : ( list @ A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Omember,type,
% 2.74/1.52 member:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Onth,type,
% 2.74/1.52 nth:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 2.74/1.52 ord_lexordp_eq:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Oproduct__lists,type,
% 2.74/1.52 product_lists:
% 2.74/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Osublists,type,
% 2.74/1.52 sublists:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_List_Oupt,type,
% 2.74/1.52 upt: nat > nat > ( list @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Nat_OSuc,type,
% 2.74/1.52 suc: nat > nat ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Nat__Bijection_Otriangle,type,
% 2.74/1.52 nat_triangle: nat > nat ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_OBitM,type,
% 2.74/1.52 bitM: num > num ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Oinc,type,
% 2.74/1.52 inc: num > num ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 2.74/1.52 neg_numeral_dbl:
% 2.74/1.52 !>[A: $tType] : ( A > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 2.74/1.52 neg_numeral_dbl_dec:
% 2.74/1.52 !>[A: $tType] : ( A > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Oneg__numeral__class_Osub,type,
% 2.74/1.52 neg_numeral_sub:
% 2.74/1.52 !>[A: $tType] : ( num > num > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Onum_OBit0,type,
% 2.74/1.52 bit0: num > num ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Onum_OOne,type,
% 2.74/1.52 one2: num ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 2.74/1.52 numeral_numeral:
% 2.74/1.52 !>[A: $tType] : ( num > A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Num_Oring__1__class_Oiszero,type,
% 2.74/1.52 ring_1_iszero:
% 2.74/1.52 !>[A: $tType] : ( A > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.74/1.52 ord_less:
% 2.74/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Pure_Otype,type,
% 2.74/1.52 type2:
% 2.74/1.52 !>[A: $tType] : ( itself @ A ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_c_Sublist_Oprefixes,type,
% 2.74/1.52 prefixes:
% 2.74/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(sy_v_ma____,type,
% 2.74/1.52 ma: nat ).
% 2.74/1.52
% 2.74/1.52 thf(sy_v_na____,type,
% 2.74/1.52 na: nat ).
% 2.74/1.52
% 2.74/1.52 thf(fact_0_llist__of__inject,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.74/1.52 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.74/1.52 = ( coindu1079202755ist_of @ A @ Ys ) )
% 2.74/1.52 = ( Xs = Ys ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_1_add__Suc__right,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 2.74/1.52 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_2_upt__conv__Cons__Cons,axiom,
% 2.74/1.52 ! [M: nat,N: nat,Ns: list @ nat,Q: nat] :
% 2.74/1.52 ( ( ( cons @ nat @ M @ ( cons @ nat @ N @ Ns ) )
% 2.74/1.52 = ( upt @ M @ Q ) )
% 2.74/1.52 = ( ( cons @ nat @ N @ Ns )
% 2.74/1.52 = ( upt @ ( suc @ M ) @ Q ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_3_nat_Oinject,axiom,
% 2.74/1.52 ! [X2: nat,Y2: nat] :
% 2.74/1.52 ( ( ( suc @ X2 )
% 2.74/1.52 = ( suc @ Y2 ) )
% 2.74/1.52 = ( X2 = Y2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_4_old_Onat_Oinject,axiom,
% 2.74/1.52 ! [Nat: nat,Nat2: nat] :
% 2.74/1.52 ( ( ( suc @ Nat )
% 2.74/1.52 = ( suc @ Nat2 ) )
% 2.74/1.52 = ( Nat = Nat2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_5_add__left__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ A2 @ B )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ C ) )
% 2.74/1.52 = ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_6_add__right__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ B @ A2 )
% 2.74/1.52 = ( plus_plus @ A @ C @ A2 ) )
% 2.74/1.52 = ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_7_list_Oinject,axiom,
% 2.74/1.52 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.74/1.52 ( ( ( cons @ A @ X21 @ X22 )
% 2.74/1.52 = ( cons @ A @ Y21 @ Y22 ) )
% 2.74/1.52 = ( ( X21 = Y21 )
% 2.74/1.52 & ( X22 = Y22 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_8_add__Suc__shift,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.74/1.52 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_9_add__Suc,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.74/1.52 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_10__092_060open_062_092_060And_062xs_Ax_O_ALCons_Ax_A_Illist__of_Axs_J_A_061_Allist__of_A_Ix_A_D_Axs_J_092_060close_062,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.74/1.52 ( ( coindu1121789889_LCons @ A @ X @ ( coindu1079202755ist_of @ A @ Xs ) )
% 2.74/1.52 = ( coindu1079202755ist_of @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_11_nat__add__left__cancel,axiom,
% 2.74/1.52 ! [K: nat,M: nat,N: nat] :
% 2.74/1.52 ( ( ( plus_plus @ nat @ K @ M )
% 2.74/1.52 = ( plus_plus @ nat @ K @ N ) )
% 2.74/1.52 = ( M = N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_12_llist_Oinject,axiom,
% 2.74/1.52 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 2.74/1.52 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 2.74/1.52 = ( ( X21 = Y21 )
% 2.74/1.52 & ( X22 = Y22 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_13_llist__of__eq__LCons__conv,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.74/1.52 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.74/1.52 = ( ? [Xs2: list @ A] :
% 2.74/1.52 ( ( Xs
% 2.74/1.52 = ( cons @ A @ Y @ Xs2 ) )
% 2.74/1.52 & ( Ys
% 2.74/1.52 = ( coindu1079202755ist_of @ A @ Xs2 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_14_not__Cons__self2,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.74/1.52 ( ( cons @ A @ X @ Xs )
% 2.74/1.52 != Xs ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_15_add__right__imp__eq,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ B @ A2 )
% 2.74/1.52 = ( plus_plus @ A @ C @ A2 ) )
% 2.74/1.52 => ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_16_add__left__imp__eq,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ A2 @ B )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ C ) )
% 2.74/1.52 => ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_17_add_Oleft__commute,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_18_add_Ocommute,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( plus_plus @ A )
% 2.74/1.52 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_19_add_Oright__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ B @ A2 )
% 2.74/1.52 = ( plus_plus @ A @ C @ A2 ) )
% 2.74/1.52 = ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_20_add_Oleft__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( ( plus_plus @ A @ A2 @ B )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ C ) )
% 2.74/1.52 = ( B = C ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_21_add_Oassoc,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_22_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [I: A,J: A,K: A,L: A] :
% 2.74/1.52 ( ( ( I = J )
% 2.74/1.52 & ( K = L ) )
% 2.74/1.52 => ( ( plus_plus @ A @ I @ K )
% 2.74/1.52 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_23_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_24_n__not__Suc__n,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ( N
% 2.74/1.52 != ( suc @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_25_Suc__inject,axiom,
% 2.74/1.52 ! [X: nat,Y: nat] :
% 2.74/1.52 ( ( ( suc @ X )
% 2.74/1.52 = ( suc @ Y ) )
% 2.74/1.52 => ( X = Y ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_26_nat__add__right__cancel,axiom,
% 2.74/1.52 ! [M: nat,K: nat,N: nat] :
% 2.74/1.52 ( ( ( plus_plus @ nat @ M @ K )
% 2.74/1.52 = ( plus_plus @ nat @ N @ K ) )
% 2.74/1.52 = ( M = N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_27_list__of__aux__code_I2_J,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.74/1.52 = ( coindu1542816657of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_28_gen__length__code_I2_J,axiom,
% 2.74/1.52 ! [B3: $tType,N: nat,X: B3,Xs: list @ B3] :
% 2.74/1.52 ( ( gen_length @ B3 @ N @ ( cons @ B3 @ X @ Xs ) )
% 2.74/1.52 = ( gen_length @ B3 @ ( suc @ N ) @ Xs ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_29_upt__conv__Cons,axiom,
% 2.74/1.52 ! [I: nat,J: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ( upt @ I @ J )
% 2.74/1.52 = ( cons @ nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_30_lmember__code_I2_J,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.74/1.52 = ( ( X = Y )
% 2.74/1.52 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_31_semiring__normalization__rules_I20_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A,D: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) )
% 2.74/1.52 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_32_semiring__normalization__rules_I21_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_33_semiring__normalization__rules_I22_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,C: A,D: A] :
% 2.74/1.52 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 2.74/1.52 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_34_semiring__normalization__rules_I23_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_35_semiring__normalization__rules_I24_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( plus_plus @ A )
% 2.74/1.52 = ( ^ [A3: A,C2: A] : ( plus_plus @ A @ C2 @ A3 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_36_semiring__normalization__rules_I25_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,C: A,D: A] :
% 2.74/1.52 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 2.74/1.52 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ D ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_37_linordered__field__class_Osign__simps_I26_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_38_add__less__cancel__left,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [C: A,A2: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.74/1.52 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_39_add__less__cancel__right,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,C: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.74/1.52 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_40_lessI,axiom,
% 2.74/1.52 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_41_Suc__mono,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_42_Suc__less__eq,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.74/1.52 = ( ord_less @ nat @ M @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_43_nat__add__left__cancel__less,axiom,
% 2.74/1.52 ! [K: nat,M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.74/1.52 = ( ord_less @ nat @ M @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_44_nat__neq__iff,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( M != N )
% 2.74/1.52 = ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_45_less__not__refl,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ~ ( ord_less @ nat @ N @ N ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_46_less__not__refl2,axiom,
% 2.74/1.52 ! [N: nat,M: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ N @ M )
% 2.74/1.52 => ( M != N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_47_less__not__refl3,axiom,
% 2.74/1.52 ! [S: nat,T: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ S @ T )
% 2.74/1.52 => ( S != T ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_48_measure__induct,axiom,
% 2.74/1.52 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.74/1.52 ( ! [X3: A] :
% 2.74/1.52 ( ! [Y3: A] :
% 2.74/1.52 ( ( ord_less @ nat @ ( F @ Y3 ) @ ( F @ X3 ) )
% 2.74/1.52 => ( P @ Y3 ) )
% 2.74/1.52 => ( P @ X3 ) )
% 2.74/1.52 => ( P @ A2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_49_less__irrefl__nat,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ~ ( ord_less @ nat @ N @ N ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_50_nat__less__induct,axiom,
% 2.74/1.52 ! [P: nat > $o,N: nat] :
% 2.74/1.52 ( ! [N2: nat] :
% 2.74/1.52 ( ! [M2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M2 @ N2 )
% 2.74/1.52 => ( P @ M2 ) )
% 2.74/1.52 => ( P @ N2 ) )
% 2.74/1.52 => ( P @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_51_infinite__descent,axiom,
% 2.74/1.52 ! [P: nat > $o,N: nat] :
% 2.74/1.52 ( ! [N2: nat] :
% 2.74/1.52 ( ~ ( P @ N2 )
% 2.74/1.52 => ? [M2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M2 @ N2 )
% 2.74/1.52 & ~ ( P @ M2 ) ) )
% 2.74/1.52 => ( P @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_52_linorder__neqE__nat,axiom,
% 2.74/1.52 ! [X: nat,Y: nat] :
% 2.74/1.52 ( ( X != Y )
% 2.74/1.52 => ( ~ ( ord_less @ nat @ X @ Y )
% 2.74/1.52 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_53_measure__induct__rule,axiom,
% 2.74/1.52 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.74/1.52 ( ! [X3: A] :
% 2.74/1.52 ( ! [Y3: A] :
% 2.74/1.52 ( ( ord_less @ nat @ ( F @ Y3 ) @ ( F @ X3 ) )
% 2.74/1.52 => ( P @ Y3 ) )
% 2.74/1.52 => ( P @ X3 ) )
% 2.74/1.52 => ( P @ A2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_54_infinite__descent__measure,axiom,
% 2.74/1.52 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 2.74/1.52 ( ! [X3: A] :
% 2.74/1.52 ( ~ ( P @ X3 )
% 2.74/1.52 => ? [Y3: A] :
% 2.74/1.52 ( ( ord_less @ nat @ ( V @ Y3 ) @ ( V @ X3 ) )
% 2.74/1.52 & ~ ( P @ Y3 ) ) )
% 2.74/1.52 => ( P @ X ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_55_linordered__field__no__ub,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X4: A] :
% 2.74/1.52 ? [X1: A] : ( ord_less @ A @ X4 @ X1 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_56_linordered__field__no__lb,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X4: A] :
% 2.74/1.52 ? [Y4: A] : ( ord_less @ A @ Y4 @ X4 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_57_lift__Suc__mono__less__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [F: nat > A,N: nat,M: nat] :
% 2.74/1.52 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.74/1.52 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 2.74/1.52 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_58_lift__Suc__mono__less,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [F: nat > A,N: nat,N3: nat] :
% 2.74/1.52 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.74/1.52 => ( ( ord_less @ nat @ N @ N3 )
% 2.74/1.52 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_59_add__mono__thms__linordered__field_I5_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [I: A,J: A,K: A,L: A] :
% 2.74/1.52 ( ( ( ord_less @ A @ I @ J )
% 2.74/1.52 & ( ord_less @ A @ K @ L ) )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_60_add__mono__thms__linordered__field_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [I: A,J: A,K: A,L: A] :
% 2.74/1.52 ( ( ( I = J )
% 2.74/1.52 & ( ord_less @ A @ K @ L ) )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_61_add__mono__thms__linordered__field_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [I: A,J: A,K: A,L: A] :
% 2.74/1.52 ( ( ( ord_less @ A @ I @ J )
% 2.74/1.52 & ( K = L ) )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_62_add__strict__mono,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A,D: A] :
% 2.74/1.52 ( ( ord_less @ A @ A2 @ B )
% 2.74/1.52 => ( ( ord_less @ A @ C @ D )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_63_add__strict__left__mono,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( ord_less @ A @ A2 @ B )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_64_add__strict__right__mono,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( ord_less @ A @ A2 @ B )
% 2.74/1.52 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_65_add__less__imp__less__left,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [C: A,A2: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.74/1.52 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_66_add__less__imp__less__right,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,C: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.74/1.52 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_67_lessE,axiom,
% 2.74/1.52 ! [I: nat,K: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ K )
% 2.74/1.52 => ( ( K
% 2.74/1.52 != ( suc @ I ) )
% 2.74/1.52 => ~ ! [J2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J2 )
% 2.74/1.52 => ( K
% 2.74/1.52 != ( suc @ J2 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_68_Suc__lessD,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 2.74/1.52 => ( ord_less @ nat @ M @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_69_Suc__lessE,axiom,
% 2.74/1.52 ! [I: nat,K: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 2.74/1.52 => ~ ! [J2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J2 )
% 2.74/1.52 => ( K
% 2.74/1.52 != ( suc @ J2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_70_Suc__lessI,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 => ( ( ( suc @ M )
% 2.74/1.52 != N )
% 2.74/1.52 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_71_less__SucE,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.74/1.52 => ( ~ ( ord_less @ nat @ M @ N )
% 2.74/1.52 => ( M = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_72_less__SucI,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_73_less__Suc__eq,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.74/1.52 = ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 | ( M = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_74_not__less__eq,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 2.74/1.52 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_75_Suc__less__eq2,axiom,
% 2.74/1.52 ! [N: nat,M: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 2.74/1.52 = ( ? [M3: nat] :
% 2.74/1.52 ( ( M
% 2.74/1.52 = ( suc @ M3 ) )
% 2.74/1.52 & ( ord_less @ nat @ N @ M3 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_76_less__antisym,axiom,
% 2.74/1.52 ! [N: nat,M: nat] :
% 2.74/1.52 ( ~ ( ord_less @ nat @ N @ M )
% 2.74/1.52 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.74/1.52 => ( M = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_77_Suc__less__SucD,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.74/1.52 => ( ord_less @ nat @ M @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_78_less__trans__Suc,axiom,
% 2.74/1.52 ! [I: nat,J: nat,K: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ( ord_less @ nat @ J @ K )
% 2.74/1.52 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_79_less__Suc__induct,axiom,
% 2.74/1.52 ! [I: nat,J: nat,P: nat > nat > $o] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 2.74/1.52 => ( ! [I2: nat,J2: nat,K2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I2 @ J2 )
% 2.74/1.52 => ( ( ord_less @ nat @ J2 @ K2 )
% 2.74/1.52 => ( ( P @ I2 @ J2 )
% 2.74/1.52 => ( ( P @ J2 @ K2 )
% 2.74/1.52 => ( P @ I2 @ K2 ) ) ) ) )
% 2.74/1.52 => ( P @ I @ J ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_80_strict__inc__induct,axiom,
% 2.74/1.52 ! [I: nat,J: nat,P: nat > $o] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ! [I2: nat] :
% 2.74/1.52 ( ( J
% 2.74/1.52 = ( suc @ I2 ) )
% 2.74/1.52 => ( P @ I2 ) )
% 2.74/1.52 => ( ! [I2: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I2 @ J )
% 2.74/1.52 => ( ( P @ ( suc @ I2 ) )
% 2.74/1.52 => ( P @ I2 ) ) )
% 2.74/1.52 => ( P @ I ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_81_not__less__less__Suc__eq,axiom,
% 2.74/1.52 ! [N: nat,M: nat] :
% 2.74/1.52 ( ~ ( ord_less @ nat @ N @ M )
% 2.74/1.52 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.74/1.52 = ( N = M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_82_add__lessD1,axiom,
% 2.74/1.52 ! [I: nat,J: nat,K: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 2.74/1.52 => ( ord_less @ nat @ I @ K ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_83_add__less__mono,axiom,
% 2.74/1.52 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ( ord_less @ nat @ K @ L )
% 2.74/1.52 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_84_not__add__less1,axiom,
% 2.74/1.52 ! [I: nat,J: nat] :
% 2.74/1.52 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_85_not__add__less2,axiom,
% 2.74/1.52 ! [J: nat,I: nat] :
% 2.74/1.52 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_86_add__less__mono1,axiom,
% 2.74/1.52 ! [I: nat,J: nat,K: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_87_trans__less__add1,axiom,
% 2.74/1.52 ! [I: nat,J: nat,M: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_88_trans__less__add2,axiom,
% 2.74/1.52 ! [I: nat,J: nat,M: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_89_less__add__eq__less,axiom,
% 2.74/1.52 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ K @ L )
% 2.74/1.52 => ( ( ( plus_plus @ nat @ M @ L )
% 2.74/1.52 = ( plus_plus @ nat @ K @ N ) )
% 2.74/1.52 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_90_less__add__Suc1,axiom,
% 2.74/1.52 ! [I: nat,M: nat] : ( ord_less @ nat @ I @ ( suc @ ( plus_plus @ nat @ I @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_91_less__add__Suc2,axiom,
% 2.74/1.52 ! [I: nat,M: nat] : ( ord_less @ nat @ I @ ( suc @ ( plus_plus @ nat @ M @ I ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_92_less__iff__Suc__add,axiom,
% 2.74/1.52 ( ( ord_less @ nat )
% 2.74/1.52 = ( ^ [M4: nat,N4: nat] :
% 2.74/1.52 ? [K3: nat] :
% 2.74/1.52 ( N4
% 2.74/1.52 = ( suc @ ( plus_plus @ nat @ M4 @ K3 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_93_less__imp__Suc__add,axiom,
% 2.74/1.52 ! [M: nat,N: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ M @ N )
% 2.74/1.52 => ? [K2: nat] :
% 2.74/1.52 ( N
% 2.74/1.52 = ( suc @ ( plus_plus @ nat @ M @ K2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_94_linordered__field__class_Osign__simps_I28_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_95_linordered__field__class_Osign__simps_I27_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( plus_plus @ A )
% 2.74/1.52 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_96_upt__eq__Cons__conv,axiom,
% 2.74/1.52 ! [I: nat,J: nat,X: nat,Xs: list @ nat] :
% 2.74/1.52 ( ( ( upt @ I @ J )
% 2.74/1.52 = ( cons @ nat @ X @ Xs ) )
% 2.74/1.52 = ( ( ord_less @ nat @ I @ J )
% 2.74/1.52 & ( I = X )
% 2.74/1.52 & ( ( upt @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) @ J )
% 2.74/1.52 = Xs ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_97_upt__rec,axiom,
% 2.74/1.52 ( upt
% 2.74/1.52 = ( ^ [I3: nat,J3: nat] : ( if @ ( list @ nat ) @ ( ord_less @ nat @ I3 @ J3 ) @ ( cons @ nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ ( nil @ nat ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_98_nth__upt,axiom,
% 2.74/1.52 ! [I: nat,K: nat,J: nat] :
% 2.74/1.52 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ J )
% 2.74/1.52 => ( ( nth @ nat @ ( upt @ I @ J ) @ K )
% 2.74/1.52 = ( plus_plus @ nat @ I @ K ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_99_lexordp__eq__simps_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.74/1.52 = ( ( ord_less @ A @ X @ Y )
% 2.74/1.52 | ( ~ ( ord_less @ A @ Y @ X )
% 2.74/1.52 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_100_is__num__normalize_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A,C: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.74/1.52 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_101_member__rec_I1_J,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Xs: list @ A,Y: A] :
% 2.74/1.52 ( ( member @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 2.74/1.52 = ( ( X = Y )
% 2.74/1.52 | ( member @ A @ Xs @ Y ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_102_ex__gt__or__lt,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A] :
% 2.74/1.52 ? [B4: A] :
% 2.74/1.52 ( ( ord_less @ A @ A2 @ B4 )
% 2.74/1.52 | ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_103_linorder__neqE__linordered__idom,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A,Y: A] :
% 2.74/1.52 ( ( X != Y )
% 2.74/1.52 => ( ~ ( ord_less @ A @ X @ Y )
% 2.74/1.52 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_104_lexordp__eq__simps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_105_lexordp__eq__simps_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Xs: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 2.74/1.52 = ( Xs
% 2.74/1.52 = ( nil @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_106_nth__Cons__Suc,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Xs: list @ A,N: nat] :
% 2.74/1.52 ( ( nth @ A @ ( cons @ A @ X @ Xs ) @ ( suc @ N ) )
% 2.74/1.52 = ( nth @ A @ Xs @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_107_lexordp__eq__simps_I3_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A,Xs: list @ A] :
% 2.74/1.52 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_108_less__numeral__extra_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_109_transpose_Ocases,axiom,
% 2.74/1.52 ! [A: $tType,X: list @ ( list @ A )] :
% 2.74/1.52 ( ( X
% 2.74/1.52 != ( nil @ ( list @ A ) ) )
% 2.74/1.52 => ( ! [Xss: list @ ( list @ A )] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.74/1.52 => ~ ! [X3: A,Xs3: list @ A,Xss: list @ ( list @ A )] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs3 ) @ Xss ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_110_lexordp__eq__antisym,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Xs: list @ A,Ys: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.74/1.52 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 2.74/1.52 => ( Xs = Ys ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_111_lexordp__eq__linear,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Xs: list @ A,Ys: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.74/1.52 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_112_lexordp__eq__trans,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.74/1.52 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 2.74/1.52 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_113_lexordp__eq__refl,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_114_lexordp__eq_ONil,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_115_one__reorient,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( one @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A] :
% 2.74/1.52 ( ( ( one_one @ A )
% 2.74/1.52 = X )
% 2.74/1.52 = ( X
% 2.74/1.52 = ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_116_member__rec_I2_J,axiom,
% 2.74/1.52 ! [A: $tType,Y: A] :
% 2.74/1.52 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_117_lexordp__eq_Oinducts,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X12: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ X12 @ X2 )
% 2.74/1.52 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.74/1.52 => ( ! [X3: A,Y4: A,Xs3: list @ A,Ys2: list @ A] :
% 2.74/1.52 ( ( ord_less @ A @ X3 @ Y4 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 2.74/1.52 => ( ! [X3: A,Y4: A,Xs3: list @ A,Ys2: list @ A] :
% 2.74/1.52 ( ~ ( ord_less @ A @ X3 @ Y4 )
% 2.74/1.52 => ( ~ ( ord_less @ A @ Y4 @ X3 )
% 2.74/1.52 => ( ( ord_lexordp_eq @ A @ Xs3 @ Ys2 )
% 2.74/1.52 => ( ( P @ Xs3 @ Ys2 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) ) ) )
% 2.74/1.52 => ( P @ X12 @ X2 ) ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_118_lexordp__eq_Osimps,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( ord_lexordp_eq @ A )
% 2.74/1.52 = ( ^ [A1: list @ A,A22: list @ A] :
% 2.74/1.52 ( ? [Ys3: list @ A] :
% 2.74/1.52 ( ( A1
% 2.74/1.52 = ( nil @ A ) )
% 2.74/1.52 & ( A22 = Ys3 ) )
% 2.74/1.52 | ? [X5: A,Y5: A,Xs4: list @ A,Ys3: list @ A] :
% 2.74/1.52 ( ( A1
% 2.74/1.52 = ( cons @ A @ X5 @ Xs4 ) )
% 2.74/1.52 & ( A22
% 2.74/1.52 = ( cons @ A @ Y5 @ Ys3 ) )
% 2.74/1.52 & ( ord_less @ A @ X5 @ Y5 ) )
% 2.74/1.52 | ? [X5: A,Y5: A,Xs4: list @ A,Ys3: list @ A] :
% 2.74/1.52 ( ( A1
% 2.74/1.52 = ( cons @ A @ X5 @ Xs4 ) )
% 2.74/1.52 & ( A22
% 2.74/1.52 = ( cons @ A @ Y5 @ Ys3 ) )
% 2.74/1.52 & ~ ( ord_less @ A @ X5 @ Y5 )
% 2.74/1.52 & ~ ( ord_less @ A @ Y5 @ X5 )
% 2.74/1.52 & ( ord_lexordp_eq @ A @ Xs4 @ Ys3 ) ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_119_lexordp__eq_Ocases,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A12: list @ A,A23: list @ A] :
% 2.74/1.52 ( ( ord_lexordp_eq @ A @ A12 @ A23 )
% 2.74/1.52 => ( ( ( A12
% 2.74/1.52 = ( nil @ A ) )
% 2.74/1.52 => ! [Ys2: list @ A] : ( A23 != Ys2 ) )
% 2.74/1.52 => ( ! [X3: A] :
% 2.74/1.52 ( ? [Xs3: list @ A] :
% 2.74/1.52 ( A12
% 2.74/1.52 = ( cons @ A @ X3 @ Xs3 ) )
% 2.74/1.52 => ! [Y4: A] :
% 2.74/1.52 ( ? [Ys2: list @ A] :
% 2.74/1.52 ( A23
% 2.74/1.52 = ( cons @ A @ Y4 @ Ys2 ) )
% 2.74/1.52 => ~ ( ord_less @ A @ X3 @ Y4 ) ) )
% 2.74/1.52 => ~ ! [X3: A,Y4: A,Xs3: list @ A] :
% 2.74/1.52 ( ( A12
% 2.74/1.52 = ( cons @ A @ X3 @ Xs3 ) )
% 2.74/1.52 => ! [Ys2: list @ A] :
% 2.74/1.52 ( ( A23
% 2.74/1.52 = ( cons @ A @ Y4 @ Ys2 ) )
% 2.74/1.52 => ( ~ ( ord_less @ A @ X3 @ Y4 )
% 2.74/1.52 => ( ~ ( ord_less @ A @ Y4 @ X3 )
% 2.74/1.52 => ~ ( ord_lexordp_eq @ A @ Xs3 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_120_map__tailrec__rev_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,B3: $tType,P: ( A > B3 ) > ( list @ A ) > ( list @ B3 ) > $o,A0: A > B3,A12: list @ A,A23: list @ B3] :
% 2.74/1.52 ( ! [F2: A > B3,X1: list @ B3] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 2.74/1.52 => ( ! [F2: A > B3,A4: A,As: list @ A,Bs: list @ B3] :
% 2.74/1.52 ( ( P @ F2 @ As @ ( cons @ B3 @ ( F2 @ A4 ) @ Bs ) )
% 2.74/1.52 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.74/1.52 => ( P @ A0 @ A12 @ A23 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_121_list__nonempty__induct,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.74/1.52 ( ( Xs
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.74/1.52 => ( ! [X3: A,Xs3: list @ A] :
% 2.74/1.52 ( ( Xs3
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 => ( ( P @ Xs3 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) ) )
% 2.74/1.52 => ( P @ Xs ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_122_remdups__adj_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.74/1.52 ( ( P @ ( nil @ A ) )
% 2.74/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.74/1.52 => ( ! [X3: A,Y4: A,Xs3: list @ A] :
% 2.74/1.52 ( ( ( X3 = Y4 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) )
% 2.74/1.52 => ( ( ( X3 != Y4 )
% 2.74/1.52 => ( P @ ( cons @ A @ Y4 @ Xs3 ) ) )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y4 @ Xs3 ) ) ) ) )
% 2.74/1.52 => ( P @ A0 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_123_remdups__adj_Ocases,axiom,
% 2.74/1.52 ! [A: $tType,X: list @ A] :
% 2.74/1.52 ( ( X
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 => ( ! [X3: A] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.74/1.52 => ~ ! [X3: A,Y4: A,Xs3: list @ A] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ A @ X3 @ ( cons @ A @ Y4 @ Xs3 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_124_splice_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A12: list @ A] :
% 2.74/1.52 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.74/1.52 => ( ! [V2: A,Va: list @ A] : ( P @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) )
% 2.74/1.52 => ( ! [X3: A,Xs3: list @ A,Y4: A,Ys2: list @ A] :
% 2.74/1.52 ( ( P @ Xs3 @ Ys2 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 2.74/1.52 => ( P @ A0 @ A12 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_125_list__induct2_H,axiom,
% 2.74/1.52 ! [A: $tType,B3: $tType,P: ( list @ A ) > ( list @ B3 ) > $o,Xs: list @ A,Ys: list @ B3] :
% 2.74/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B3 ) )
% 2.74/1.52 => ( ! [X3: A,Xs3: list @ A] : ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( nil @ B3 ) )
% 2.74/1.52 => ( ! [Y4: B3,Ys2: list @ B3] : ( P @ ( nil @ A ) @ ( cons @ B3 @ Y4 @ Ys2 ) )
% 2.74/1.52 => ( ! [X3: A,Xs3: list @ A,Y4: B3,Ys2: list @ B3] :
% 2.74/1.52 ( ( P @ Xs3 @ Ys2 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ B3 @ Y4 @ Ys2 ) ) )
% 2.74/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_126_neq__Nil__conv,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A] :
% 2.74/1.52 ( ( Xs
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 = ( ? [Y5: A,Ys3: list @ A] :
% 2.74/1.52 ( Xs
% 2.74/1.52 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_127_list_Oinducts,axiom,
% 2.74/1.52 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.74/1.52 ( ( P @ ( nil @ A ) )
% 2.74/1.52 => ( ! [X1: A,X23: list @ A] :
% 2.74/1.52 ( ( P @ X23 )
% 2.74/1.52 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.74/1.52 => ( P @ List ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_128_list_Oexhaust,axiom,
% 2.74/1.52 ! [A: $tType,Y: list @ A] :
% 2.74/1.52 ( ( Y
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 => ~ ! [X212: A,X222: list @ A] :
% 2.74/1.52 ( Y
% 2.74/1.52 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_129_list_OdiscI,axiom,
% 2.74/1.52 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.74/1.52 ( ( List
% 2.74/1.52 = ( cons @ A @ X21 @ X22 ) )
% 2.74/1.52 => ( List
% 2.74/1.52 != ( nil @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_130_list_Odistinct_I1_J,axiom,
% 2.74/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.74/1.52 ( ( nil @ A )
% 2.74/1.52 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_131_less__add__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_132_gen__length__code_I1_J,axiom,
% 2.74/1.52 ! [A: $tType,N: nat] :
% 2.74/1.52 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 2.74/1.52 = N ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_133_Suc__eq__plus1__left,axiom,
% 2.74/1.52 ( suc
% 2.74/1.52 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_134_Suc__eq__plus1,axiom,
% 2.74/1.52 ( suc
% 2.74/1.52 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_135_lexordp__eq_OCons,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.74/1.52 ( ( ord_less @ A @ X @ Y )
% 2.74/1.52 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_136_lexordp__eq_OCons__eq,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.74/1.52 ( ~ ( ord_less @ A @ X @ Y )
% 2.74/1.52 => ( ~ ( ord_less @ A @ Y @ X )
% 2.74/1.52 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.74/1.52 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_137_fold__atLeastAtMost__nat_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A12: nat,A23: nat,A32: A] :
% 2.74/1.52 ( ! [F2: nat > A > A,A4: nat,B4: nat,Acc: A] :
% 2.74/1.52 ( ( ~ ( ord_less @ nat @ B4 @ A4 )
% 2.74/1.52 => ( P @ F2 @ ( plus_plus @ nat @ A4 @ ( one_one @ nat ) ) @ B4 @ ( F2 @ A4 @ Acc ) ) )
% 2.74/1.52 => ( P @ F2 @ A4 @ B4 @ Acc ) )
% 2.74/1.52 => ( P @ A0 @ A12 @ A23 @ A32 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_138_list__encode_Oinduct,axiom,
% 2.74/1.52 ! [P: ( list @ nat ) > $o,A0: list @ nat] :
% 2.74/1.52 ( ( P @ ( nil @ nat ) )
% 2.74/1.52 => ( ! [X3: nat,Xs3: list @ nat] :
% 2.74/1.52 ( ( P @ Xs3 )
% 2.74/1.52 => ( P @ ( cons @ nat @ X3 @ Xs3 ) ) )
% 2.74/1.52 => ( P @ A0 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_139_list__encode_Ocases,axiom,
% 2.74/1.52 ! [X: list @ nat] :
% 2.74/1.52 ( ( X
% 2.74/1.52 != ( nil @ nat ) )
% 2.74/1.52 => ~ ! [X3: nat,Xs3: list @ nat] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ nat @ X3 @ Xs3 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_140_gen__llength__code_I2_J,axiom,
% 2.74/1.52 ! [B3: $tType,N: nat,X: B3,Xs: coindu1593790203_llist @ B3] :
% 2.74/1.52 ( ( coindu493225792length @ B3 @ N @ ( coindu1121789889_LCons @ B3 @ X @ Xs ) )
% 2.74/1.52 = ( coindu493225792length @ B3 @ ( plus_plus @ nat @ N @ ( one_one @ nat ) ) @ Xs ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_141_upt__rec__numeral,axiom,
% 2.74/1.52 ! [M: num,N: num] :
% 2.74/1.52 ( ( ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 2.74/1.52 => ( ( upt @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 2.74/1.52 = ( cons @ nat @ ( numeral_numeral @ nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral @ nat @ M ) ) @ ( numeral_numeral @ nat @ N ) ) ) ) )
% 2.74/1.52 & ( ~ ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 2.74/1.52 => ( ( upt @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) )
% 2.74/1.52 = ( nil @ nat ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_142_numeral__eq__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( ( numeral_numeral @ A @ M )
% 2.74/1.52 = ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( M = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_143_numeral__less__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( ord_less @ num @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_144_add__numeral__left,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [V3: num,W: num,Z: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V3 ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 2.74/1.52 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V3 @ W ) ) @ Z ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_145_numeral__plus__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_146_not__numeral__less__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ~ ( ord_less @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_147_one__plus__numeral__commute,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X ) )
% 2.74/1.52 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_148_sublists_Osimps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( sublists @ A @ ( nil @ A ) )
% 2.74/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_149_triangle__Suc,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ( ( nat_triangle @ ( suc @ N ) )
% 2.74/1.52 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_150_longest__common__prefix_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A12: list @ A] :
% 2.74/1.52 ( ! [X3: A,Xs3: list @ A,Y4: A,Ys2: list @ A] :
% 2.74/1.52 ( ( ( X3 = Y4 )
% 2.74/1.52 => ( P @ Xs3 @ Ys2 ) )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 2.74/1.52 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.74/1.52 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 2.74/1.52 => ( P @ A0 @ A12 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_151_prefixes_Ocases,axiom,
% 2.74/1.52 ! [A: $tType,X: list @ A] :
% 2.74/1.52 ( ( X
% 2.74/1.52 != ( nil @ A ) )
% 2.74/1.52 => ~ ! [X3: A,Xs3: list @ A] :
% 2.74/1.52 ( X
% 2.74/1.52 != ( cons @ A @ X3 @ Xs3 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_152_prefixes_Oinduct,axiom,
% 2.74/1.52 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.74/1.52 ( ( P @ ( nil @ A ) )
% 2.74/1.52 => ( ! [X3: A,Xs3: list @ A] :
% 2.74/1.52 ( ( P @ Xs3 )
% 2.74/1.52 => ( P @ ( cons @ A @ X3 @ Xs3 ) ) )
% 2.74/1.52 => ( P @ A0 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_153_enat__ord__number_I2_J,axiom,
% 2.74/1.52 ! [M: num,N: num] :
% 2.74/1.52 ( ( ord_less @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( numeral_numeral @ extended_enat @ N ) )
% 2.74/1.52 = ( ord_less @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_154_product__lists_Osimps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.74/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_155__092_060open_062LNil_A_061_Allist__of_A_091_093_092_060close_062,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( coindu1598213697e_LNil @ A )
% 2.74/1.52 = ( coindu1079202755ist_of @ A @ ( nil @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_156_enat__less__induct,axiom,
% 2.74/1.52 ! [P: extended_enat > $o,N: extended_enat] :
% 2.74/1.52 ( ! [N2: extended_enat] :
% 2.74/1.52 ( ! [M2: extended_enat] :
% 2.74/1.52 ( ( ord_less @ extended_enat @ M2 @ N2 )
% 2.74/1.52 => ( P @ M2 ) )
% 2.74/1.52 => ( P @ N2 ) )
% 2.74/1.52 => ( P @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_157_llist_Odistinct_I1_J,axiom,
% 2.74/1.52 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( coindu1598213697e_LNil @ A )
% 2.74/1.52 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_158_llist_Oexhaust,axiom,
% 2.74/1.52 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( Y
% 2.74/1.52 != ( coindu1598213697e_LNil @ A ) )
% 2.74/1.52 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 2.74/1.52 ( Y
% 2.74/1.52 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_159_neq__LNil__conv,axiom,
% 2.74/1.52 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.74/1.52 ( ( Xs
% 2.74/1.52 != ( coindu1598213697e_LNil @ A ) )
% 2.74/1.52 = ( ? [X5: A,Xs2: coindu1593790203_llist @ A] :
% 2.74/1.52 ( Xs
% 2.74/1.52 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_160_lmember__code_I1_J,axiom,
% 2.74/1.52 ! [A: $tType,X: A] :
% 2.74/1.52 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_161_llist__of__eq__LNil__conv,axiom,
% 2.74/1.52 ! [A: $tType,Xs: list @ A] :
% 2.74/1.52 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.74/1.52 = ( coindu1598213697e_LNil @ A ) )
% 2.74/1.52 = ( Xs
% 2.74/1.52 = ( nil @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_162_count__list_Osimps_I2_J,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Y: A,Xs: list @ A] :
% 2.74/1.52 ( ( ( X = Y )
% 2.74/1.52 => ( ( count_list @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 2.74/1.52 = ( plus_plus @ nat @ ( count_list @ A @ Xs @ Y ) @ ( one_one @ nat ) ) ) )
% 2.74/1.52 & ( ( X != Y )
% 2.74/1.52 => ( ( count_list @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 2.74/1.52 = ( count_list @ A @ Xs @ Y ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_163_one__less__numeral__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( ord_less @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( ord_less @ num @ one2 @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_164_one__plus__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_165_one__eq__numeral__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( ( one_one @ A )
% 2.74/1.52 = ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( one2 = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_166_numeral__eq__one__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( ( numeral_numeral @ A @ N )
% 2.74/1.52 = ( one_one @ A ) )
% 2.74/1.52 = ( N = one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_167_Suc__numeral,axiom,
% 2.74/1.52 ! [N: num] :
% 2.74/1.52 ( ( suc @ ( numeral_numeral @ nat @ N ) )
% 2.74/1.52 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N @ one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_168_numeral__plus__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_169_add__One__commute,axiom,
% 2.74/1.52 ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ num @ one2 @ N )
% 2.74/1.52 = ( plus_plus @ num @ N @ one2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_170_numeral__One,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( numeral_numeral @ A @ one2 )
% 2.74/1.52 = ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_171_numerals_I1_J,axiom,
% 2.74/1.52 ( ( numeral_numeral @ nat @ one2 )
% 2.74/1.52 = ( one_one @ nat ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_172_Suc__nat__number__of__add,axiom,
% 2.74/1.52 ! [V3: num,N: nat] :
% 2.74/1.52 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V3 ) @ N ) )
% 2.74/1.52 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V3 @ one2 ) ) @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_173_semiring__norm_I75_J,axiom,
% 2.74/1.52 ! [M: num] :
% 2.74/1.52 ~ ( ord_less @ num @ M @ one2 ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_174_prefixes_Osimps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( prefixes @ A @ ( nil @ A ) )
% 2.74/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_175_Suc__1,axiom,
% 2.74/1.52 ( ( suc @ ( one_one @ nat ) )
% 2.74/1.52 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_176_num_Oinject_I1_J,axiom,
% 2.74/1.52 ! [X2: num,Y2: num] :
% 2.74/1.52 ( ( ( bit0 @ X2 )
% 2.74/1.52 = ( bit0 @ Y2 ) )
% 2.74/1.52 = ( X2 = Y2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_177_semiring__norm_I6_J,axiom,
% 2.74/1.52 ! [M: num,N: num] :
% 2.74/1.52 ( ( plus_plus @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 2.74/1.52 = ( bit0 @ ( plus_plus @ num @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_178_semiring__norm_I78_J,axiom,
% 2.74/1.52 ! [M: num,N: num] :
% 2.74/1.52 ( ( ord_less @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 2.74/1.52 = ( ord_less @ num @ M @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_179_semiring__norm_I2_J,axiom,
% 2.74/1.52 ( ( plus_plus @ num @ one2 @ one2 )
% 2.74/1.52 = ( bit0 @ one2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_180_semiring__norm_I76_J,axiom,
% 2.74/1.52 ! [N: num] : ( ord_less @ num @ one2 @ ( bit0 @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_181_one__add__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_182_add__2__eq__Suc,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N )
% 2.74/1.52 = ( suc @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_183_add__2__eq__Suc_H,axiom,
% 2.74/1.52 ! [N: nat] :
% 2.74/1.52 ( ( plus_plus @ nat @ N @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 2.74/1.52 = ( suc @ ( suc @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_184_num_Odistinct_I1_J,axiom,
% 2.74/1.52 ! [X2: num] :
% 2.74/1.52 ( one2
% 2.74/1.52 != ( bit0 @ X2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_185_numeral__Bit0,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 2.74/1.52 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_186_nat__1__add__1,axiom,
% 2.74/1.52 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 2.74/1.52 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_187_dbl__simps_I3_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_188_add__neg__numeral__special_I9_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_189_dbl__simps_I5_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [K: num] :
% 2.74/1.52 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_190_neg__equal__iff__equal,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( ( uminus_uminus @ A @ A2 )
% 2.74/1.52 = ( uminus_uminus @ A @ B ) )
% 2.74/1.52 = ( A2 = B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_191_add_Oinverse__inverse,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A] :
% 2.74/1.52 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 2.74/1.52 = A2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_192_neg__less__iff__less,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [B: A,A2: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) )
% 2.74/1.52 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_193_neg__numeral__eq__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( M = N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_194_minus__add__distrib,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 2.74/1.52 = ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ A @ B ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_195_minus__add__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ ( plus_plus @ A @ A2 @ B ) )
% 2.74/1.52 = B ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_196_add__minus__cancel,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ ( uminus_uminus @ A @ A2 ) @ B ) )
% 2.74/1.52 = B ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_197_add__neg__numeral__simps_I3_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_198_dbl__simps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [K: num] :
% 2.74/1.52 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_199_neg__one__eq__numeral__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( N = one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_200_numeral__eq__neg__one__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( N = one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_201_semiring__norm_I168_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [V3: num,W: num,Y: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V3 ) ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 2.74/1.52 = ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V3 @ W ) ) ) @ Y ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_202_neg__numeral__less__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( ord_less @ num @ N @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_203_neg__numeral__less__neg__one__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ( ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( M != one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_204_dbl__simps_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_205_not__numeral__less__neg__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ~ ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_206_neg__numeral__less__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_207_less__minus__one__simps_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_208_less__minus__one__simps_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_209_numeral__neq__neg__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( numeral_numeral @ A @ N )
% 2.74/1.52 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_210_one__neq__neg__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( one_one @ A )
% 2.74/1.52 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_211_neg__numeral__neq__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 2.74/1.52 != ( numeral_numeral @ A @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_212_numeral__neq__neg__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( numeral_numeral @ A @ M )
% 2.74/1.52 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_213_less__minus__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 2.74/1.52 = ( ord_less @ A @ B @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_214_minus__less__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 2.74/1.52 = ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ A2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_215_one__neq__neg__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( one_one @ A )
% 2.74/1.52 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_216_minus__equation__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( ( uminus_uminus @ A @ A2 )
% 2.74/1.52 = B )
% 2.74/1.52 = ( ( uminus_uminus @ A @ B )
% 2.74/1.52 = A2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_217_equation__minus__iff,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( A2
% 2.74/1.52 = ( uminus_uminus @ A @ B ) )
% 2.74/1.52 = ( B
% 2.74/1.52 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_218_is__num__normalize_I8_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 2.74/1.52 = ( plus_plus @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_219_add_Oinverse__distrib__swap,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [A2: A,B: A] :
% 2.74/1.52 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A2 @ B ) )
% 2.74/1.52 = ( plus_plus @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_220_dbl__def,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( neg_numeral_dbl @ A )
% 2.74/1.52 = ( ^ [X5: A] : ( plus_plus @ A @ X5 @ X5 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_221_uminus__numeral__One,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ one2 ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_222_neg__numeral__less__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_223_neg__one__less__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] : ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( numeral_numeral @ A @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_224_not__numeral__less__neg__one,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ~ ( ord_less @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_225_not__one__less__neg__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_226_not__neg__one__less__neg__numeral,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ~ ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_227_add__neg__numeral__special_I5_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ N ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_228_add__neg__numeral__special_I6_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ M ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_229_num__induct,axiom,
% 2.74/1.52 ! [P: num > $o,X: num] :
% 2.74/1.52 ( ( P @ one2 )
% 2.74/1.52 => ( ! [X3: num] :
% 2.74/1.52 ( ( P @ X3 )
% 2.74/1.52 => ( P @ ( inc @ X3 ) ) )
% 2.74/1.52 => ( P @ X ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_230_add__inc,axiom,
% 2.74/1.52 ! [X: num,Y: num] :
% 2.74/1.52 ( ( plus_plus @ num @ X @ ( inc @ Y ) )
% 2.74/1.52 = ( inc @ ( plus_plus @ num @ X @ Y ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_231_inc_Osimps_I1_J,axiom,
% 2.74/1.52 ( ( inc @ one2 )
% 2.74/1.52 = ( bit0 @ one2 ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_232_add__One,axiom,
% 2.74/1.52 ! [X: num] :
% 2.74/1.52 ( ( plus_plus @ num @ X @ one2 )
% 2.74/1.52 = ( inc @ X ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_233_numeral__inc,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [X: num] :
% 2.74/1.52 ( ( numeral_numeral @ A @ ( inc @ X ) )
% 2.74/1.52 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_234_add__neg__numeral__special_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ N @ one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_235_add__neg__numeral__special_I3_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ M @ one2 ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_236_sub__num__simps_I6_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [K: num,L: num] :
% 2.74/1.52 ( ( neg_numeral_sub @ A @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 2.74/1.52 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K @ L ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_237_semiring__norm_I166_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [V3: num,W: num,Y: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V3 ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 2.74/1.52 = ( plus_plus @ A @ ( neg_numeral_sub @ A @ V3 @ W ) @ Y ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_238_semiring__norm_I167_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [V3: num,W: num,Y: A] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V3 ) ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Y ) )
% 2.74/1.52 = ( plus_plus @ A @ ( neg_numeral_sub @ A @ W @ V3 ) @ Y ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_239_add__neg__numeral__simps_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ M @ N ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_240_add__neg__numeral__simps_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num,N: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ N @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_241_add__neg__numeral__special_I1_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ one2 @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_242_add__neg__numeral__special_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [M: num] :
% 2.74/1.52 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( one_one @ A ) )
% 2.74/1.52 = ( neg_numeral_sub @ A @ one2 @ M ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_243_sub__num__simps_I2_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [L: num] :
% 2.74/1.52 ( ( neg_numeral_sub @ A @ one2 @ ( bit0 @ L ) )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bitM @ L ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_244_sub__num__simps_I4_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [K: num] :
% 2.74/1.52 ( ( neg_numeral_sub @ A @ ( bit0 @ K ) @ one2 )
% 2.74/1.52 = ( numeral_numeral @ A @ ( bitM @ K ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_245_eval__nat__numeral_I2_J,axiom,
% 2.74/1.52 ! [N: num] :
% 2.74/1.52 ( ( numeral_numeral @ nat @ ( bit0 @ N ) )
% 2.74/1.52 = ( suc @ ( numeral_numeral @ nat @ ( bitM @ N ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_246_one__plus__BitM,axiom,
% 2.74/1.52 ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ num @ one2 @ ( bitM @ N ) )
% 2.74/1.52 = ( bit0 @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_247_BitM__plus__one,axiom,
% 2.74/1.52 ! [N: num] :
% 2.74/1.52 ( ( plus_plus @ num @ ( bitM @ N ) @ one2 )
% 2.74/1.52 = ( bit0 @ N ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_248_dbl__dec__simps_I5_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [K: num] :
% 2.74/1.52 ( ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K ) )
% 2.74/1.52 = ( numeral_numeral @ A @ ( bitM @ K ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_249_eq__numeral__iff__iszero_I8_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.74/1.52 => ! [Y: num] :
% 2.74/1.52 ( ( ( one_one @ A )
% 2.74/1.52 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ Y ) ) )
% 2.74/1.52 = ( ring_1_iszero @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ Y ) ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(fact_250_dbl__dec__simps_I3_J,axiom,
% 2.74/1.52 ! [A: $tType] :
% 2.74/1.52 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.74/1.52 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 2.74/1.52 = ( one_one @ A ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.74/1.52 ! [A5: $tType,A6: $tType] :
% 2.74/1.52 ( ( order @ A6 @ ( type2 @ A6 ) )
% 2.74/1.52 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_fun___Orderings_Oord,axiom,
% 2.74/1.52 ! [A5: $tType,A6: $tType] :
% 2.74/1.52 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 2.74/1.52 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_fun___Groups_Ouminus,axiom,
% 2.74/1.52 ! [A5: $tType,A6: $tType] :
% 2.74/1.52 ( ( uminus @ A6 @ ( type2 @ A6 ) )
% 2.74/1.52 => ( uminus @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.74/1.52 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.74/1.52 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.74/1.52 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.74/1.52 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.74/1.52 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.74/1.52 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.74/1.52 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.74/1.52 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.74/1.52 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 2.74/1.52 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.74/1.52 linorder @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 2.74/1.52 order @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Orderings_Oord_2,axiom,
% 2.74/1.52 ord @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 2.74/1.52 numeral @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.74/1.52 one @ nat @ ( type2 @ nat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Num_Onum___Orderings_Olinorder_3,axiom,
% 2.74/1.52 linorder @ num @ ( type2 @ num ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Num_Onum___Orderings_Oorder_4,axiom,
% 2.74/1.52 order @ num @ ( type2 @ num ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Num_Onum___Orderings_Oord_5,axiom,
% 2.74/1.52 ord @ num @ ( type2 @ num ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder_6,axiom,
% 2.74/1.52 linorder @ $o @ ( type2 @ $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_7,axiom,
% 2.74/1.52 order @ $o @ ( type2 @ $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_HOL_Obool___Orderings_Oord_8,axiom,
% 2.74/1.52 ord @ $o @ ( type2 @ $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_HOL_Obool___Groups_Ouminus_9,axiom,
% 2.74/1.52 uminus @ $o @ ( type2 @ $o ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_10,axiom,
% 2.74/1.52 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11,axiom,
% 2.74/1.52 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12,axiom,
% 2.74/1.52 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_13,axiom,
% 2.74/1.52 comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_14,axiom,
% 2.74/1.52 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_15,axiom,
% 2.74/1.52 semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_16,axiom,
% 2.74/1.52 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_17,axiom,
% 2.74/1.52 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_18,axiom,
% 2.74/1.52 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_19,axiom,
% 2.74/1.52 numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(tcon_Extended__Nat_Oenat___Groups_Oone_20,axiom,
% 2.74/1.52 one @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.74/1.52
% 2.74/1.52 thf(help_If_3_1_T,axiom,
% 2.74/1.52 ! [P: $o] :
% 2.74/1.52 ( ( P = $true )
% 2.74/1.52 | ( P = $false ) ) ).
% 2.74/1.52
% 2.74/1.52 thf(help_If_2_1_T,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Y: A] :
% 2.74/1.52 ( ( if @ A @ $false @ X @ Y )
% 2.74/1.52 = Y ) ).
% 2.74/1.52
% 2.74/1.52 thf(help_If_1_1_T,axiom,
% 2.74/1.52 ! [A: $tType,X: A,Y: A] :
% 2.74/1.52 ( ( if @ A @ $true @ X @ Y )
% 2.74/1.52 = X ) ).
% 2.74/1.52
% 2.74/1.52 thf(conj_0,conjecture,
% 2.74/1.52 ( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
% 2.74/1.52 = ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ) ).
% 2.74/1.52 ------------------------
% 2.74/1.55 % (16797)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/27Mi)
% 2.74/1.55 % (16795)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/183Mi)
% 2.74/1.55 % (16796)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/4Mi)
% 2.74/1.55 % (16796)Instruction limit reached!
% 2.74/1.55 % (16796)------------------------------
% 2.74/1.55 % (16796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.55 % (16796)Termination reason: Unknown
% 2.74/1.55 % (16796)Termination phase: shuffling
% 2.74/1.55
% 2.74/1.55 % (16796)Memory used [KB]: 1407
% 2.74/1.55 % (16796)Time elapsed: 0.003 s
% 2.74/1.55 % (16796)Instructions burned: 6 (million)
% 2.74/1.55 % (16796)------------------------------
% 2.74/1.55 % (16796)------------------------------
% 2.74/1.56 % (16798)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/2Mi)
% 2.74/1.56 % (16799)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/2Mi)
% 2.74/1.56 % (16800)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/275Mi)
% 2.74/1.56 % (16801)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/18Mi)
% 2.74/1.56 % (16797)Instruction limit reached!
% 2.74/1.56 % (16797)------------------------------
% 2.74/1.56 % (16797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.56 % (16797)Termination reason: Unknown
% 2.74/1.56 % (16797)Termination phase: Property scanning
% 2.74/1.56
% 2.74/1.56 % (16797)Memory used [KB]: 1663
% 2.74/1.56 % (16797)Time elapsed: 0.010 s
% 2.74/1.56 % (16797)Instructions burned: 28 (million)
% 2.74/1.56 % (16797)------------------------------
% 2.74/1.56 % (16797)------------------------------
% 2.74/1.56 % (16798)Instruction limit reached!
% 2.74/1.56 % (16798)------------------------------
% 2.74/1.56 % (16798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.56 % (16798)Termination reason: Unknown
% 2.74/1.56 % (16798)Termination phase: shuffling
% 2.74/1.56
% 2.74/1.56 % (16798)Memory used [KB]: 1407
% 2.74/1.56 % (16798)Time elapsed: 0.004 s
% 2.74/1.56 % (16798)Instructions burned: 3 (million)
% 2.74/1.56 % (16798)------------------------------
% 2.74/1.56 % (16798)------------------------------
% 2.74/1.56 % (16799)Instruction limit reached!
% 2.74/1.56 % (16799)------------------------------
% 2.74/1.56 % (16799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.56 % (16799)Termination reason: Unknown
% 2.74/1.56 % (16799)Termination phase: shuffling
% 2.74/1.56
% 2.74/1.56 % (16799)Memory used [KB]: 1407
% 2.74/1.56 % (16799)Time elapsed: 0.004 s
% 2.74/1.56 % (16799)Instructions burned: 3 (million)
% 2.74/1.56 % (16799)------------------------------
% 2.74/1.56 % (16799)------------------------------
% 2.74/1.56 % (16802)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/3Mi)
% 2.74/1.56 % (16802)Instruction limit reached!
% 2.74/1.56 % (16802)------------------------------
% 2.74/1.56 % (16802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.56 % (16802)Termination reason: Unknown
% 2.74/1.56 % (16802)Termination phase: shuffling
% 2.74/1.56
% 2.74/1.56 % (16802)Memory used [KB]: 1407
% 2.74/1.56 % (16802)Time elapsed: 0.003 s
% 2.74/1.56 % (16802)Instructions burned: 4 (million)
% 2.74/1.56 % (16802)------------------------------
% 2.74/1.56 % (16802)------------------------------
% 2.74/1.57 % (16803)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/37Mi)
% 2.74/1.57 % (16801)Instruction limit reached!
% 2.74/1.57 % (16801)------------------------------
% 2.74/1.57 % (16801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.57 % (16801)Termination reason: Unknown
% 2.74/1.57 % (16801)Termination phase: Property scanning
% 2.74/1.57
% 2.74/1.57 % (16801)Memory used [KB]: 1663
% 2.74/1.57 % (16801)Time elapsed: 0.014 s
% 2.74/1.57 % (16801)Instructions burned: 19 (million)
% 2.74/1.57 % (16801)------------------------------
% 2.74/1.57 % (16801)------------------------------
% 2.74/1.57 % (16806)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/1041Mi)
% 2.74/1.58 % (16804)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/15Mi)
% 2.74/1.58 % (16805)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/3Mi)
% 2.74/1.58 % (16803)Instruction limit reached!
% 2.74/1.58 % (16803)------------------------------
% 2.74/1.58 % (16803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (16803)Termination reason: Unknown
% 2.74/1.58 % (16803)Termination phase: Property scanning
% 2.74/1.58
% 2.74/1.58 % (16803)Memory used [KB]: 2046
% 2.74/1.58 % (16803)Time elapsed: 0.012 s
% 2.74/1.58 % (16803)Instructions burned: 39 (million)
% 2.74/1.58 % (16803)------------------------------
% 2.74/1.58 % (16803)------------------------------
% 2.74/1.58 % (16805)Instruction limit reached!
% 2.74/1.58 % (16805)------------------------------
% 2.74/1.58 % (16805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (16805)Termination reason: Unknown
% 2.74/1.58 % (16805)Termination phase: shuffling
% 2.74/1.58
% 2.74/1.58 % (16805)Memory used [KB]: 1407
% 2.74/1.58 % (16805)Time elapsed: 0.004 s
% 2.74/1.58 % (16805)Instructions burned: 3 (million)
% 2.74/1.58 % (16805)------------------------------
% 2.74/1.58 % (16805)------------------------------
% 2.74/1.59 % (16807)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/7Mi)
% 2.74/1.59 % (16804)Instruction limit reached!
% 2.74/1.59 % (16804)------------------------------
% 2.74/1.59 % (16804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.59 % (16804)Termination reason: Unknown
% 2.74/1.59 % (16804)Termination phase: shuffling
% 2.74/1.59
% 2.74/1.59 % (16804)Memory used [KB]: 1663
% 2.74/1.59 % (16804)Time elapsed: 0.012 s
% 2.74/1.59 % (16804)Instructions burned: 16 (million)
% 2.74/1.59 % (16804)------------------------------
% 2.74/1.59 % (16804)------------------------------
% 2.74/1.59 % (16808)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/16Mi)
% 2.74/1.59 % (16807)Instruction limit reached!
% 2.74/1.59 % (16807)------------------------------
% 2.74/1.59 % (16807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.59 % (16807)Termination reason: Unknown
% 2.74/1.59 % (16807)Termination phase: shuffling
% 2.74/1.59
% 2.74/1.59 % (16807)Memory used [KB]: 1407
% 2.74/1.59 % (16807)Time elapsed: 0.005 s
% 2.74/1.59 % (16807)Instructions burned: 7 (million)
% 2.74/1.59 % (16807)------------------------------
% 2.74/1.59 % (16807)------------------------------
% 2.74/1.60 % (16808)Instruction limit reached!
% 2.74/1.60 % (16808)------------------------------
% 2.74/1.60 % (16808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (16808)Termination reason: Unknown
% 2.74/1.60 % (16808)Termination phase: Property scanning
% 2.74/1.60
% 2.74/1.60 % (16808)Memory used [KB]: 1663
% 2.74/1.60 % (16808)Time elapsed: 0.007 s
% 2.74/1.60 % (16808)Instructions burned: 18 (million)
% 2.74/1.60 % (16808)------------------------------
% 2.74/1.60 % (16808)------------------------------
% 2.77/1.60 % (16809)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/3Mi)
% 2.77/1.60 % (16800)First to succeed.
% 2.77/1.60 % (16809)Instruction limit reached!
% 2.77/1.60 % (16809)------------------------------
% 2.77/1.60 % (16809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (16809)Termination reason: Unknown
% 2.77/1.60 % (16809)Termination phase: shuffling
% 2.77/1.60
% 2.77/1.60 % (16809)Memory used [KB]: 1407
% 2.77/1.60 % (16809)Time elapsed: 0.004 s
% 2.77/1.60 % (16809)Instructions burned: 4 (million)
% 2.77/1.60 % (16809)------------------------------
% 2.77/1.60 % (16809)------------------------------
% 2.77/1.60 % (16811)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16466 for (2999ds/7Mi)
% 2.77/1.60 % (16800)Refutation found. Thanks to Tanya!
% 2.77/1.60 % SZS status Theorem for DTF2THF_16466
% 2.77/1.60 % SZS output start Proof for DTF2THF_16466
% 2.77/1.60 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.77/1.60 thf(type_def_7, type, nat: $tType).
% 2.77/1.60 thf(type_def_8, type, coindu1593790203_llist: ($tType) > $tType).
% 2.77/1.60 thf(type_def_9, type, extended_enat: $tType).
% 2.77/1.60 thf(type_def_10, type, list: ($tType) > $tType).
% 2.77/1.60 thf(type_def_11, type, num: $tType).
% 2.77/1.60 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 2.77/1.60 thf(func_def_1, type, extended_enat: $tType).
% 2.77/1.60 thf(func_def_2, type, list: ($tType) > $tType).
% 2.77/1.60 thf(func_def_3, type, num: $tType).
% 2.77/1.60 thf(func_def_4, type, nat: $tType).
% 2.77/1.60 thf(func_def_5, type, itself: ($tType) > $tType).
% 2.77/1.60 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_7, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_8, type, numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_9, type, ring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_10, type, uminus: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_11, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_12, type, ring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_14, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_15, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_16, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_17, type, ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_18, type, semiring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_19, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_20, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_21, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_22, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_23, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_24, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_25, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_26, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_27, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_28, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_29, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_30, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_31, type, condit1656338222tinuum: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.77/1.60 thf(func_def_32, type, coindu493225792length: !>[X0: $tType]:(nat > coindu1593790203_llist @ X0 > extended_enat)).
% 2.77/1.60 thf(func_def_33, type, coindu1542816657of_aux: !>[X0: $tType]:(list @ X0 > coindu1593790203_llist @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_34, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.77/1.60 thf(func_def_35, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.77/1.60 thf(func_def_36, type, coindu1079202755ist_of: !>[X0: $tType]:(list @ X0 > coindu1593790203_llist @ X0)).
% 2.77/1.60 thf(func_def_37, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 2.77/1.60 thf(func_def_38, type, one_one: !>[X0: $tType]:(X0)).
% 2.77/1.60 thf(func_def_39, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.77/1.60 thf(func_def_40, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 2.77/1.60 thf(func_def_41, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.77/1.60 thf(func_def_42, type, count_list: !>[X0: $tType]:(list @ X0 > X0 > nat)).
% 2.77/1.60 thf(func_def_43, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 2.77/1.60 thf(func_def_44, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_45, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.77/1.60 thf(func_def_46, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 2.77/1.60 thf(func_def_47, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 2.77/1.60 thf(func_def_48, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.77/1.60 thf(func_def_49, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.77/1.60 thf(func_def_50, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.77/1.60 thf(func_def_51, type, upt: nat > nat > list @ nat).
% 2.77/1.60 thf(func_def_52, type, suc: nat > nat).
% 2.77/1.60 thf(func_def_53, type, nat_triangle: nat > nat).
% 2.77/1.60 thf(func_def_54, type, bitM: num > num).
% 2.77/1.60 thf(func_def_55, type, inc: num > num).
% 2.77/1.60 thf(func_def_56, type, neg_numeral_dbl: !>[X0: $tType]:(X0 > X0)).
% 2.77/1.60 thf(func_def_57, type, neg_numeral_dbl_dec: !>[X0: $tType]:(X0 > X0)).
% 2.77/1.60 thf(func_def_58, type, neg_numeral_sub: !>[X0: $tType]:(num > num > X0)).
% 2.77/1.60 thf(func_def_59, type, bit0: num > num).
% 2.77/1.60 thf(func_def_60, type, one2: num).
% 2.77/1.60 thf(func_def_61, type, numeral_numeral: !>[X0: $tType]:(num > X0)).
% 2.77/1.60 thf(func_def_62, type, ring_1_iszero: !>[X0: $tType]:(X0 > $o)).
% 2.77/1.60 thf(func_def_63, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.77/1.60 thf(func_def_64, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.77/1.60 thf(func_def_65, type, prefixes: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.77/1.60 thf(func_def_66, type, ma: nat).
% 2.77/1.60 thf(func_def_67, type, na: nat).
% 2.77/1.60 thf(func_def_83, type, sK0: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.77/1.60 thf(func_def_84, type, sK1: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 2.77/1.60 thf(func_def_85, type, sK2: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_86, type, sK3: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.77/1.60 thf(func_def_87, type, sK4: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_88, type, sK5: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.77/1.60 thf(func_def_89, type, sK6: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_90, type, sK7: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.77/1.60 thf(func_def_91, type, sK8: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.77/1.60 thf(func_def_92, type, sK9: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.77/1.60 thf(func_def_93, type, sK10: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_94, type, sK11: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.77/1.60 thf(func_def_95, type, sK12: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.77/1.60 thf(func_def_96, type, sK13: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_97, type, sK14: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_98, type, sK15: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_99, type, sK16: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_100, type, sK17: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_101, type, sK18: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_102, type, sK19: (nat > $o) > nat).
% 2.77/1.60 thf(func_def_103, type, sK20: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_104, type, sK21: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_105, type, sK22: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_106, type, sK23: nat > nat > nat).
% 2.77/1.60 thf(func_def_107, type, sK24: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_108, type, sK25: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_109, type, sK26: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_110, type, sK27: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_111, type, sK28: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.77/1.60 thf(func_def_112, type, sK29: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.77/1.60 thf(func_def_113, type, sK30: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.77/1.60 thf(func_def_114, type, sK31: nat > nat > nat).
% 2.77/1.60 thf(func_def_115, type, sK32: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_116, type, sK33: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_117, type, sK34: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_118, type, sK35: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.77/1.60 thf(func_def_119, type, sK36: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.77/1.60 thf(func_def_120, type, sK37: (list @ nat > $o) > nat).
% 2.77/1.60 thf(func_def_121, type, sK38: (list @ nat > $o) > list @ nat).
% 2.77/1.60 thf(func_def_122, type, sK39: (nat > $o) > nat).
% 2.77/1.60 thf(func_def_123, type, sK40: nat > nat > nat).
% 2.77/1.60 thf(func_def_124, type, sK41: nat > nat > nat).
% 2.77/1.60 thf(func_def_125, type, sK42: (nat > nat > $o) > nat).
% 2.77/1.60 thf(func_def_126, type, sK43: (nat > nat > $o) > nat).
% 2.77/1.60 thf(func_def_127, type, sK44: (nat > nat > $o) > nat).
% 2.77/1.60 thf(func_def_128, type, sK45: (nat > nat > $o) > nat).
% 2.77/1.60 thf(func_def_129, type, sK46: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_130, type, sK47: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_131, type, sK48: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_132, type, sK49: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_133, type, sK50: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_134, type, sK51: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_135, type, sK52: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_136, type, sK53: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_137, type, sK54: list @ nat > nat).
% 2.77/1.60 thf(func_def_138, type, sK55: list @ nat > list @ nat).
% 2.77/1.60 thf(func_def_139, type, sK56: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.77/1.60 thf(func_def_140, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.77/1.60 thf(func_def_141, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 2.77/1.60 thf(func_def_142, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_143, type, sK60: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.77/1.60 thf(func_def_144, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.77/1.60 thf(func_def_145, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.77/1.60 thf(func_def_146, type, sK63: (nat > $o) > nat > nat).
% 2.77/1.60 thf(func_def_147, type, sK64: (nat > $o) > nat > nat).
% 2.77/1.60 thf(func_def_148, type, sK65: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat > X0 > X0)).
% 2.77/1.60 thf(func_def_149, type, sK66: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat)).
% 2.77/1.60 thf(func_def_150, type, sK67: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat)).
% 2.77/1.60 thf(func_def_151, type, sK68: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_152, type, sK69: !>[X0: $tType]:(list @ X0 > X0)).
% 2.77/1.60 thf(func_def_153, type, sK70: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.77/1.60 thf(func_def_154, type, sK71: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_155, type, sK72: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_156, type, sK73: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_157, type, sK74: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_158, type, sK75: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_159, type, sK76: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_160, type, sK77: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_161, type, sK78: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.77/1.60 thf(func_def_162, type, sK79: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.77/1.60 thf(func_def_164, type, ph81: !>[X0: $tType]:(X0)).
% 2.77/1.60 thf(f1226,plain,(
% 2.77/1.60 $false),
% 2.77/1.60 inference(subsumption_resolution,[status(thm)],[f1213,f1201])).
% 2.77/1.60 thf(f1201,plain,(
% 2.77/1.60 ( ! [X1 : nat] : (($true = (ord_less @ nat @ X1 @ (plus_plus @ nat @ one_one @ nat @ X1)))) )),
% 2.77/1.60 inference(equality_resolution,[status(thm)],[f1175])).
% 2.77/1.60 thf(f1175,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X0 @ (plus_plus @ nat @ one_one @ nat @ X1))) | (X0 != X1)) )),
% 2.77/1.60 inference(definition_unfolding,[status(thm)],[f1119,f1033])).
% 2.77/1.60 thf(f1033,plain,(
% 2.77/1.60 (suc = (plus_plus @ nat @ one_one @ nat))),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f134])).
% 2.77/1.60 thf(f134,axiom,(
% 2.77/1.60 (suc = (plus_plus @ nat @ one_one @ nat))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',fact_133_Suc__eq__plus1__left)).
% 2.77/1.60 thf(f1119,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X0 @ (suc @ X1))) | (X0 != X1)) )),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f979])).
% 2.77/1.60 thf(f979,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : ((($true = (ord_less @ nat @ X0 @ (suc @ X1))) | (($true != (ord_less @ nat @ X0 @ X1)) & (X0 != X1))) & (($true = (ord_less @ nat @ X0 @ X1)) | (X0 = X1) | ($true != (ord_less @ nat @ X0 @ (suc @ X1)))))),
% 2.77/1.60 inference(flattening,[status(thm)],[f978])).
% 2.77/1.60 thf(f978,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : ((($true = (ord_less @ nat @ X0 @ (suc @ X1))) | (($true != (ord_less @ nat @ X0 @ X1)) & (X0 != X1))) & ((($true = (ord_less @ nat @ X0 @ X1)) | (X0 = X1)) | ($true != (ord_less @ nat @ X0 @ (suc @ X1)))))),
% 2.77/1.60 inference(nnf_transformation,[status(thm)],[f533])).
% 2.77/1.60 thf(f533,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X0 @ (suc @ X1))) <=> (($true = (ord_less @ nat @ X0 @ X1)) | (X0 = X1)))),
% 2.77/1.60 inference(fool_elimination,[status(thm)],[f532])).
% 2.77/1.60 thf(f532,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : ((X0 = X1) | (ord_less @ nat @ X0 @ X1) = (ord_less @ nat @ X0 @ (suc @ X1)))),
% 2.77/1.60 inference(rectify,[status(thm)],[f74])).
% 2.77/1.60 thf(f74,axiom,(
% 2.77/1.60 ! [X3 : nat,X4 : nat] : ((X3 = X4) | (ord_less @ nat @ X3 @ X4) = (ord_less @ nat @ X3 @ (suc @ X4)))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',fact_73_less__Suc__eq)).
% 2.77/1.60 thf(f1213,plain,(
% 2.77/1.60 ((ord_less @ nat @ ma @ (plus_plus @ nat @ one_one @ nat @ ma)) != $true)),
% 2.77/1.60 inference(trivial_inequality_removal,[status(thm)],[f1208])).
% 2.77/1.60 thf(f1208,plain,(
% 2.77/1.60 ($true != $true) | ((ord_less @ nat @ ma @ (plus_plus @ nat @ one_one @ nat @ ma)) != $true)),
% 2.77/1.60 inference(superposition,[status(thm)],[f1207,f1031])).
% 2.77/1.60 thf(f1031,plain,(
% 2.77/1.60 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ (plus_plus @ nat @ X2 @ X1)) = $true) | ($true != (ord_less @ nat @ X0 @ X1))) )),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f863])).
% 2.77/1.60 thf(f863,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less @ nat @ X0 @ (plus_plus @ nat @ X2 @ X1)) = $true) | ($true != (ord_less @ nat @ X0 @ X1)))),
% 2.77/1.60 inference(ennf_transformation,[status(thm)],[f731])).
% 2.77/1.60 thf(f731,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less @ nat @ X0 @ X1)) => ((ord_less @ nat @ X0 @ (plus_plus @ nat @ X2 @ X1)) = $true))),
% 2.77/1.60 inference(fool_elimination,[status(thm)],[f730])).
% 2.77/1.60 thf(f730,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X0 @ (plus_plus @ nat @ X2 @ X1)))),
% 2.77/1.60 inference(rectify,[status(thm)],[f89])).
% 2.77/1.60 thf(f89,axiom,(
% 2.77/1.60 ! [X24 : nat,X25 : nat,X3 : nat] : ((ord_less @ nat @ X24 @ X25) => (ord_less @ nat @ X24 @ (plus_plus @ nat @ X3 @ X25)))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',fact_88_trans__less__add2)).
% 2.77/1.60 thf(f1207,plain,(
% 2.77/1.60 ((ord_less @ nat @ ma @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma))) != $true)),
% 2.77/1.60 inference(trivial_inequality_removal,[status(thm)],[f1204])).
% 2.77/1.60 thf(f1204,plain,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma)))) != (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma))))) | ((ord_less @ nat @ ma @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma))) != $true)),
% 2.77/1.60 inference(superposition,[status(thm)],[f1202,f1147])).
% 2.77/1.60 thf(f1147,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (((upt @ X0 @ X1) = (cons @ nat @ X0 @ (upt @ (plus_plus @ nat @ one_one @ nat @ X0) @ X1))) | ($true != (ord_less @ nat @ X0 @ X1))) )),
% 2.77/1.60 inference(definition_unfolding,[status(thm)],[f1057,f1033])).
% 2.77/1.60 thf(f1057,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ((cons @ nat @ X0 @ (upt @ (suc @ X0) @ X1)) = (upt @ X0 @ X1))) )),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f874])).
% 2.77/1.60 thf(f874,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ((cons @ nat @ X0 @ (upt @ (suc @ X0) @ X1)) = (upt @ X0 @ X1)))),
% 2.77/1.60 inference(ennf_transformation,[status(thm)],[f441])).
% 2.77/1.60 thf(f441,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X0 @ X1)) => ((cons @ nat @ X0 @ (upt @ (suc @ X0) @ X1)) = (upt @ X0 @ X1)))),
% 2.77/1.60 inference(fool_elimination,[status(thm)],[f440])).
% 2.77/1.60 thf(f440,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => ((cons @ nat @ X0 @ (upt @ (suc @ X0) @ X1)) = (upt @ X0 @ X1)))),
% 2.77/1.60 inference(rectify,[status(thm)],[f30])).
% 2.77/1.60 thf(f30,axiom,(
% 2.77/1.60 ! [X24 : nat,X25 : nat] : ((ord_less @ nat @ X24 @ X25) => ((upt @ X24 @ X25) = (cons @ nat @ X24 @ (upt @ (suc @ X24) @ X25))))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',fact_29_upt__conv__Cons)).
% 2.77/1.60 thf(f1202,plain,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (plus_plus @ nat @ one_one @ nat @ ma) @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma))))) != (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma)))))),
% 2.77/1.60 inference(forward_demodulation,[status(thm)],[f1171,f1126])).
% 2.77/1.60 thf(f1126,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ X0 @ (plus_plus @ nat @ one_one @ nat @ X1)) = (plus_plus @ nat @ (plus_plus @ nat @ one_one @ nat @ X0) @ X1))) )),
% 2.77/1.60 inference(definition_unfolding,[status(thm)],[f1003,f1033,f1033])).
% 2.77/1.60 thf(f1003,plain,(
% 2.77/1.60 ( ! [X0 : nat,X1 : nat] : (((plus_plus @ nat @ (suc @ X0) @ X1) = (plus_plus @ nat @ X0 @ (suc @ X1)))) )),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f784])).
% 2.77/1.60 thf(f784,plain,(
% 2.77/1.60 ! [X0 : nat,X1 : nat] : ((plus_plus @ nat @ (suc @ X0) @ X1) = (plus_plus @ nat @ X0 @ (suc @ X1)))),
% 2.77/1.60 inference(rectify,[status(thm)],[f9])).
% 2.77/1.60 thf(f9,axiom,(
% 2.77/1.60 ! [X3 : nat,X4 : nat] : ((plus_plus @ nat @ X3 @ (suc @ X4)) = (plus_plus @ nat @ (suc @ X3) @ X4))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',fact_8_add__Suc__shift)).
% 2.77/1.60 thf(f1171,plain,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (plus_plus @ nat @ one_one @ nat @ ma) @ (plus_plus @ nat @ na @ (plus_plus @ nat @ one_one @ nat @ ma))))) != (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ (plus_plus @ nat @ one_one @ nat @ na) @ ma))))),
% 2.77/1.60 inference(definition_unfolding,[status(thm)],[f1113,f1033,f1033,f1033])).
% 2.77/1.60 thf(f1113,plain,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (suc @ ma) @ (plus_plus @ nat @ na @ (suc @ ma))))) != (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ (suc @ na) @ ma))))),
% 2.77/1.60 inference(cnf_transformation,[status(thm)],[f774])).
% 2.77/1.60 thf(f774,plain,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (suc @ ma) @ (plus_plus @ nat @ na @ (suc @ ma))))) != (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ (suc @ na) @ ma))))),
% 2.77/1.60 inference(flattening,[status(thm)],[f292])).
% 2.77/1.60 thf(f292,negated_conjecture,(
% 2.77/1.60 ~((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (suc @ ma) @ (plus_plus @ nat @ na @ (suc @ ma))))) = (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ (suc @ na) @ ma))))),
% 2.77/1.60 inference(negated_conjecture,[status(cth)],[f291])).
% 2.77/1.60 thf(f291,conjecture,(
% 2.77/1.60 ((coindu1079202755ist_of @ nat @ (cons @ nat @ ma @ (upt @ (suc @ ma) @ (plus_plus @ nat @ na @ (suc @ ma))))) = (coindu1079202755ist_of @ nat @ (upt @ ma @ (plus_plus @ nat @ (suc @ na) @ ma))))),
% 2.77/1.60 file('/export/starexec/sandbox/tmp/tmp.enllOJIy89/DTF2THF_16466.p',conj_0)).
% 2.77/1.60 % SZS output end Proof for DTF2THF_16466
% 2.77/1.60 % (16800)------------------------------
% 2.77/1.60 % (16800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (16800)Termination reason: Refutation
% 2.77/1.60
% 2.77/1.60 % (16800)Memory used [KB]: 6652
% 2.77/1.60 % (16800)Time elapsed: 0.044 s
% 2.77/1.60 % (16800)Instructions burned: 69 (million)
% 2.77/1.60 % (16800)------------------------------
% 2.77/1.60 % (16800)------------------------------
% 2.77/1.60 % (16794)Success in time 0.072 s
%------------------------------------------------------------------------------