%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP169^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.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 08:56:07 AM UTC 2026
% Result : Theorem 2.79s 1.62s
% Output : Refutation 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP169^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 08:28:38 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.44 ---- Original DTF file ---
% 0.15/0.44 thf(spec,logic,$$dhol).
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 % File : ITP169^2 : TPTP v9.2.1. Released v7.5.0.
% 0.15/0.44 % Domain : Interactive Theorem Proving
% 0.15/0.44 % Problem : Sledgehammer Safety_Regular problem prob_273__3352790_1
% 0.15/0.44 % Version : Especial.
% 0.15/0.44 % English :
% 0.15/0.44
% 0.15/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.15/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.15/0.44 % Source : [Des21]
% 0.15/0.44 % Names : Safety_Regular/prob_273__3352790_1 [Des21]
% 0.15/0.44
% 0.15/0.44 % Status : Theorem
% 0.15/0.44 % Rating : 0.00 v7.5.0
% 0.15/0.44 % Syntax : Number of formulae : 333 ( 104 unt; 54 typ; 0 def)
% 0.15/0.44 % Number of atoms : 1022 ( 483 equ; 0 cnn)
% 0.15/0.44 % Maximal formula atoms : 17 ( 3 avg)
% 0.15/0.44 % Number of connectives : 5544 ( 62 ~; 38 |; 434 &;4772 @)
% 0.15/0.44 % ( 0 <=>; 238 =>; 0 <=; 0 <~>)
% 0.15/0.44 % Maximal formula depth : 24 ( 8 avg)
% 0.15/0.44 % Number of types : 8 ( 7 usr)
% 0.15/0.44 % Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% 0.15/0.44 % Number of symbols : 48 ( 47 usr; 9 con; 0-4 aty)
% 0.15/0.44 % Number of variables : 962 ( 10 ^; 772 !; 158 ?; 962 :)
% 0.15/0.44 % ( 22 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.44 % SPC : TH1_THM_EQU_NAR
% 0.15/0.44
% 0.15/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 16:22:47.514
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 % Could-be-implicit typings (8)
% 0.15/0.44 thf(ty_t_Views_Oview_Oview__ext,type,
% 0.15/0.44 view_ext: $tType > $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_Product__Type_Ounit,type,
% 0.15/0.44 product_unit: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_RealInt_Oreal__int,type,
% 0.15/0.44 real_int: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_Traffic_Otraffic,type,
% 0.15/0.44 traffic: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_NatInt_Onat__int,type,
% 0.15/0.44 nat_int: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_Real_Oreal,type,
% 0.15/0.44 real: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_Cars_Ocars,type,
% 0.15/0.44 cars: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(ty_t_Nat_Onat,type,
% 0.15/0.44 nat: $tType ).
% 0.15/0.44
% 0.15/0.44 % Explicit typings (46)
% 0.15/0.44 thf(sy_cl_Groups_Oone,type,
% 0.15/0.44 one:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Ozero,type,
% 0.15/0.44 zero:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Omonoid__add,type,
% 0.15/0.44 monoid_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Orderings_Owellorder,type,
% 0.15/0.44 wellorder:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.15/0.44 cancel_semigroup_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.15/0.44 cancel1352612707id_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.15/0.44 linord219039673up_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.15/0.44 ordere779506340up_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.15/0.44 canoni770627133id_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.15/0.44 ordere236663937imp_le:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.15/0.44 ordere223160158up_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.15/0.44 strict2144017051up_add:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.15/0.44 ordere516151231imp_le:
% 0.15/0.44 !>[A: $tType] : $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.15/0.44 one_one:
% 0.15/0.44 !>[A: $tType] : A ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.15/0.44 plus_plus:
% 0.15/0.44 !>[A: $tType] : ( A > A > A ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.15/0.44 zero_zero:
% 0.15/0.44 !>[A: $tType] : A ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Length_Osensors_Olen,type,
% 0.15/0.44 len: ( cars > traffic > cars > real ) > ( view_ext @ product_unit ) > traffic > cars > real_int ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Move_Otraffic_Omove,type,
% 0.15/0.44 move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 0.15/0.44 nat_card: nat_int > nat ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.15/0.44 bot_bot:
% 0.15/0.44 !>[A: $tType] : A ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.15/0.44 ord_less:
% 0.15/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.15/0.44 ord_less_eq:
% 0.15/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 0.15/0.44 real_length: real_int > real ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Regular__Sensors_Oregular,type,
% 0.15/0.44 regular_regular: cars > traffic > cars > real ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Restriction_Orestriction_Orestrict,type,
% 0.15/0.44 restrict: ( view_ext @ product_unit ) > ( cars > nat_int ) > cars > nat_int ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 0.15/0.44 abstract: traffic > traffic > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 0.15/0.44 clm: traffic > cars > nat_int ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 0.15/0.44 create_claim: traffic > cars > nat > traffic > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 0.15/0.44 create_reservation: traffic > cars > traffic > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Ores,type,
% 0.15/0.44 res: traffic > cars > nat_int ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 0.15/0.44 withdraw_claim: traffic > cars > traffic > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 0.15/0.44 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Views_Oview_Oext,type,
% 0.15/0.44 ext:
% 0.15/0.44 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Views_Oview_Ohchop,type,
% 0.15/0.44 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Views_Oview_Olan,type,
% 0.15/0.44 lan:
% 0.15/0.44 !>[Z: $tType] : ( ( view_ext @ Z ) > nat_int ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Views_Oview_Oown,type,
% 0.15/0.44 own:
% 0.15/0.44 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 0.15/0.44
% 0.15/0.44 thf(sy_c_Views_Oview_Ovchop,type,
% 0.15/0.44 vchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_c____,type,
% 0.15/0.44 c: cars ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_d____,type,
% 0.15/0.44 d: cars ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_e____,type,
% 0.15/0.44 e: cars ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_thesis____,type,
% 0.15/0.44 thesis: $o ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_ts_H_H____,type,
% 0.15/0.44 ts: traffic ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_ts_H____,type,
% 0.15/0.44 ts2: traffic ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_ts_Ha____,type,
% 0.15/0.44 ts_a: traffic ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_ts____,type,
% 0.15/0.44 ts3: traffic ).
% 0.15/0.44
% 0.15/0.44 thf(sy_v_v____,type,
% 0.15/0.44 v: view_ext @ product_unit ).
% 0.15/0.44
% 0.15/0.44 % Relevant facts (253)
% 0.15/0.44 thf(fact_0_neg,axiom,
% 0.15/0.44 c != e ).
% 0.15/0.44
% 0.15/0.44 % neg
% 0.15/0.44 thf(fact_1_local_Ohmlsl_Osensors__ge,axiom,
% 0.15/0.44 ! [E: cars,Ts: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ E @ Ts @ C ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.sensors_ge
% 0.15/0.44 thf(fact_2_local_Ohmlsl_Olength__geq__zero,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.length_geq_zero
% 0.15/0.44 thf(fact_3_hmlsl_Olen__empty__subview,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V3: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V2 ) )
% 0.15/0.44 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_empty_subview
% 0.15/0.44 thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,axiom,
% 0.15/0.44 ? [V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( ord_less_eq @ ( view_ext @ product_unit ) @ V4 @ ( move @ ts3 @ ts @ v ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V4 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V4 @ ts @ c )
% 0.15/0.44 = ( ext @ product_unit @ V4 ) )
% 0.15/0.44 & ( ( restrict @ V4 @ ( res @ ts ) @ c )
% 0.15/0.44 = ( lan @ product_unit @ V4 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V4 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V4 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V4 @ ts @ e )
% 0.15/0.44 = ( ext @ product_unit @ V4 ) )
% 0.15/0.44 & ( ( restrict @ V4 @ ( res @ ts ) @ e )
% 0.15/0.44 = ( lan @ product_unit @ V4 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V4 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % \<open>\<exists>v'\<le>move ts ts'' v. (0 < \<parallel>ext v'\<parallel> \<and> len v' ts'' c = ext v' \<and> restrict v' (res ts'') c = lan v' \<and> |lan v'| = 1) \<and> 0 < \<parallel>ext v'\<parallel> \<and> len v' ts'' e = ext v' \<and> restrict v' (res ts'') e = lan v' \<and> |lan v'| = 1\<close>
% 0.15/0.44 thf(fact_5_local_Ohmlsl_Ores__ge__zero,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_ge_zero
% 0.15/0.44 thf(fact_6_local_Ohmlsl_Owidth__res,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_res
% 0.15/0.44 thf(fact_7_abs,axiom,
% 0.15/0.44 abstract @ ts3 @ ts2 ).
% 0.15/0.44
% 0.15/0.44 % abs
% 0.15/0.44 thf(fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 0.15/0.44 ( ( move @ ts3 @ ts_a @ v )
% 0.15/0.44 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % \<open>move ts ts' v = move ts' ts'' (move ts ts' v)\<close>
% 0.15/0.44 thf(fact_9_move__stab,axiom,
% 0.15/0.44 ( ( move @ ts3 @ ts_a @ v )
% 0.15/0.44 = ( move @ ts3 @ ts @ v ) ) ).
% 0.15/0.44
% 0.15/0.44 % move_stab
% 0.15/0.44 thf(fact_10_local_Ohmlsl_Ores__compose,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_compose
% 0.15/0.44 thf(fact_11_local_Ohmlsl_Ores__decompose,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va2 ) )
% 0.15/0.44 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U2 ) )
% 0.15/0.44 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_decompose
% 0.15/0.44 thf(fact_12_local_Ohmlsl_Ores__dense,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ W ) )
% 0.15/0.44 & ( ( restrict @ W @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ W ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U3 ) )
% 0.15/0.44 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U3 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_dense
% 0.15/0.44 thf(fact_13_local_Ohmlsl_Ocar__one__lane__non__empty,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) )
% 0.15/0.44 => ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.car_one_lane_non_empty
% 0.15/0.44 thf(fact_14_local_Ohmlsl_Oempty__no__car,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 => ~ ? [X: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.empty_no_car
% 0.15/0.44 thf(fact_15_local_Ohmlsl_Otwo__lanes__no__car,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 != ( one_one @ nat ) )
% 0.15/0.44 => ~ ? [X: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.two_lanes_no_car
% 0.15/0.44 thf(fact_16_local_Ohmlsl_Ores__at__most__two,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ U @ Vb @ Ua )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Vb ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Vb @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Vb ) )
% 0.15/0.44 & ( ( restrict @ Vb @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Vb ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Vb ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_at_most_two
% 0.15/0.44 thf(fact_17_local_Ohmlsl_Otwo__res__not__res,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.two_res_not_res
% 0.15/0.44 thf(fact_18_local_Ohmlsl_Oclm__ge__zero,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_ge_zero
% 0.15/0.44 thf(fact_19_local_Ohmlsl_Ohchop__weaken2,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( Phi @ Ts2 @ V )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_weaken2
% 0.15/0.44 thf(fact_20_local_Ohmlsl_Ohchop__weaken1,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( Phi @ Ts2 @ V )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.44 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_weaken1
% 0.15/0.44 thf(fact_21_local_Ohmlsl_Ohchop__weaken,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( Phi @ Ts2 @ V )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ? [Vb2: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb2 @ X_1 )
% 0.15/0.44 & ( Phi @ Ts2 @ Vb2 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_weaken
% 0.15/0.44 thf(fact_22_local_Ohmlsl_Ohchop__neg2,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ~ ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( Phi @ Ts2 @ U2 ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_neg2
% 0.15/0.44 thf(fact_23_local_Ohmlsl_Ohchop__neg1,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ~ ? [Va2: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.44 & ( Phi @ Ts2 @ Va2 ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.44 & ~ ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_neg1
% 0.15/0.44 thf(fact_24_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 0.15/0.44 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ( Psi @ Ts2 @ W )
% 0.15/0.44 | ( Chi @ Ts2 @ W ) )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Psi @ Ts2 @ W )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) )
% 0.15/0.44 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Chi @ Ts2 @ W )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_disj_distr2
% 0.15/0.44 thf(fact_25_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( ( Psi @ Ts2 @ U3 )
% 0.15/0.44 | ( Chi @ Ts2 @ U3 ) ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( Psi @ Ts2 @ U3 ) )
% 0.15/0.44 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_disj_distr1
% 0.15/0.44 thf(fact_26_local_Ohmlsl_Ohchop__assoc,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ U3 @ X2 @ Y )
% 0.15/0.44 & ( Psi @ Ts2 @ X2 )
% 0.15/0.44 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ W @ X2 @ Y )
% 0.15/0.44 & ( Phi @ Ts2 @ X2 )
% 0.15/0.44 & ( Psi @ Ts2 @ Y ) )
% 0.15/0.44 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.hchop_assoc
% 0.15/0.44 thf(fact_27_local_Ohmlsl_Ovchop__disj__distr2,axiom,
% 0.15/0.44 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( ( Psi @ Ts2 @ W )
% 0.15/0.44 | ( Chi @ Ts2 @ W ) )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Psi @ Ts2 @ W )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) )
% 0.15/0.44 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Chi @ Ts2 @ W )
% 0.15/0.44 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.vchop_disj_distr2
% 0.15/0.44 thf(fact_28_local_Ohmlsl_Ovchop__disj__distr1,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( ( Psi @ Ts2 @ U3 )
% 0.15/0.44 | ( Chi @ Ts2 @ U3 ) ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( Psi @ Ts2 @ U3 ) )
% 0.15/0.44 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.vchop_disj_distr1
% 0.15/0.44 thf(fact_29_local_Ohmlsl_Ov__chop__weaken2,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( Phi @ Ts2 @ V )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.v_chop_weaken2
% 0.15/0.44 thf(fact_30_local_Ohmlsl_Ov__chop__weaken1,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( Phi @ Ts2 @ V )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_1: view_ext @ product_unit] : ( vchop @ V @ Va2 @ X_1 )
% 0.15/0.44 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.v_chop_weaken1
% 0.15/0.44 thf(fact_31_local_Ohmlsl_Ov__chop__assoc,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( Phi @ Ts2 @ W )
% 0.15/0.44 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ U3 @ X2 @ Y )
% 0.15/0.44 & ( Psi @ Ts2 @ X2 )
% 0.15/0.44 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ W @ X2 @ Y )
% 0.15/0.44 & ( Phi @ Ts2 @ X2 )
% 0.15/0.44 & ( Psi @ Ts2 @ Y ) )
% 0.15/0.44 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.v_chop_assoc
% 0.15/0.44 thf(fact_32_local_Ohmlsl_Oglobally__refl,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ! [Ts3: traffic] :
% 0.15/0.44 ( ( abstract @ Ts2 @ Ts3 )
% 0.15/0.44 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 0.15/0.44 => ( Phi @ Ts2 @ V ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.globally_refl
% 0.15/0.44 thf(fact_33_local_Ohmlsl_Oglobally__all__iff_H,axiom,
% 0.15/0.44 ! [A: $tType,B: $tType,Ts: traffic,Phi: traffic > ( view_ext @ product_unit ) > $o,V2: view_ext @ product_unit] :
% 0.15/0.44 ( ( ! [Ts4: traffic] :
% 0.15/0.44 ( ( abstract @ Ts @ Ts4 )
% 0.15/0.44 => ! [X2: A] : ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V2 ) ) ) )
% 0.15/0.44 = ( ! [X2: B,Ts4: traffic] :
% 0.15/0.44 ( ( abstract @ Ts @ Ts4 )
% 0.15/0.44 => ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V2 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.globally_all_iff'
% 0.15/0.44 thf(fact_34_local_Ohmlsl_Oglobally__all__iff,axiom,
% 0.15/0.44 ! [A: $tType,B: $tType,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ! [Ts4: traffic] :
% 0.15/0.44 ( ( abstract @ Ts2 @ Ts4 )
% 0.15/0.44 => ! [X2: A] : ( Phi @ Ts4 @ ( move @ Ts2 @ Ts4 @ V ) ) ) )
% 0.15/0.44 = ( ! [X2: B,Ts4: traffic] :
% 0.15/0.44 ( ( abstract @ Ts2 @ Ts4 )
% 0.15/0.44 => ( Phi @ Ts4 @ ( move @ Ts2 @ Ts4 @ V ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.globally_all_iff
% 0.15/0.44 thf(fact_35_local_Ohmlsl_Oglobally__4,axiom,
% 0.15/0.44 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ! [Ts3: traffic] :
% 0.15/0.44 ( ( abstract @ Ts2 @ Ts3 )
% 0.15/0.44 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 0.15/0.44 => ! [Ts5: traffic] :
% 0.15/0.44 ( ( abstract @ Ts2 @ Ts5 )
% 0.15/0.44 => ! [Ts_a: traffic] :
% 0.15/0.44 ( ( abstract @ Ts5 @ Ts_a )
% 0.15/0.44 => ( Phi @ Ts_a @ ( move @ Ts5 @ Ts_a @ ( move @ Ts2 @ Ts5 @ V ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.globally_4
% 0.15/0.44 thf(fact_36_wd__clm_Ohyps_I1_J,axiom,
% 0.15/0.44 abstract @ ts3 @ ts_a ).
% 0.15/0.44
% 0.15/0.44 % wd_clm.hyps(1)
% 0.15/0.44 thf(fact_37_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 0.15/0.44 ! [X3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 0.15/0.44 = X3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_hchop_stable
% 0.15/0.44 thf(fact_38_local_Ohmlsl_Olength__vchop__stable,axiom,
% 0.15/0.44 ! [X3: real,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ W @ U3 )
% 0.15/0.44 & ( ( real_length @ ( ext @ product_unit @ W ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 & ( ( real_length @ ( ext @ product_unit @ U3 ) )
% 0.15/0.44 = X3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.length_vchop_stable
% 0.15/0.44 thf(fact_39_hmlsl_Olen__stable__up,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_stable_up
% 0.15/0.44 thf(fact_40_hmlsl_Olen__stable__down,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( len @ regular_regular @ V1 @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_stable_down
% 0.15/0.44 thf(fact_41_hmlsl_Olen__stable,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.44 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_stable
% 0.15/0.44 thf(fact_42_hmlsl_Olen__view__hchop__right,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.44 => ( ( len @ regular_regular @ V22 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V22 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_view_hchop_right
% 0.15/0.44 thf(fact_43_hmlsl_Olen__view__hchop__left,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.44 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V1 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_view_hchop_left
% 0.15/0.44 thf(fact_44_hmlsl_Olen__compose__hchop,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V1 ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V22 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V22 ) ) )
% 0.15/0.44 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_compose_hchop
% 0.15/0.44 thf(fact_45_ext,axiom,
% 0.15/0.44 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.15/0.44 ( ! [X4: A] :
% 0.15/0.44 ( ( F @ X4 )
% 0.15/0.44 = ( G @ X4 ) )
% 0.15/0.44 => ( F = G ) ) ).
% 0.15/0.44
% 0.15/0.44 % ext
% 0.15/0.44 thf(fact_46_wd__clm_Ohyps_I2_J,axiom,
% 0.15/0.44 ? [C2: cars] : ( withdraw_claim @ ts_a @ C2 @ ts ) ).
% 0.15/0.44
% 0.15/0.44 % wd_clm.hyps(2)
% 0.15/0.44 thf(fact_47_local_Ohmlsl_Olength__split,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.length_split
% 0.15/0.44 thf(fact_48_local_Ohmlsl_Olength__meld,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) ) )
% 0.15/0.44 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.length_meld
% 0.15/0.44 thf(fact_49_local_Ohmlsl_Olength__dense,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.length_dense
% 0.15/0.44 thf(fact_50_hmlsl_Olen__empty__on__subview2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.44 => ( ( real_length @ ( len @ regular_regular @ V22 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_empty_on_subview2
% 0.15/0.44 thf(fact_51_hmlsl_Olen__empty__on__subview1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.44 => ( ( real_length @ ( len @ regular_regular @ V1 @ Ts @ C ) )
% 0.15/0.44 = ( zero_zero @ real ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_empty_on_subview1
% 0.15/0.44 thf(fact_52_hmlsl_Olen__fills__subview,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) )
% 0.15/0.44 => ? [V12: view_ext @ product_unit,V23: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ V12 @ V23 )
% 0.15/0.44 & ( hchop @ V23 @ V4 @ V32 )
% 0.15/0.44 & ( ( len @ regular_regular @ V4 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V4 ) )
% 0.15/0.44 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C ) )
% 0.15/0.44 = ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_fills_subview
% 0.15/0.44 thf(fact_53_d__def,axiom,
% 0.15/0.44 withdraw_claim @ ts_a @ d @ ts ).
% 0.15/0.44
% 0.15/0.44 % d_def
% 0.15/0.44 thf(fact_54_local_Ohmlsl_Owidth__clm,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_clm
% 0.15/0.44 thf(fact_55_local_Ohmlsl_Oclm__dense,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ W ) )
% 0.15/0.44 & ( ( restrict @ W @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ W ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U3 ) )
% 0.15/0.44 & ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U3 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_dense
% 0.15/0.44 thf(fact_56_local_Ohmlsl_Oclm__decompose,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va2 ) )
% 0.15/0.44 & ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U2 ) )
% 0.15/0.44 & ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_decompose
% 0.15/0.44 thf(fact_57_local_Ohmlsl_Oclm__compose,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_compose
% 0.15/0.44 thf(fact_58_local_Ohmlsl_Oclm__sing__not__interrupted,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ U @ Vb @ Ua )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( restrict @ Ua @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_sing_not_interrupted
% 0.15/0.44 thf(fact_59_local_Ohmlsl_Oclm__sing,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_sing
% 0.15/0.44 thf(fact_60_local_Ohmlsl_Ono__clm__before__res2,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ U @ Vb @ Ua )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Ua ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.no_clm_before_res2
% 0.15/0.44 thf(fact_61_local_Ohmlsl_Ono__clm__before__res,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.no_clm_before_res
% 0.15/0.44 thf(fact_62_local_Ohmlsl_Otwo__res__no__car,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ Va ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ Va ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ U ) )
% 0.15/0.44 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ U ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ~ ? [X: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.two_res_no_car
% 0.15/0.44 thf(fact_63__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.15/0.44 ~ ! [D: cars] :
% 0.15/0.44 ~ ( withdraw_claim @ ts_a @ D @ ts ) ).
% 0.15/0.44
% 0.15/0.44 % \<open>\<And>thesis. (\<And>d. ts' \<^bold>\<midarrow>wdc( d ) \<^bold>\<rightarrow> ts'' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.15/0.44 thf(fact_64_local_Ohmlsl_Ofree__dense,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C3: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C3 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ W @ U3 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C3: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ W @ Ts2 @ C3 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ W @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ W @ ( res @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C3: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ U3 @ Ts2 @ C3 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C3 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_dense
% 0.15/0.44 thf(fact_65_local_Ohmlsl_Ofree__decompose,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C4: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ Va2 @ Ts2 @ C4 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C4: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ U2 @ Ts2 @ C4 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_decompose
% 0.15/0.44 thf(fact_66_local_Ohmlsl_Ofree__compose,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V @ Va @ U )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ Va @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ Va @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ U @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ U @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ U @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C4: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C4 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C4 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_compose
% 0.15/0.44 thf(fact_67_local_Ohmlsl_Owidth__free,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_free
% 0.15/0.44 thf(fact_68_local_Ohmlsl_Ores__not__free,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ? [X4: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X4 )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.res_not_free
% 0.15/0.44 thf(fact_69_local_Ohmlsl_Ofree__no__res,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ~ ? [X: cars] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_no_res
% 0.15/0.44 thf(fact_70_local_Ohmlsl_Ofree__no__clm,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ~ ? [X: cars] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_no_clm
% 0.15/0.44 thf(fact_71_local_Ohmlsl_Ofree__ge__zero,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) )
% 0.15/0.44 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.free_ge_zero
% 0.15/0.44 thf(fact_72_local_Ohmlsl_Oclm__not__free,axiom,
% 0.15/0.44 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ? [X4: cars] :
% 0.15/0.44 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X4 )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) )
% 0.15/0.44 & ! [C2: cars] :
% 0.15/0.44 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.44 = ( zero_zero @ real ) )
% 0.15/0.44 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.44 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.clm_not_free
% 0.15/0.44 thf(fact_73_hmlsl__regular_Obackwards__wdc__res__stab,axiom,
% 0.15/0.44 ! [Ts: traffic,D2: cars,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 0.15/0.44 ( ( ( withdraw_claim @ Ts @ D2 @ Ts6 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.backwards_wdc_res_stab
% 0.15/0.44 thf(fact_74_view_Ohorizontal__chop__non__empty,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit] :
% 0.15/0.44 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 => ? [U2: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ U2 @ W2 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W2 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_non_empty
% 0.15/0.44 thf(fact_75_not__gr__zero,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [N: A] :
% 0.15/0.44 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.15/0.44 = ( N
% 0.15/0.44 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % not_gr_zero
% 0.15/0.44 thf(fact_76_le__zero__eq,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [N: A] :
% 0.15/0.44 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.15/0.44 = ( N
% 0.15/0.44 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_zero_eq
% 0.15/0.44 thf(fact_77_hmlsl__regular_Obackwards__c__res__stab,axiom,
% 0.15/0.44 ! [Ts: traffic,D2: cars,N: nat,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 0.15/0.44 ( ( ( create_claim @ Ts @ D2 @ N @ Ts6 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.backwards_c_res_stab
% 0.15/0.44 thf(fact_78_hmlsl__regular_Obackwards__wdr__res__stab,axiom,
% 0.15/0.44 ! [Ts: traffic,D2: cars,N: nat,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 0.15/0.44 ( ( ( withdraw_reservation @ Ts @ D2 @ N @ Ts6 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.backwards_wdr_res_stab
% 0.15/0.44 thf(fact_79_hmlsl_Olen__sub__int,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( ext @ product_unit @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.len_sub_int
% 0.15/0.44 thf(fact_80_view_Overtical__chop__width__mon,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit,X3: nat] :
% 0.15/0.44 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( vchop @ V22 @ V33 @ V42 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V33 ) )
% 0.15/0.44 = X3 ) )
% 0.15/0.44 => ( ord_less_eq @ nat @ X3 @ ( nat_card @ ( lan @ product_unit @ V2 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_width_mon
% 0.15/0.44 thf(fact_81_zero__reorient,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( zero @ A )
% 0.15/0.44 => ! [X3: A] :
% 0.15/0.44 ( ( ( zero_zero @ A )
% 0.15/0.44 = X3 )
% 0.15/0.44 = ( X3
% 0.15/0.44 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % zero_reorient
% 0.15/0.44 thf(fact_82_view_Overtical__chop__singleton,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ( nat_card @ ( lan @ product_unit @ U4 ) )
% 0.15/0.44 = ( zero_zero @ nat ) )
% 0.15/0.44 | ( ( nat_card @ ( lan @ product_unit @ W3 ) )
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_singleton
% 0.15/0.44 thf(fact_83_one__reorient,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( one @ A )
% 0.15/0.44 => ! [X3: A] :
% 0.15/0.44 ( ( ( one_one @ A )
% 0.15/0.44 = X3 )
% 0.15/0.44 = ( X3
% 0.15/0.44 = ( one_one @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % one_reorient
% 0.15/0.44 thf(fact_84_view_Ohorizontal__chop1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit] :
% 0.15/0.44 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop1
% 0.15/0.44 thf(fact_85_view_Ohorizontal__chop__assoc1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( hchop @ V22 @ V33 @ V42 ) )
% 0.15/0.44 => ? [V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ V4 @ V42 )
% 0.15/0.44 & ( hchop @ V4 @ V1 @ V33 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_assoc1
% 0.15/0.44 thf(fact_86_view_Ohorizontal__chop__assoc2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( hchop @ V1 @ V33 @ V42 ) )
% 0.15/0.44 => ? [V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ V33 @ V4 )
% 0.15/0.44 & ( hchop @ V4 @ V42 @ V22 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_assoc2
% 0.15/0.44 thf(fact_87_view_Ohorizontal__chop__empty__left,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ? [U2: view_ext @ product_unit] : ( hchop @ V @ U2 @ V ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_empty_left
% 0.15/0.44 thf(fact_88_view_Ohorizontal__chop__empty__right,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ? [X_1: view_ext @ product_unit] : ( hchop @ V @ V @ X_1 ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_empty_right
% 0.15/0.44 thf(fact_89_view_Overtical__chop1,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( vchop @ V @ U2 @ X_1 ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop1
% 0.15/0.44 thf(fact_90_view_Overtical__chop__assoc1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( vchop @ V22 @ V33 @ V42 ) )
% 0.15/0.44 => ? [V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ V4 @ V42 )
% 0.15/0.44 & ( vchop @ V4 @ V1 @ V33 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_assoc1
% 0.15/0.44 thf(fact_91_view_Overtical__chop__assoc2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( vchop @ V1 @ V33 @ V42 ) )
% 0.15/0.44 => ? [V4: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ V33 @ V4 )
% 0.15/0.44 & ( vchop @ V4 @ V42 @ V22 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_assoc2
% 0.15/0.44 thf(fact_92_view_Overtical__chop__empty__up,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ? [U2: view_ext @ product_unit] : ( vchop @ V @ U2 @ V ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_empty_up
% 0.15/0.44 thf(fact_93_view_Overtical__chop__empty__down,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ? [X_1: view_ext @ product_unit] : ( vchop @ V @ V @ X_1 ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_empty_down
% 0.15/0.44 thf(fact_94_zero__le,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 0.15/0.44
% 0.15/0.44 % zero_le
% 0.15/0.44 thf(fact_95_zero__less__iff__neq__zero,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [N: A] :
% 0.15/0.44 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.15/0.44 = ( N
% 0.15/0.44 != ( zero_zero @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % zero_less_iff_neq_zero
% 0.15/0.44 thf(fact_96_gr__implies__not__zero,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [M: A,N: A] :
% 0.15/0.44 ( ( ord_less @ A @ M @ N )
% 0.15/0.44 => ( N
% 0.15/0.44 != ( zero_zero @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % gr_implies_not_zero
% 0.15/0.44 thf(fact_97_not__less__zero,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [N: A] :
% 0.15/0.44 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % not_less_zero
% 0.15/0.44 thf(fact_98_gr__zeroI,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( canoni770627133id_add @ A )
% 0.15/0.44 => ! [N: A] :
% 0.15/0.44 ( ( N
% 0.15/0.44 != ( zero_zero @ A ) )
% 0.15/0.44 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % gr_zeroI
% 0.15/0.44 thf(fact_99_view_Ohorizontal__chop__leq2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W3 @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_leq2
% 0.15/0.44 thf(fact_100_view_Ohorizontal__chop__leq1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_leq1
% 0.15/0.44 thf(fact_101_view_Overtical__chop__leq2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W3 @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_leq2
% 0.15/0.44 thf(fact_102_view_Overtical__chop__leq1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_leq1
% 0.15/0.44 thf(fact_103_view_Ohorizontal__chop__width__stable,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( nat_card @ ( lan @ product_unit @ U4 ) ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( nat_card @ ( lan @ product_unit @ W3 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_width_stable
% 0.15/0.44 thf(fact_104_view_Overtical__chop__length__stable,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.15/0.44 = ( real_length @ ( ext @ product_unit @ U4 ) ) )
% 0.15/0.44 & ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.15/0.44 = ( real_length @ ( ext @ product_unit @ W3 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_length_stable
% 0.15/0.44 thf(fact_105_view_Osomewhere__leq,axiom,
% 0.15/0.44 ( ( ord_less_eq @ ( view_ext @ product_unit ) )
% 0.15/0.44 = ( ^ [V5: view_ext @ product_unit,V6: view_ext @ product_unit] :
% 0.15/0.44 ? [V13: view_ext @ product_unit,V24: view_ext @ product_unit,V34: view_ext @ product_unit,Vl: view_ext @ product_unit,Vr: view_ext @ product_unit,Vu: view_ext @ product_unit,Vd: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V6 @ Vl @ V13 )
% 0.15/0.44 & ( hchop @ V13 @ V24 @ Vr )
% 0.15/0.44 & ( vchop @ V24 @ Vd @ V34 )
% 0.15/0.44 & ( vchop @ V34 @ V5 @ Vu ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.somewhere_leq
% 0.15/0.44 thf(fact_106_hmlsl_Oview__leq__len__leq,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V2 ) @ ( ext @ product_unit @ V3 ) )
% 0.15/0.44 & ( ( own @ product_unit @ V2 )
% 0.15/0.44 = ( own @ product_unit @ V3 ) )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) )
% 0.15/0.44 => ( ord_less_eq @ real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.view_leq_len_leq
% 0.15/0.44 thf(fact_107_restriction_Orestriction__card__somewhere__mon,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Vl2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Vr2: view_ext @ product_unit,Vu2: view_ext @ product_unit,V33: view_ext @ product_unit,V3: view_ext @ product_unit,Vd2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( ( hchop @ V2 @ Vl2 @ V1 )
% 0.15/0.44 & ( hchop @ V1 @ V22 @ Vr2 )
% 0.15/0.44 & ( vchop @ V22 @ Vu2 @ V33 )
% 0.15/0.44 & ( vchop @ V33 @ V3 @ Vd2 )
% 0.15/0.44 & ( ( nat_card @ ( restrict @ V3 @ F @ C ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_card_somewhere_mon
% 0.15/0.44 thf(fact_108_hmlsl__regular_Obackwards__res__act,axiom,
% 0.15/0.44 ! [Ts: traffic,C: cars,Ts6: traffic,V2: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( create_reservation @ Ts @ C @ Ts6 )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( clm @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.backwards_res_act
% 0.15/0.44 thf(fact_109_hmlsl__regular_Oreservation2,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ! [Ts3: traffic] :
% 0.15/0.44 ( ( create_reservation @ Ts2 @ C @ Ts3 )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts3 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts3 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) )
% 0.15/0.44 => ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.reservation2
% 0.15/0.44 thf(fact_110_hmlsl__regular_Oreservation1,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) )
% 0.15/0.44 => ! [Ts5: traffic] :
% 0.15/0.44 ( ( create_reservation @ Ts2 @ C @ Ts5 )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts5 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts5 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.reservation1
% 0.15/0.44 thf(fact_111_hmlsl__regular_Oreservation,axiom,
% 0.15/0.44 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ! [Ts4: traffic] :
% 0.15/0.44 ( ( create_reservation @ Ts2 @ C @ Ts4 )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts4 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts4 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) )
% 0.15/0.44 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V ) )
% 0.15/0.44 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.reservation
% 0.15/0.44 thf(fact_112_hmlsl_Oext__eq__len__eq,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C: cars] :
% 0.15/0.44 ( ( ( ( ext @ product_unit @ V2 )
% 0.15/0.44 = ( ext @ product_unit @ V3 ) )
% 0.15/0.44 & ( ( own @ product_unit @ V2 )
% 0.15/0.44 = ( own @ product_unit @ V3 ) ) )
% 0.15/0.44 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl.ext_eq_len_eq
% 0.15/0.44 thf(fact_113_view_Ohorizontal__chop__own__trans,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( own @ product_unit @ U4 )
% 0.15/0.44 = ( own @ product_unit @ W3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.horizontal_chop_own_trans
% 0.15/0.44 thf(fact_114_view_Overtical__chop__own__trans,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( own @ product_unit @ U4 )
% 0.15/0.44 = ( own @ product_unit @ W3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % view.vertical_chop_own_trans
% 0.15/0.44 thf(fact_115_restriction_Orestrict__subseteq,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( F @ C ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restrict_subseteq
% 0.15/0.44 thf(fact_116_restriction_Orestrict__view,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan @ product_unit @ V2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restrict_view
% 0.15/0.44 thf(fact_117_restriction_Orestrict__res,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ ( res @ Ts ) @ C ) @ ( res @ Ts @ C ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restrict_res
% 0.15/0.44 thf(fact_118_restriction_Orestriction__stable,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( restrict @ U4 @ F @ C )
% 0.15/0.44 = ( restrict @ W3 @ F @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_stable
% 0.15/0.44 thf(fact_119_restriction_Orestriction__stable1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.44 = ( restrict @ U4 @ F @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_stable1
% 0.15/0.44 thf(fact_120_restriction_Orestriction__stable2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.44 = ( restrict @ W3 @ F @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_stable2
% 0.15/0.44 thf(fact_121_restriction_Orestrict__clm,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) @ ( clm @ Ts @ C ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restrict_clm
% 0.15/0.44 thf(fact_122_restriction_Orestriction__mon2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ nat_int @ ( restrict @ W3 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_mon2
% 0.15/0.44 thf(fact_123_restriction_Orestriction__mon1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ nat_int @ ( restrict @ U4 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_mon1
% 0.15/0.44 thf(fact_124_restriction_Orestriction__eq__view__card,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( ( restrict @ V2 @ F @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 => ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 0.15/0.44 = ( nat_card @ ( lan @ product_unit @ V2 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_eq_view_card
% 0.15/0.44 thf(fact_125_restriction_Orestrict__eq__lan__subs,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 0.15/0.44 = ( nat_card @ ( lan @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan @ product_unit @ V2 ) ) )
% 0.15/0.44 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restrict_eq_lan_subs
% 0.15/0.44 thf(fact_126_restriction_Orestriction__card__mon1,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ U4 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_card_mon1
% 0.15/0.44 thf(fact_127_restriction_Orestriction__card__mon2,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ W3 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_card_mon2
% 0.15/0.44 thf(fact_128_restriction_Orestriction__clm__leq__one,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) ) @ ( one_one @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_clm_leq_one
% 0.15/0.44 thf(fact_129_restriction_Orestriction__card__mon__trans,axiom,
% 0.15/0.44 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 0.15/0.44 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.44 & ( vchop @ V22 @ V33 @ V42 )
% 0.15/0.44 & ( ( nat_card @ ( restrict @ V33 @ F @ C ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % restriction.restriction_card_mon_trans
% 0.15/0.44 thf(fact_130_hmlsl__regular_Obackwards__res__stab,axiom,
% 0.15/0.44 ! [Ts: traffic,D2: cars,Ts6: traffic,C: cars,V2: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( create_reservation @ Ts @ D2 @ Ts6 )
% 0.15/0.44 & ( D2 != C )
% 0.15/0.44 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) )
% 0.15/0.44 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.15/0.44 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.44 = ( ext @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.44 = ( lan @ product_unit @ V2 ) )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.15/0.44 = ( one_one @ nat ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % hmlsl_regular.backwards_res_stab
% 0.15/0.44 thf(fact_131_less__one,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.15/0.44 = ( N
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_one
% 0.15/0.44 thf(fact_132_le0,axiom,
% 0.15/0.44 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.15/0.44
% 0.15/0.44 % le0
% 0.15/0.44 thf(fact_133_bot__nat__0_Oextremum,axiom,
% 0.15/0.44 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.15/0.44
% 0.15/0.44 % bot_nat_0.extremum
% 0.15/0.44 thf(fact_134_card__non__empty__geq__one,axiom,
% 0.15/0.44 ! [I: nat_int] :
% 0.15/0.44 ( ( I
% 0.15/0.44 != ( bot_bot @ nat_int ) )
% 0.15/0.44 = ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ I ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % card_non_empty_geq_one
% 0.15/0.44 thf(fact_135_bot__nat__0_Onot__eq__extremum,axiom,
% 0.15/0.44 ! [A2: nat] :
% 0.15/0.44 ( ( A2
% 0.15/0.44 != ( zero_zero @ nat ) )
% 0.15/0.44 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % bot_nat_0.not_eq_extremum
% 0.15/0.44 thf(fact_136_less__nat__zero__code,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_nat_zero_code
% 0.15/0.44 thf(fact_137_neq0__conv,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ( ( N
% 0.15/0.44 != ( zero_zero @ nat ) )
% 0.15/0.44 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % neq0_conv
% 0.15/0.44 thf(fact_138_infinite__descent__measure,axiom,
% 0.15/0.44 ! [A: $tType,P: A > $o,V7: A > nat,X3: A] :
% 0.15/0.44 ( ! [X4: A] :
% 0.15/0.44 ( ~ ( P @ X4 )
% 0.15/0.44 => ? [Y2: A] :
% 0.15/0.44 ( ( ord_less @ nat @ ( V7 @ Y2 ) @ ( V7 @ X4 ) )
% 0.15/0.44 & ~ ( P @ Y2 ) ) )
% 0.15/0.44 => ( P @ X3 ) ) ).
% 0.15/0.44
% 0.15/0.44 % infinite_descent_measure
% 0.15/0.44 thf(fact_139_linorder__neqE__nat,axiom,
% 0.15/0.44 ! [X3: nat,Y3: nat] :
% 0.15/0.44 ( ( X3 != Y3 )
% 0.15/0.44 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 0.15/0.44 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % linorder_neqE_nat
% 0.15/0.44 thf(fact_140_infinite__descent,axiom,
% 0.15/0.44 ! [P: nat > $o,N: nat] :
% 0.15/0.44 ( ! [N2: nat] :
% 0.15/0.44 ( ~ ( P @ N2 )
% 0.15/0.44 => ? [M2: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M2 @ N2 )
% 0.15/0.44 & ~ ( P @ M2 ) ) )
% 0.15/0.44 => ( P @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % infinite_descent
% 0.15/0.44 thf(fact_141_nat__less__induct,axiom,
% 0.15/0.44 ! [P: nat > $o,N: nat] :
% 0.15/0.44 ( ! [N2: nat] :
% 0.15/0.44 ( ! [M2: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M2 @ N2 )
% 0.15/0.44 => ( P @ M2 ) )
% 0.15/0.44 => ( P @ N2 ) )
% 0.15/0.44 => ( P @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % nat_less_induct
% 0.15/0.44 thf(fact_142_less__irrefl__nat,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ N @ N ) ).
% 0.15/0.44
% 0.15/0.44 % less_irrefl_nat
% 0.15/0.44 thf(fact_143_less__not__refl3,axiom,
% 0.15/0.44 ! [S: nat,T: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ S @ T )
% 0.15/0.44 => ( S != T ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_not_refl3
% 0.15/0.44 thf(fact_144_less__not__refl2,axiom,
% 0.15/0.44 ! [N: nat,M: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ N @ M )
% 0.15/0.44 => ( M != N ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_not_refl2
% 0.15/0.44 thf(fact_145_less__not__refl,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ N @ N ) ).
% 0.15/0.44
% 0.15/0.44 % less_not_refl
% 0.15/0.44 thf(fact_146_nat__neq__iff,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( M != N )
% 0.15/0.44 = ( ( ord_less @ nat @ M @ N )
% 0.15/0.44 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % nat_neq_iff
% 0.15/0.44 thf(fact_147_measure__induct__rule,axiom,
% 0.15/0.44 ! [B: $tType,A: $tType] :
% 0.15/0.44 ( ( wellorder @ B )
% 0.15/0.44 => ! [F: A > B,P: A > $o,A2: A] :
% 0.15/0.44 ( ! [X4: A] :
% 0.15/0.44 ( ! [Y2: A] :
% 0.15/0.44 ( ( ord_less @ B @ ( F @ Y2 ) @ ( F @ X4 ) )
% 0.15/0.44 => ( P @ Y2 ) )
% 0.15/0.44 => ( P @ X4 ) )
% 0.15/0.44 => ( P @ A2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % measure_induct_rule
% 0.15/0.44 thf(fact_148_measure__induct,axiom,
% 0.15/0.44 ! [B: $tType,A: $tType] :
% 0.15/0.44 ( ( wellorder @ B )
% 0.15/0.44 => ! [F: A > B,P: A > $o,A2: A] :
% 0.15/0.44 ( ! [X4: A] :
% 0.15/0.44 ( ! [Y2: A] :
% 0.15/0.44 ( ( ord_less @ B @ ( F @ Y2 ) @ ( F @ X4 ) )
% 0.15/0.44 => ( P @ Y2 ) )
% 0.15/0.44 => ( P @ X4 ) )
% 0.15/0.44 => ( P @ A2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % measure_induct
% 0.15/0.44 thf(fact_149_infinite__descent0__measure,axiom,
% 0.15/0.44 ! [A: $tType,V7: A > nat,P: A > $o,X3: A] :
% 0.15/0.44 ( ! [X4: A] :
% 0.15/0.44 ( ( ( V7 @ X4 )
% 0.15/0.44 = ( zero_zero @ nat ) )
% 0.15/0.44 => ( P @ X4 ) )
% 0.15/0.44 => ( ! [X4: A] :
% 0.15/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V7 @ X4 ) )
% 0.15/0.44 => ( ~ ( P @ X4 )
% 0.15/0.44 => ? [Y2: A] :
% 0.15/0.44 ( ( ord_less @ nat @ ( V7 @ Y2 ) @ ( V7 @ X4 ) )
% 0.15/0.44 & ~ ( P @ Y2 ) ) ) )
% 0.15/0.44 => ( P @ X3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % infinite_descent0_measure
% 0.15/0.44 thf(fact_150_bot__nat__0_Oextremum__strict,axiom,
% 0.15/0.44 ! [A2: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % bot_nat_0.extremum_strict
% 0.15/0.44 thf(fact_151_infinite__descent0,axiom,
% 0.15/0.44 ! [P: nat > $o,N: nat] :
% 0.15/0.44 ( ( P @ ( zero_zero @ nat ) )
% 0.15/0.44 => ( ! [N2: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.15/0.44 => ( ~ ( P @ N2 )
% 0.15/0.44 => ? [M2: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M2 @ N2 )
% 0.15/0.44 & ~ ( P @ M2 ) ) ) )
% 0.15/0.44 => ( P @ N ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % infinite_descent0
% 0.15/0.44 thf(fact_152_gr__implies__not0,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M @ N )
% 0.15/0.44 => ( N
% 0.15/0.44 != ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % gr_implies_not0
% 0.15/0.44 thf(fact_153_less__zeroE,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_zeroE
% 0.15/0.44 thf(fact_154_not__less0,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % not_less0
% 0.15/0.44 thf(fact_155_not__gr0,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.15/0.44 = ( N
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % not_gr0
% 0.15/0.44 thf(fact_156_gr0I,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ( ( N
% 0.15/0.44 != ( zero_zero @ nat ) )
% 0.15/0.44 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % gr0I
% 0.15/0.44 thf(fact_157_less__mono__imp__le__mono,axiom,
% 0.15/0.44 ! [F: nat > nat,I: nat,J: nat] :
% 0.15/0.44 ( ! [I2: nat,J2: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ I2 @ J2 )
% 0.15/0.44 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.15/0.44 => ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_mono_imp_le_mono
% 0.15/0.44 thf(fact_158_le__neq__implies__less,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ M @ N )
% 0.15/0.44 => ( ( M != N )
% 0.15/0.44 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_neq_implies_less
% 0.15/0.44 thf(fact_159_Nat_Oex__has__greatest__nat,axiom,
% 0.15/0.44 ! [P: nat > $o,K: nat,B2: nat] :
% 0.15/0.44 ( ( P @ K )
% 0.15/0.44 => ( ! [Y4: nat] :
% 0.15/0.44 ( ( P @ Y4 )
% 0.15/0.44 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 0.15/0.44 => ? [X4: nat] :
% 0.15/0.44 ( ( P @ X4 )
% 0.15/0.44 & ! [Y2: nat] :
% 0.15/0.44 ( ( P @ Y2 )
% 0.15/0.44 => ( ord_less_eq @ nat @ Y2 @ X4 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % Nat.ex_has_greatest_nat
% 0.15/0.44 thf(fact_160_less__or__eq__imp__le,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ( ord_less @ nat @ M @ N )
% 0.15/0.44 | ( M = N ) )
% 0.15/0.44 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_or_eq_imp_le
% 0.15/0.44 thf(fact_161_le__eq__less__or__eq,axiom,
% 0.15/0.44 ( ( ord_less_eq @ nat )
% 0.15/0.44 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M3 @ N3 )
% 0.15/0.44 | ( M3 = N3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_eq_less_or_eq
% 0.15/0.44 thf(fact_162_less__imp__le__nat,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ M @ N )
% 0.15/0.44 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % less_imp_le_nat
% 0.15/0.44 thf(fact_163_nat__le__linear,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ M @ N )
% 0.15/0.44 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.15/0.44
% 0.15/0.44 % nat_le_linear
% 0.15/0.44 thf(fact_164_nat__less__le,axiom,
% 0.15/0.44 ( ( ord_less @ nat )
% 0.15/0.44 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 0.15/0.44 & ( M3 != N3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % nat_less_le
% 0.15/0.44 thf(fact_165_le__antisym,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ M @ N )
% 0.15/0.44 => ( ( ord_less_eq @ nat @ N @ M )
% 0.15/0.44 => ( M = N ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_antisym
% 0.15/0.44 thf(fact_166_eq__imp__le,axiom,
% 0.15/0.44 ! [M: nat,N: nat] :
% 0.15/0.44 ( ( M = N )
% 0.15/0.44 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.15/0.44
% 0.15/0.44 % eq_imp_le
% 0.15/0.44 thf(fact_167_le__trans,axiom,
% 0.15/0.44 ! [I: nat,J: nat,K: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.44 => ( ( ord_less_eq @ nat @ J @ K )
% 0.15/0.44 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_trans
% 0.15/0.44 thf(fact_168_le__refl,axiom,
% 0.15/0.44 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.15/0.44
% 0.15/0.44 % le_refl
% 0.15/0.44 thf(fact_169_card__subset__less,axiom,
% 0.15/0.44 ! [I: nat_int,I3: nat_int] :
% 0.15/0.44 ( ( ord_less @ nat_int @ I @ I3 )
% 0.15/0.44 => ( ord_less @ nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % card_subset_less
% 0.15/0.44 thf(fact_170_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.15/0.44 ! [A2: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.15/0.44 => ( A2
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % bot_nat_0.extremum_uniqueI
% 0.15/0.44 thf(fact_171_bot__nat__0_Oextremum__unique,axiom,
% 0.15/0.44 ! [A2: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.15/0.44 = ( A2
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % bot_nat_0.extremum_unique
% 0.15/0.44 thf(fact_172_ex__least__nat__le,axiom,
% 0.15/0.44 ! [P: nat > $o,N: nat] :
% 0.15/0.44 ( ( P @ N )
% 0.15/0.44 => ( ~ ( P @ ( zero_zero @ nat ) )
% 0.15/0.44 => ? [K2: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.15/0.44 & ! [I4: nat] :
% 0.15/0.44 ( ( ord_less @ nat @ I4 @ K2 )
% 0.15/0.44 => ~ ( P @ I4 ) )
% 0.15/0.44 & ( P @ K2 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % ex_least_nat_le
% 0.15/0.44 thf(fact_173_le__0__eq,axiom,
% 0.15/0.44 ! [N: nat] :
% 0.15/0.44 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.15/0.44 = ( N
% 0.15/0.44 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % le_0_eq
% 0.15/0.44 thf(fact_174_less__eq__nat_Osimps_I1_J,axiom,
% 0.15/0.44 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.15/0.44
% 0.15/0.44 % less_eq_nat.simps(1)
% 0.15/0.44 thf(fact_175_card__subset__le,axiom,
% 0.15/0.44 ! [I: nat_int,I3: nat_int] :
% 0.15/0.44 ( ( ord_less_eq @ nat_int @ I @ I3 )
% 0.15/0.44 => ( ord_less_eq @ nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % card_subset_le
% 0.15/0.44 thf(fact_176_card__empty__zero,axiom,
% 0.15/0.44 ( ( nat_card @ ( bot_bot @ nat_int ) )
% 0.15/0.44 = ( zero_zero @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % card_empty_zero
% 0.15/0.44 thf(fact_177_local_Ohmlsl_Owidth__ge,axiom,
% 0.15/0.44 ! [V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit] :
% 0.15/0.44 ( ? [X_12: view_ext @ product_unit] : ( vchop @ V @ Va @ X_12 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = ( plus_plus @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) )
% 0.15/0.44 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat_card @ ( lan @ product_unit @ V ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_ge
% 0.15/0.44 thf(fact_178_traffic_Ocreate__res__subseteq2,axiom,
% 0.15/0.44 ! [Ts: traffic,C: cars,Ts6: traffic] :
% 0.15/0.44 ( ( create_reservation @ Ts @ C @ Ts6 )
% 0.15/0.44 => ( ord_less_eq @ nat_int @ ( clm @ Ts @ C ) @ ( res @ Ts6 @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % traffic.create_res_subseteq2
% 0.15/0.44 thf(fact_179_traffic_OatMostOneClm,axiom,
% 0.15/0.44 ! [Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( clm @ Ts @ C ) ) @ ( one_one @ nat ) ) ).
% 0.15/0.44
% 0.15/0.44 % traffic.atMostOneClm
% 0.15/0.44 thf(fact_180_traffic_OatLeastOneRes,axiom,
% 0.15/0.44 ! [Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( res @ Ts @ C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % traffic.atLeastOneRes
% 0.15/0.44 thf(fact_181_local_Ohmlsl_Owidth__add1,axiom,
% 0.15/0.44 ! [X3: nat,Y3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va @ U )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.15/0.44 = Y3 ) )
% 0.15/0.44 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( plus_plus @ nat @ X3 @ Y3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_add1
% 0.15/0.44 thf(fact_182_local_Ohmlsl_Owidth__add2,axiom,
% 0.15/0.44 ! [X3: nat,Y3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 0.15/0.44 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.15/0.44 = ( plus_plus @ nat @ X3 @ Y3 ) )
% 0.15/0.44 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.15/0.44 ( ( vchop @ V @ Va2 @ U2 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 0.15/0.44 = X3 )
% 0.15/0.44 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 0.15/0.44 = Y3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % local.hmlsl.width_add2
% 0.15/0.44 thf(fact_183_add__left__cancel,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( cancel_semigroup_add @ A )
% 0.15/0.44 => ! [A2: A,B2: A,C: A] :
% 0.15/0.44 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.15/0.44 = ( plus_plus @ A @ A2 @ C ) )
% 0.15/0.44 = ( B2 = C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % add_left_cancel
% 0.15/0.44 thf(fact_184_add__right__cancel,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( cancel_semigroup_add @ A )
% 0.15/0.44 => ! [B2: A,A2: A,C: A] :
% 0.15/0.44 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.15/0.44 = ( plus_plus @ A @ C @ A2 ) )
% 0.15/0.44 = ( B2 = C ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % add_right_cancel
% 0.15/0.44 thf(fact_185_add__le__cancel__left,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( ordere236663937imp_le @ A )
% 0.15/0.44 => ! [C: A,A2: A,B2: A] :
% 0.15/0.44 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.15/0.44 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % add_le_cancel_left
% 0.15/0.44 thf(fact_186_add__le__cancel__right,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( ordere236663937imp_le @ A )
% 0.15/0.44 => ! [A2: A,C: A,B2: A] :
% 0.15/0.44 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.15/0.44 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 % add_le_cancel_right
% 0.15/0.44 thf(fact_187_add_Oleft__neutral,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( monoid_add @ A )
% 0.15/0.44 => ! [A2: A] :
% 0.15/0.44 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.15/0.44 = A2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % add.left_neutral
% 0.15/0.44 thf(fact_188_add_Oright__neutral,axiom,
% 0.15/0.44 ! [A: $tType] :
% 0.15/0.44 ( ( monoid_add @ A )
% 0.15/0.44 => ! [A2: A] :
% 0.15/0.44 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.15/0.44 = A2 ) ) ).
% 0.15/0.44
% 0.15/0.44 % add.right_neutral
% 0.15/0.44 thf(fact_189_double__zero,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.15/0.45 = ( zero_zero @ A ) )
% 0.15/0.45 = ( A2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % double_zero
% 0.15/0.45 thf(fact_190_double__zero__sym,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ( zero_zero @ A )
% 0.15/0.45 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.15/0.45 = ( A2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % double_zero_sym
% 0.15/0.45 thf(fact_191_add__cancel__left__left,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( cancel1352612707id_add @ A )
% 0.15/0.45 => ! [B2: A,A2: A] :
% 0.15/0.45 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.15/0.45 = A2 )
% 0.15/0.45 = ( B2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_cancel_left_left
% 0.15/0.45 thf(fact_192_add__cancel__left__right,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( cancel1352612707id_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.15/0.45 = A2 )
% 0.15/0.45 = ( B2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_cancel_left_right
% 0.15/0.45 thf(fact_193_add__cancel__right__left,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( cancel1352612707id_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( A2
% 0.15/0.45 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.15/0.45 = ( B2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_cancel_right_left
% 0.15/0.45 thf(fact_194_add__cancel__right__right,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( cancel1352612707id_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( A2
% 0.15/0.45 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.15/0.45 = ( B2
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_cancel_right_right
% 0.15/0.45 thf(fact_195_add__eq__0__iff__both__eq__0,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( canoni770627133id_add @ A )
% 0.15/0.45 => ! [X3: A,Y3: A] :
% 0.15/0.45 ( ( ( plus_plus @ A @ X3 @ Y3 )
% 0.15/0.45 = ( zero_zero @ A ) )
% 0.15/0.45 = ( ( X3
% 0.15/0.45 = ( zero_zero @ A ) )
% 0.15/0.45 & ( Y3
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_eq_0_iff_both_eq_0
% 0.15/0.45 thf(fact_196_zero__eq__add__iff__both__eq__0,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( canoni770627133id_add @ A )
% 0.15/0.45 => ! [X3: A,Y3: A] :
% 0.15/0.45 ( ( ( zero_zero @ A )
% 0.15/0.45 = ( plus_plus @ A @ X3 @ Y3 ) )
% 0.15/0.45 = ( ( X3
% 0.15/0.45 = ( zero_zero @ A ) )
% 0.15/0.45 & ( Y3
% 0.15/0.45 = ( zero_zero @ A ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % zero_eq_add_iff_both_eq_0
% 0.15/0.45 thf(fact_197_add__less__cancel__left,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [C: A,A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.15/0.45 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_cancel_left
% 0.15/0.45 thf(fact_198_add__less__cancel__right,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [A2: A,C: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.15/0.45 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_cancel_right
% 0.15/0.45 thf(fact_199_add__is__0,axiom,
% 0.15/0.45 ! [M: nat,N: nat] :
% 0.15/0.45 ( ( ( plus_plus @ nat @ M @ N )
% 0.15/0.45 = ( zero_zero @ nat ) )
% 0.15/0.45 = ( ( M
% 0.15/0.45 = ( zero_zero @ nat ) )
% 0.15/0.45 & ( N
% 0.15/0.45 = ( zero_zero @ nat ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_is_0
% 0.15/0.45 thf(fact_200_Nat_Oadd__0__right,axiom,
% 0.15/0.45 ! [M: nat] :
% 0.15/0.45 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 0.15/0.45 = M ) ).
% 0.15/0.45
% 0.15/0.45 % Nat.add_0_right
% 0.15/0.45 thf(fact_201_nat__add__left__cancel__less,axiom,
% 0.15/0.45 ! [K: nat,M: nat,N: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.15/0.45 = ( ord_less @ nat @ M @ N ) ) ).
% 0.15/0.45
% 0.15/0.45 % nat_add_left_cancel_less
% 0.15/0.45 thf(fact_202_nat__add__left__cancel__le,axiom,
% 0.15/0.45 ! [K: nat,M: nat,N: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.15/0.45 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.15/0.45
% 0.15/0.45 % nat_add_left_cancel_le
% 0.15/0.45 thf(fact_203_add__le__same__cancel1,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [B2: A,A2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.15/0.45 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_same_cancel1
% 0.15/0.45 thf(fact_204_add__le__same__cancel2,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.15/0.45 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_same_cancel2
% 0.15/0.45 thf(fact_205_le__add__same__cancel1,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.15/0.45 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_add_same_cancel1
% 0.15/0.45 thf(fact_206_le__add__same__cancel2,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.15/0.45 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_add_same_cancel2
% 0.15/0.45 thf(fact_207_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.15/0.45 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % double_add_le_zero_iff_single_add_le_zero
% 0.15/0.45 thf(fact_208_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.15/0.45 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % zero_le_double_add_iff_zero_le_single_add
% 0.15/0.45 thf(fact_209_add__less__same__cancel1,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [B2: A,A2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.15/0.45 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_same_cancel1
% 0.15/0.45 thf(fact_210_add__less__same__cancel2,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.15/0.45 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_same_cancel2
% 0.15/0.45 thf(fact_211_less__add__same__cancel1,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.15/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % less_add_same_cancel1
% 0.15/0.45 thf(fact_212_less__add__same__cancel2,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere516151231imp_le @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.15/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % less_add_same_cancel2
% 0.15/0.45 thf(fact_213_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.15/0.45 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % double_add_less_zero_iff_single_add_less_zero
% 0.15/0.45 thf(fact_214_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( linord219039673up_add @ A )
% 0.15/0.45 => ! [A2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.15/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % zero_less_double_add_iff_zero_less_single_add
% 0.15/0.45 thf(fact_215_add__gr__0,axiom,
% 0.15/0.45 ! [M: nat,N: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ M @ N ) )
% 0.15/0.45 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.15/0.45 | ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_gr_0
% 0.15/0.45 thf(fact_216_add__leE,axiom,
% 0.15/0.45 ! [M: nat,K: nat,N: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.15/0.45 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.15/0.45 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_leE
% 0.15/0.45 thf(fact_217_le__add1,axiom,
% 0.15/0.45 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_add1
% 0.15/0.45 thf(fact_218_le__add2,axiom,
% 0.15/0.45 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_add2
% 0.15/0.45 thf(fact_219_add__leD1,axiom,
% 0.15/0.45 ! [M: nat,K: nat,N: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.15/0.45 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_leD1
% 0.15/0.45 thf(fact_220_add__leD2,axiom,
% 0.15/0.45 ! [M: nat,K: nat,N: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.15/0.45 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_leD2
% 0.15/0.45 thf(fact_221_le__Suc__ex,axiom,
% 0.15/0.45 ! [K: nat,L: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ K @ L )
% 0.15/0.45 => ? [N2: nat] :
% 0.15/0.45 ( L
% 0.15/0.45 = ( plus_plus @ nat @ K @ N2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_Suc_ex
% 0.15/0.45 thf(fact_222_add__le__mono,axiom,
% 0.15/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.45 => ( ( ord_less_eq @ nat @ K @ L )
% 0.15/0.45 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_mono
% 0.15/0.45 thf(fact_223_add__le__mono1,axiom,
% 0.15/0.45 ! [I: nat,J: nat,K: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.45 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_mono1
% 0.15/0.45 thf(fact_224_trans__le__add1,axiom,
% 0.15/0.45 ! [I: nat,J: nat,M: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.45 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % trans_le_add1
% 0.15/0.45 thf(fact_225_trans__le__add2,axiom,
% 0.15/0.45 ! [I: nat,J: nat,M: nat] :
% 0.15/0.45 ( ( ord_less_eq @ nat @ I @ J )
% 0.15/0.45 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % trans_le_add2
% 0.15/0.45 thf(fact_226_nat__le__iff__add,axiom,
% 0.15/0.45 ( ( ord_less_eq @ nat )
% 0.15/0.45 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.45 ? [K3: nat] :
% 0.15/0.45 ( N3
% 0.15/0.45 = ( plus_plus @ nat @ M3 @ K3 ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % nat_le_iff_add
% 0.15/0.45 thf(fact_227_plus__nat_Oadd__0,axiom,
% 0.15/0.45 ! [N: nat] :
% 0.15/0.45 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 0.15/0.45 = N ) ).
% 0.15/0.45
% 0.15/0.45 % plus_nat.add_0
% 0.15/0.45 thf(fact_228_add__eq__self__zero,axiom,
% 0.15/0.45 ! [M: nat,N: nat] :
% 0.15/0.45 ( ( ( plus_plus @ nat @ M @ N )
% 0.15/0.45 = M )
% 0.15/0.45 => ( N
% 0.15/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_eq_self_zero
% 0.15/0.45 thf(fact_229_add__le__imp__le__right,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [A2: A,C: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.15/0.45 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_imp_le_right
% 0.15/0.45 thf(fact_230_add__le__imp__le__left,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [C: A,A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.15/0.45 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_le_imp_le_left
% 0.15/0.45 thf(fact_231_le__iff__add,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( canoni770627133id_add @ A )
% 0.15/0.45 => ( ( ord_less_eq @ A )
% 0.15/0.45 = ( ^ [A3: A,B3: A] :
% 0.15/0.45 ? [C3: A] :
% 0.15/0.45 ( B3
% 0.15/0.45 = ( plus_plus @ A @ A3 @ C3 ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % le_iff_add
% 0.15/0.45 thf(fact_232_add__right__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_right_mono
% 0.15/0.45 thf(fact_233_less__eqE,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( canoni770627133id_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.15/0.45 => ~ ! [C2: A] :
% 0.15/0.45 ( B2
% 0.15/0.45 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % less_eqE
% 0.15/0.45 thf(fact_234_add__left__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_left_mono
% 0.15/0.45 thf(fact_235_add__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A,D2: A] :
% 0.15/0.45 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.15/0.45 => ( ( ord_less_eq @ A @ C @ D2 )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono
% 0.15/0.45 thf(fact_236_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( ord_less_eq @ A @ I @ J )
% 0.15/0.45 & ( ord_less_eq @ A @ K @ L ) )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_semiring(1)
% 0.15/0.45 thf(fact_237_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( I = J )
% 0.15/0.45 & ( ord_less_eq @ A @ K @ L ) )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_semiring(2)
% 0.15/0.45 thf(fact_238_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere779506340up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( ord_less_eq @ A @ I @ J )
% 0.15/0.45 & ( K = L ) )
% 0.15/0.45 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_semiring(3)
% 0.15/0.45 thf(fact_239_add__less__imp__less__right,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [A2: A,C: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.15/0.45 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_imp_less_right
% 0.15/0.45 thf(fact_240_add__less__imp__less__left,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere236663937imp_le @ A )
% 0.15/0.45 => ! [C: A,A2: A,B2: A] :
% 0.15/0.45 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.15/0.45 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_imp_less_left
% 0.15/0.45 thf(fact_241_add__strict__right__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere223160158up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A] :
% 0.15/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_strict_right_mono
% 0.15/0.45 thf(fact_242_add__strict__left__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere223160158up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A] :
% 0.15/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_strict_left_mono
% 0.15/0.45 thf(fact_243_add__strict__mono,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( strict2144017051up_add @ A )
% 0.15/0.45 => ! [A2: A,B2: A,C: A,D2: A] :
% 0.15/0.45 ( ( ord_less @ A @ A2 @ B2 )
% 0.15/0.45 => ( ( ord_less @ A @ C @ D2 )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_strict_mono
% 0.15/0.45 thf(fact_244_add__mono__thms__linordered__field_I1_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere223160158up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( ord_less @ A @ I @ J )
% 0.15/0.45 & ( K = L ) )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_field(1)
% 0.15/0.45 thf(fact_245_add__mono__thms__linordered__field_I2_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere223160158up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( I = J )
% 0.15/0.45 & ( ord_less @ A @ K @ L ) )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_field(2)
% 0.15/0.45 thf(fact_246_add__mono__thms__linordered__field_I5_J,axiom,
% 0.15/0.45 ! [A: $tType] :
% 0.15/0.45 ( ( ordere223160158up_add @ A )
% 0.15/0.45 => ! [I: A,J: A,K: A,L: A] :
% 0.15/0.45 ( ( ( ord_less @ A @ I @ J )
% 0.15/0.45 & ( ord_less @ A @ K @ L ) )
% 0.15/0.45 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_mono_thms_linordered_field(5)
% 0.15/0.45 thf(fact_247_less__add__eq__less,axiom,
% 0.15/0.45 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ K @ L )
% 0.15/0.45 => ( ( ( plus_plus @ nat @ M @ L )
% 0.15/0.45 = ( plus_plus @ nat @ K @ N ) )
% 0.15/0.45 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % less_add_eq_less
% 0.15/0.45 thf(fact_248_trans__less__add2,axiom,
% 0.15/0.45 ! [I: nat,J: nat,M: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ I @ J )
% 0.15/0.45 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % trans_less_add2
% 0.15/0.45 thf(fact_249_trans__less__add1,axiom,
% 0.15/0.45 ! [I: nat,J: nat,M: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ I @ J )
% 0.15/0.45 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % trans_less_add1
% 0.15/0.45 thf(fact_250_add__less__mono1,axiom,
% 0.15/0.45 ! [I: nat,J: nat,K: nat] :
% 0.15/0.45 ( ( ord_less @ nat @ I @ J )
% 0.15/0.45 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.15/0.45
% 0.15/0.45 % add_less_mono1
% 0.15/0.45 thf(fact_251_not__add__less2,axiom,
% 0.15/0.45 ! [J: nat,I: nat] :
% 0.15/0.45 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.15/0.45
% 0.15/0.45 % not_add_less2
% 0.15/0.45 thf(fact_252_not__add__less1,axiom,
% 0.15/0.45 ! [I: nat,J: nat] :
% 0.15/0.45 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.15/0.45
% 0.15/0.45 % not_add_less1
% 0.15/0.45
% 0.15/0.45 % Type constructors (24)
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.15/0.45 ordere516151231imp_le @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.15/0.45 strict2144017051up_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.15/0.45 ordere223160158up_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.15/0.45 ordere236663937imp_le @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.15/0.45 canoni770627133id_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.15/0.45 ordere779506340up_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.15/0.45 cancel1352612707id_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.15/0.45 cancel_semigroup_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.15/0.45 wellorder @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.15/0.45 monoid_add @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.15/0.45 zero @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.15/0.45 one @ nat ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_1,axiom,
% 0.15/0.45 ordere516151231imp_le @ real ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_2,axiom,
% 0.15/0.45 strict2144017051up_add @ real ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_3,axiom,
% 0.15/0.45 ordere223160158up_add @ real ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_4,axiom,
% 0.15/0.45 ordere236663937imp_le @ real ).
% 0.15/0.45
% 0.15/0.45 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_5,axiom,
% 0.24/0.45 ordere779506340up_add @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.24/0.45 linord219039673up_add @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_6,axiom,
% 0.24/0.45 cancel1352612707id_add @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_7,axiom,
% 0.24/0.45 cancel_semigroup_add @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Omonoid__add_8,axiom,
% 0.24/0.45 monoid_add @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Ozero_9,axiom,
% 0.24/0.45 zero @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Real_Oreal___Groups_Oone_10,axiom,
% 0.24/0.45 one @ real ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_11,axiom,
% 0.24/0.45 wellorder @ product_unit ).
% 0.24/0.45
% 0.24/0.45 % Conjectures (2)
% 0.24/0.45 thf(conj_0,hypothesis,
% 0.24/0.45 ! [V8: view_ext @ product_unit] :
% 0.24/0.45 ( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ V8 @ ( move @ ts3 @ ts @ v ) )
% 0.24/0.45 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V8 ) ) )
% 0.24/0.45 & ( ( len @ regular_regular @ V8 @ ts @ c )
% 0.24/0.45 = ( ext @ product_unit @ V8 ) )
% 0.24/0.45 & ( ( restrict @ V8 @ ( res @ ts ) @ c )
% 0.24/0.45 = ( lan @ product_unit @ V8 ) )
% 0.24/0.45 & ( ( nat_card @ ( lan @ product_unit @ V8 ) )
% 0.24/0.45 = ( one_one @ nat ) )
% 0.24/0.45 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V8 ) ) )
% 0.24/0.45 & ( ( len @ regular_regular @ V8 @ ts @ e )
% 0.24/0.45 = ( ext @ product_unit @ V8 ) )
% 0.24/0.45 & ( ( restrict @ V8 @ ( res @ ts ) @ e )
% 0.24/0.45 = ( lan @ product_unit @ V8 ) )
% 0.24/0.45 & ( ( nat_card @ ( lan @ product_unit @ V8 ) )
% 0.24/0.45 = ( one_one @ nat ) ) )
% 0.24/0.45 => thesis ) ).
% 0.24/0.45
% 0.24/0.45 thf(conj_1,conjecture,
% 0.24/0.45 thesis ).
% 0.24/0.45
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 ------------------------
% 2.67/1.43 ---- Embedded in THF ---
% 2.67/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.67/1.43 %%% Generated on Tue Feb 24 08:28:39 EST 2026
% 2.67/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.67/1.43 %%% Logic specification used:
% 2.67/1.43 %%% thf(spec, logic, $$dhol).
% 2.67/1.43
% 2.67/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jc752Tu92v/DTF2DTF28583.p
% 2.67/1.43 thf(ty_t_Views_Oview_Oview__ext, type, view_ext: ($tType > $tType)).
% 2.67/1.43 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.67/1.43 thf(ty_t_RealInt_Oreal__int, type, real_int: $tType).
% 2.67/1.43 thf(ty_t_Traffic_Otraffic, type, traffic: $tType).
% 2.67/1.43 thf(ty_t_NatInt_Onat__int, type, nat_int: $tType).
% 2.67/1.43 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.67/1.43 thf(ty_t_Cars_Ocars, type, cars: $tType).
% 2.67/1.43 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.67/1.43 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 2.67/1.43 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.67/1.43 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.67/1.43 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.67/1.43 thf(sy_c_Length_Osensors_Olen, type, len: ((cars > (traffic > (cars > real))) > ((view_ext @ product_unit) > (traffic > (cars > real_int))))).
% 2.67/1.43 thf(sy_c_Move_Otraffic_Omove, type, move: (traffic > (traffic > ((view_ext @ product_unit) > (view_ext @ product_unit))))).
% 2.67/1.43 thf(sy_c_NatInt_Onat__int_Ocard_H, type, nat_card: (nat_int > nat)).
% 2.67/1.43 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.67/1.43 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.67/1.43 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.67/1.43 thf(sy_c_RealInt_Oreal__int_Olength, type, real_length: (real_int > real)).
% 2.67/1.43 thf(sy_c_Regular__Sensors_Oregular, type, regular_regular: (cars > (traffic > (cars > real)))).
% 2.67/1.43 thf(sy_c_Restriction_Orestriction_Orestrict, type, restrict: ((view_ext @ product_unit) > ((cars > nat_int) > (cars > nat_int)))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Oabstract, type, abstract: (traffic > (traffic > $o))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Oclm, type, clm: (traffic > (cars > nat_int))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Ocreate__claim, type, create_claim: (traffic > (cars > (nat > (traffic > $o))))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Ocreate__reservation, type, create_reservation: (traffic > (cars > (traffic > $o)))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Ores, type, res: (traffic > (cars > nat_int))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Owithdraw__claim, type, withdraw_claim: (traffic > (cars > (traffic > $o)))).
% 2.67/1.43 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation, type, withdraw_reservation: (traffic > (cars > (nat > (traffic > $o))))).
% 2.67/1.43 thf(sy_c_Views_Oview_Oext, type, ext: (!> [Z:$tType]: (((view_ext @ Z) > real_int)))).
% 2.67/1.43 thf(sy_c_Views_Oview_Ohchop, type, hchop: ((view_ext @ product_unit) > ((view_ext @ product_unit) > ((view_ext @ product_unit) > $o)))).
% 2.67/1.43 thf(sy_c_Views_Oview_Olan, type, lan: (!> [Z:$tType]: (((view_ext @ Z) > nat_int)))).
% 2.67/1.43 thf(sy_c_Views_Oview_Oown, type, own: (!> [Z:$tType]: (((view_ext @ Z) > cars)))).
% 2.67/1.43 thf(sy_c_Views_Oview_Ovchop, type, vchop: ((view_ext @ product_unit) > ((view_ext @ product_unit) > ((view_ext @ product_unit) > $o)))).
% 2.67/1.43 thf(sy_v_c____, type, c: cars).
% 2.67/1.43 thf(sy_v_d____, type, d: cars).
% 2.67/1.43 thf(sy_v_e____, type, e: cars).
% 2.67/1.43 thf(sy_v_thesis____, type, thesis: $o).
% 2.67/1.43 thf(sy_v_ts_H_H____, type, ts: traffic).
% 2.67/1.43 thf(sy_v_ts_H____, type, ts2: traffic).
% 2.67/1.43 thf(sy_v_ts_Ha____, type, ts_a: traffic).
% 2.67/1.43 thf(sy_v_ts____, type, ts3: traffic).
% 2.67/1.43 thf(sy_v_v____, type, v: (view_ext @ product_unit)).
% 2.67/1.43 thf(fact_0_neg, axiom, (c != e)).
% 2.67/1.43 thf(fact_1_local_Ohmlsl_Osensors__ge, axiom, (! [E:cars,Ts:traffic,C:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (((regular_regular @ E) @ Ts) @ C))))).
% 2.67/1.43 thf(fact_2_local_Ohmlsl_Olength__geq__zero, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((real_length @ ((ext @ product_unit) @ V)) = (zero_zero @ real)) | (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_3_hmlsl_Olen__empty__subview, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars,V3:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C)) = (zero_zero @ real)) & (((ord_less_eq @ (view_ext @ product_unit)) @ V3) @ V2)) => ((real_length @ ((((len @ regular_regular) @ V3) @ Ts) @ C)) = (zero_zero @ real)))))).
% 2.67/1.43 thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062, axiom, (? [V4:(view_ext @ product_unit)]: (((((ord_less_eq @ (view_ext @ product_unit)) @ V4) @ (((move @ ts3) @ ts) @ v)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V4))) & ((((((len @ regular_regular) @ V4) @ ts) @ c) = ((ext @ product_unit) @ V4)) & (((((restrict @ V4) @ (res @ ts)) @ c) = ((lan @ product_unit) @ V4)) & (((nat_card @ ((lan @ product_unit) @ V4)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V4))) & ((((((len @ regular_regular) @ V4) @ ts) @ e) = ((ext @ product_unit) @ V4)) & (((((restrict @ V4) @ (res @ ts)) @ e) = ((lan @ product_unit) @ V4)) & ((nat_card @ ((lan @ product_unit) @ V4)) = (one_one @ nat))))))))))))).
% 2.67/1.43 thf(fact_5_local_Ohmlsl_Ores__ge__zero, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_6_local_Ohmlsl_Owidth__res, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))).
% 2.67/1.43 thf(fact_7_abs, axiom, ((abstract @ ts3) @ ts2)).
% 2.67/1.43 thf(fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062, axiom, ((((move @ ts3) @ ts_a) @ v) = (((move @ ts_a) @ ts) @ (((move @ ts3) @ ts_a) @ v)))).
% 2.67/1.43 thf(fact_9_move__stab, axiom, ((((move @ ts3) @ ts_a) @ v) = (((move @ ts3) @ ts) @ v))).
% 2.67/1.43 thf(fact_10_local_Ohmlsl_Ores__compose, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat)))))))))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_11_local_Ohmlsl_Ores__decompose, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va2))) & ((((((len @ regular_regular) @ Va2) @ Ts2) @ C) = ((ext @ product_unit) @ Va2)) & (((((restrict @ Va2) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Va2)) & (((nat_card @ ((lan @ product_unit) @ Va2)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))) & ((((((len @ regular_regular) @ U2) @ Ts2) @ C) = ((ext @ product_unit) @ U2)) & (((((restrict @ U2) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U2)) & ((nat_card @ ((lan @ product_unit) @ U2)) = (one_one @ nat)))))))))))))))).
% 2.67/1.43 thf(fact_12_local_Ohmlsl_Ores__dense, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W))) & ((((((len @ regular_regular) @ W) @ Ts2) @ C) = ((ext @ product_unit) @ W)) & (((((restrict @ W) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ W)) & (((nat_card @ ((lan @ product_unit) @ W)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U3))) & ((((((len @ regular_regular) @ U3) @ Ts2) @ C) = ((ext @ product_unit) @ U3)) & (((((restrict @ U3) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U3)) & ((nat_card @ ((lan @ product_unit) @ U3)) = (one_one @ nat)))))))))))))))).
% 2.67/1.43 thf(fact_13_local_Ohmlsl_Ocar__one__lane__non__empty, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: (((? [X:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))) => (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V)))))))).
% 2.67/1.43 thf(fact_14_local_Ohmlsl_Oempty__no__car, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((real_length @ ((ext @ product_unit) @ V)) = (zero_zero @ real)) => (~ ((? [X:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))))))).
% 2.67/1.43 thf(fact_15_local_Ohmlsl_Otwo__lanes__no__car, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((nat_card @ ((lan @ product_unit) @ V)) != (one_one @ nat)) => (~ ((? [X:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))))))).
% 2.67/1.43 thf(fact_16_local_Ohmlsl_Ores__at__most__two, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((~ ((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & (? [Vb:(view_ext @ product_unit),Ua:(view_ext @ product_unit)]: (((((vchop @ U) @ Vb) @ Ua) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Vb))) & ((((((len @ regular_regular) @ Vb) @ Ts2) @ C) = ((ext @ product_unit) @ Vb)) & (((((restrict @ Vb) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Vb)) & (((nat_card @ ((lan @ product_unit) @ Vb)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Ua))) & ((((((len @ regular_regular) @ Ua) @ Ts2) @ C) = ((ext @ product_unit) @ Ua)) & (((((restrict @ Ua) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Ua)) & ((nat_card @ ((lan @ product_unit) @ Ua)) = (one_one @ nat)))))))))))))))))))))))).
% 2.67/1.43 thf(fact_17_local_Ohmlsl_Otwo__res__not__res, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat)))))))))))) => (~ (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))))))))).
% 2.67/1.43 thf(fact_18_local_Ohmlsl_Oclm__ge__zero, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_19_local_Ohmlsl_Ohchop__weaken2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((Phi @ Ts2) @ U2)))))))).
% 2.67/1.43 thf(fact_20_local_Ohmlsl_Ohchop__weaken1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V) => (? [Va2:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va2) @ X_1))) & ((Phi @ Ts2) @ Va2)))))))).
% 2.67/1.43 thf(fact_21_local_Ohmlsl_Ohchop__weaken, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & (? [Vb2:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ U2) @ Vb2) @ X_1))) & ((Phi @ Ts2) @ Vb2))))))))))).
% 2.67/1.43 thf(fact_22_local_Ohmlsl_Ohchop__neg2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((~ ((? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((Phi @ Ts2) @ U2)))))) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & (~ (((Phi @ Ts2) @ U2)))))))))).
% 2.67/1.43 thf(fact_23_local_Ohmlsl_Ohchop__neg1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((~ ((? [Va2:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va2) @ X_1))) & ((Phi @ Ts2) @ Va2)))))) => (? [Va2:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va2) @ X_1))) & (~ (((Phi @ Ts2) @ Va2)))))))))).
% 2.67/1.43 thf(fact_24_local_Ohmlsl_Ohchop__disj__distr2, axiom, (! [Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((((Psi @ Ts2) @ W) | ((Chi @ Ts2) @ W)) & ((Phi @ Ts2) @ U3))))) = ((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Psi @ Ts2) @ W) & ((Phi @ Ts2) @ U3))))) | (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Chi @ Ts2) @ W) & ((Phi @ Ts2) @ U3)))))))))).
% 2.67/1.43 thf(fact_25_local_Ohmlsl_Ohchop__disj__distr1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & (((Psi @ Ts2) @ U3) | ((Chi @ Ts2) @ U3)))))) = ((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & ((Psi @ Ts2) @ U3))))) | (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & ((Chi @ Ts2) @ U3)))))))))).
% 2.67/1.43 thf(fact_26_local_Ohmlsl_Ohchop__assoc, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & (? [X2:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ U3) @ X2) @ Y) & (((Psi @ Ts2) @ X2) & ((Chi @ Ts2) @ Y))))))))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((? [X2:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ W) @ X2) @ Y) & (((Phi @ Ts2) @ X2) & ((Psi @ Ts2) @ Y))))) & ((Chi @ Ts2) @ U3))))))))).
% 2.67/1.43 thf(fact_27_local_Ohmlsl_Ovchop__disj__distr2, axiom, (! [Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & ((((Psi @ Ts2) @ W) | ((Chi @ Ts2) @ W)) & ((Phi @ Ts2) @ U3))))) = ((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Psi @ Ts2) @ W) & ((Phi @ Ts2) @ U3))))) | (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Chi @ Ts2) @ W) & ((Phi @ Ts2) @ U3)))))))))).
% 2.67/1.43 thf(fact_28_local_Ohmlsl_Ovchop__disj__distr1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & (((Psi @ Ts2) @ U3) | ((Chi @ Ts2) @ U3)))))) = ((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & ((Psi @ Ts2) @ U3))))) | (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & ((Chi @ Ts2) @ U3)))))))))).
% 2.67/1.43 thf(fact_29_local_Ohmlsl_Ov__chop__weaken2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((vchop @ V) @ Va2) @ U2) & ((Phi @ Ts2) @ U2)))))))).
% 2.67/1.43 thf(fact_30_local_Ohmlsl_Ov__chop__weaken1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V) => (? [Va2:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((vchop @ V) @ Va2) @ X_1))) & ((Phi @ Ts2) @ Va2)))))))).
% 2.67/1.43 thf(fact_31_local_Ohmlsl_Ov__chop__assoc, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((Phi @ Ts2) @ W) & (? [X2:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((vchop @ U3) @ X2) @ Y) & (((Psi @ Ts2) @ X2) & ((Chi @ Ts2) @ Y))))))))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & ((? [X2:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((vchop @ W) @ X2) @ Y) & (((Phi @ Ts2) @ X2) & ((Psi @ Ts2) @ Y))))) & ((Chi @ Ts2) @ U3))))))))).
% 2.67/1.43 thf(fact_32_local_Ohmlsl_Oglobally__refl, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((! [Ts3:traffic]: ((((abstract @ Ts2) @ Ts3) => ((Phi @ Ts3) @ (((move @ Ts2) @ Ts3) @ V))))) => ((Phi @ Ts2) @ V))))).
% 2.67/1.43 thf(fact_33_local_Ohmlsl_Oglobally__all__iff_H, axiom, (! [A:$tType,B:$tType,Ts:traffic,Phi:(traffic > ((view_ext @ product_unit) > $o)),V2:(view_ext @ product_unit)]: (((! [Ts4:traffic]: ((((abstract @ Ts) @ Ts4) => (! [X2:A]: (((Phi @ Ts4) @ (((move @ Ts) @ Ts4) @ V2))))))) = (! [X2:B,Ts4:traffic]: ((((abstract @ Ts) @ Ts4) => ((Phi @ Ts4) @ (((move @ Ts) @ Ts4) @ V2))))))))).
% 2.67/1.43 thf(fact_34_local_Ohmlsl_Oglobally__all__iff, axiom, (! [A:$tType,B:$tType,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((! [Ts4:traffic]: ((((abstract @ Ts2) @ Ts4) => (! [X2:A]: (((Phi @ Ts4) @ (((move @ Ts2) @ Ts4) @ V))))))) = (! [X2:B,Ts4:traffic]: ((((abstract @ Ts2) @ Ts4) => ((Phi @ Ts4) @ (((move @ Ts2) @ Ts4) @ V))))))))).
% 2.67/1.43 thf(fact_35_local_Ohmlsl_Oglobally__4, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V:(view_ext @ product_unit)]: (((! [Ts3:traffic]: ((((abstract @ Ts2) @ Ts3) => ((Phi @ Ts3) @ (((move @ Ts2) @ Ts3) @ V))))) => (! [Ts5:traffic]: ((((abstract @ Ts2) @ Ts5) => (! [Ts_a:traffic]: ((((abstract @ Ts5) @ Ts_a) => ((Phi @ Ts_a) @ (((move @ Ts5) @ Ts_a) @ (((move @ Ts2) @ Ts5) @ V))))))))))))).
% 2.67/1.43 thf(fact_36_wd__clm_Ohyps_I1_J, axiom, ((abstract @ ts3) @ ts_a)).
% 2.67/1.43 thf(fact_37_local_Ohmlsl_Owidth__hchop__stable, axiom, (! [X3:nat,Ts2:traffic,V:(view_ext @ product_unit)]: ((((nat_card @ ((lan @ product_unit) @ V)) = X3) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & (((nat_card @ ((lan @ product_unit) @ W)) = X3) & ((nat_card @ ((lan @ product_unit) @ U3)) = X3))))))))).
% 2.67/1.43 thf(fact_38_local_Ohmlsl_Olength__vchop__stable, axiom, (! [X3:real,Ts2:traffic,V:(view_ext @ product_unit)]: ((((real_length @ ((ext @ product_unit) @ V)) = X3) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((vchop @ V) @ W) @ U3) & (((real_length @ ((ext @ product_unit) @ W)) = X3) & ((real_length @ ((ext @ product_unit) @ U3)) = X3))))))))).
% 2.67/1.43 thf(fact_39_hmlsl_Olen__stable__up, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),Ts:traffic,C:cars]: (((((vchop @ V2) @ V1) @ V22) => (((((len @ regular_regular) @ V2) @ Ts) @ C) = ((((len @ regular_regular) @ V22) @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_40_hmlsl_Olen__stable__down, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),Ts:traffic,C:cars]: (((((vchop @ V2) @ V1) @ V22) => (((((len @ regular_regular) @ V2) @ Ts) @ C) = ((((len @ regular_regular) @ V1) @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_41_hmlsl_Olen__stable, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),Ts:traffic,C:cars]: (((((vchop @ V2) @ V1) @ V22) => (((((len @ regular_regular) @ V1) @ Ts) @ C) = ((((len @ regular_regular) @ V22) @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_42_hmlsl_Olen__view__hchop__right, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars,V1:(view_ext @ product_unit),V22:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((hchop @ V2) @ V1) @ V22)) => (((((len @ regular_regular) @ V22) @ Ts) @ C) = ((ext @ product_unit) @ V22)))))).
% 2.67/1.43 thf(fact_43_hmlsl_Olen__view__hchop__left, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars,V1:(view_ext @ product_unit),V22:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((hchop @ V2) @ V1) @ V22)) => (((((len @ regular_regular) @ V1) @ Ts) @ C) = ((ext @ product_unit) @ V1)))))).
% 2.67/1.43 thf(fact_44_hmlsl_Olen__compose__hchop, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((((hchop @ V2) @ V1) @ V22) & ((((((len @ regular_regular) @ V1) @ Ts) @ C) = ((ext @ product_unit) @ V1)) & (((((len @ regular_regular) @ V22) @ Ts) @ C) = ((ext @ product_unit) @ V22)))) => (((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)))))).
% 2.67/1.43 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.67/1.43 thf(fact_46_wd__clm_Ohyps_I2_J, axiom, (? [C2:cars]: ((((withdraw_claim @ ts_a) @ C2) @ ts)))).
% 2.67/1.43 thf(fact_47_local_Ohmlsl_Olength__split, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va2))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))))))))))).
% 2.67/1.43 thf(fact_48_local_Ohmlsl_Olength__meld, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))))))) => (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_49_local_Ohmlsl_Olength__dense, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U3))))))))))).
% 2.67/1.43 thf(fact_50_hmlsl_Olen__empty__on__subview2, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars,V1:(view_ext @ product_unit),V22:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C)) = (zero_zero @ real)) & (((hchop @ V2) @ V1) @ V22)) => ((real_length @ ((((len @ regular_regular) @ V22) @ Ts) @ C)) = (zero_zero @ real)))))).
% 2.67/1.43 thf(fact_51_hmlsl_Olen__empty__on__subview1, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars,V1:(view_ext @ product_unit),V22:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C)) = (zero_zero @ real)) & (((hchop @ V2) @ V1) @ V22)) => ((real_length @ ((((len @ regular_regular) @ V1) @ Ts) @ C)) = (zero_zero @ real)))))).
% 2.67/1.43 thf(fact_52_hmlsl_Olen__fills__subview, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C))) => (? [V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),V32:(view_ext @ product_unit),V4:(view_ext @ product_unit)]: (((((hchop @ V2) @ V12) @ V23) & ((((hchop @ V23) @ V4) @ V32) & ((((((len @ regular_regular) @ V4) @ Ts) @ C) = ((ext @ product_unit) @ V4)) & ((real_length @ ((((len @ regular_regular) @ V4) @ Ts) @ C)) = (real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C)))))))))))).
% 2.67/1.43 thf(fact_53_d__def, axiom, (((withdraw_claim @ ts_a) @ d) @ ts)).
% 2.67/1.43 thf(fact_54_local_Ohmlsl_Owidth__clm, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))).
% 2.67/1.43 thf(fact_55_local_Ohmlsl_Oclm__dense, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W))) & ((((((len @ regular_regular) @ W) @ Ts2) @ C) = ((ext @ product_unit) @ W)) & (((((restrict @ W) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ W)) & (((nat_card @ ((lan @ product_unit) @ W)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U3))) & ((((((len @ regular_regular) @ U3) @ Ts2) @ C) = ((ext @ product_unit) @ U3)) & (((((restrict @ U3) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ U3)) & ((nat_card @ ((lan @ product_unit) @ U3)) = (one_one @ nat)))))))))))))))).
% 2.67/1.43 thf(fact_56_local_Ohmlsl_Oclm__decompose, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va2))) & ((((((len @ regular_regular) @ Va2) @ Ts2) @ C) = ((ext @ product_unit) @ Va2)) & (((((restrict @ Va2) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va2)) & (((nat_card @ ((lan @ product_unit) @ Va2)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))) & ((((((len @ regular_regular) @ U2) @ Ts2) @ C) = ((ext @ product_unit) @ U2)) & (((((restrict @ U2) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ U2)) & ((nat_card @ ((lan @ product_unit) @ U2)) = (one_one @ nat)))))))))))))))).
% 2.67/1.43 thf(fact_57_local_Ohmlsl_Oclm__compose, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat)))))))))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_58_local_Ohmlsl_Oclm__sing__not__interrupted, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((~ ((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & (? [Vb:(view_ext @ product_unit),Ua:(view_ext @ product_unit)]: (((((vchop @ U) @ Vb) @ Ua) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Ua))) & ((((((len @ regular_regular) @ Ua) @ Ts2) @ C) = ((ext @ product_unit) @ Ua)) & (((((restrict @ Ua) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Ua)) & ((nat_card @ ((lan @ product_unit) @ Ua)) = (one_one @ nat)))))))))))))))))))).
% 2.67/1.43 thf(fact_59_local_Ohmlsl_Oclm__sing, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((~ ((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat))))))))))))))))).
% 2.67/1.43 thf(fact_60_local_Ohmlsl_Ono__clm__before__res2, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((~ ((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & (? [Vb:(view_ext @ product_unit),Ua:(view_ext @ product_unit)]: (((((hchop @ U) @ Vb) @ Ua) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Ua))) & ((((((len @ regular_regular) @ Ua) @ Ts2) @ C) = ((ext @ product_unit) @ Ua)) & (((((restrict @ Ua) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Ua)) & ((nat_card @ ((lan @ product_unit) @ Ua)) = (one_one @ nat)))))))))))))))))))).
% 2.67/1.43 thf(fact_61_local_Ohmlsl_Ono__clm__before__res, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: ((~ ((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat))))))))))))))))).
% 2.67/1.43 thf(fact_62_local_Ohmlsl_Otwo__res__no__car, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & ((((((len @ regular_regular) @ Va) @ Ts2) @ C) = ((ext @ product_unit) @ Va)) & (((((restrict @ Va) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ Va)) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & ((((((len @ regular_regular) @ U) @ Ts2) @ C) = ((ext @ product_unit) @ U)) & (((((restrict @ U) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ U)) & ((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat)))))))))))) => (~ ((? [X:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))))))).
% 2.67/1.43 thf(fact_63__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [D:cars]: ((~ ((((withdraw_claim @ ts_a) @ D) @ ts)))))))).
% 2.67/1.43 thf(fact_64_local_Ohmlsl_Ofree__dense, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C3:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C3)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C3) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C3) = (bot_bot @ nat_int)))))))) = (? [W:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W))) & (((nat_card @ ((lan @ product_unit) @ W)) = (one_one @ nat)) & ((! [C3:cars]: ((((real_length @ ((((len @ regular_regular) @ W) @ Ts2) @ C3)) = (zero_zero @ real)) | (((((restrict @ W) @ (clm @ Ts2)) @ C3) = (bot_bot @ nat_int)) & ((((restrict @ W) @ (res @ Ts2)) @ C3) = (bot_bot @ nat_int)))))) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U3))) & (((nat_card @ ((lan @ product_unit) @ U3)) = (one_one @ nat)) & (! [C3:cars]: ((((real_length @ ((((len @ regular_regular) @ U3) @ Ts2) @ C3)) = (zero_zero @ real)) | (((((restrict @ U3) @ (clm @ Ts2)) @ C3) = (bot_bot @ nat_int)) & ((((restrict @ U3) @ (res @ Ts2)) @ C3) = (bot_bot @ nat_int)))))))))))))))))).
% 2.67/1.43 thf(fact_65_local_Ohmlsl_Ofree__decompose, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va2))) & (((nat_card @ ((lan @ product_unit) @ Va2)) = (one_one @ nat)) & ((! [C4:cars]: ((((real_length @ ((((len @ regular_regular) @ Va2) @ Ts2) @ C4)) = (zero_zero @ real)) | (((((restrict @ Va2) @ (clm @ Ts2)) @ C4) = (bot_bot @ nat_int)) & ((((restrict @ Va2) @ (res @ Ts2)) @ C4) = (bot_bot @ nat_int)))))) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))) & (((nat_card @ ((lan @ product_unit) @ U2)) = (one_one @ nat)) & (! [C4:cars]: ((((real_length @ ((((len @ regular_regular) @ U2) @ Ts2) @ C4)) = (zero_zero @ real)) | (((((restrict @ U2) @ (clm @ Ts2)) @ C4) = (bot_bot @ nat_int)) & ((((restrict @ U2) @ (res @ Ts2)) @ C4) = (bot_bot @ nat_int)))))))))))))))))).
% 2.67/1.43 thf(fact_66_local_Ohmlsl_Ofree__compose, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & (((nat_card @ ((lan @ product_unit) @ Va)) = (one_one @ nat)) & ((! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ Va) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ Va) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ Va) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))) & (((nat_card @ ((lan @ product_unit) @ U)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ U) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ U) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ U) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))))))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C4:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C4)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C4) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C4) = (bot_bot @ nat_int)))))))))))).
% 2.67/1.43 thf(fact_67_local_Ohmlsl_Owidth__free, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))) => ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))).
% 2.67/1.43 thf(fact_68_local_Ohmlsl_Ores__not__free, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((? [X4:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X4) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X4) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (~ (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))))))))))).
% 2.67/1.43 thf(fact_69_local_Ohmlsl_Ofree__no__res, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))) => (~ ((? [X:cars]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))))))))))).
% 2.67/1.43 thf(fact_70_local_Ohmlsl_Ofree__no__clm, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))) => (~ ((? [X:cars]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))))))))))).
% 2.67/1.43 thf(fact_71_local_Ohmlsl_Ofree__ge__zero, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))) => (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_72_local_Ohmlsl_Oclm__not__free, axiom, (! [Ts2:traffic,V:(view_ext @ product_unit)]: ((? [X4:cars]: ((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ X4) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ X4) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) => (~ (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & (((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)) & (! [C2:cars]: ((((real_length @ ((((len @ regular_regular) @ V) @ Ts2) @ C2)) = (zero_zero @ real)) | (((((restrict @ V) @ (clm @ Ts2)) @ C2) = (bot_bot @ nat_int)) & ((((restrict @ V) @ (res @ Ts2)) @ C2) = (bot_bot @ nat_int)))))))))))))))).
% 2.67/1.43 thf(fact_73_hmlsl__regular_Obackwards__wdc__res__stab, axiom, (! [Ts:traffic,D2:cars,Ts6:traffic,V2:(view_ext @ product_unit),C:cars]: ((((((withdraw_claim @ Ts) @ D2) @ Ts6) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts6) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts6)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat)))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_74_view_Ohorizontal__chop__non__empty, axiom, (! [V2:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) => (? [U2:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V2) @ U2) @ W2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W2))))))))))).
% 2.67/1.43 thf(fact_75_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_76_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_77_hmlsl__regular_Obackwards__c__res__stab, axiom, (! [Ts:traffic,D2:cars,N:nat,Ts6:traffic,V2:(view_ext @ product_unit),C:cars]: (((((((create_claim @ Ts) @ D2) @ N) @ Ts6) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts6) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts6)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat)))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_78_hmlsl__regular_Obackwards__wdr__res__stab, axiom, (! [Ts:traffic,D2:cars,N:nat,Ts6:traffic,V2:(view_ext @ product_unit),C:cars]: (((((((withdraw_reservation @ Ts) @ D2) @ N) @ Ts6) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts6) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts6)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat)))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_79_hmlsl_Olen__sub__int, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((ord_less_eq @ real_int) @ ((((len @ regular_regular) @ V2) @ Ts) @ C)) @ ((ext @ product_unit) @ V2))))).
% 2.67/1.43 thf(fact_80_view_Overtical__chop__width__mon, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit),X3:nat]: ((((((vchop @ V2) @ V1) @ V22) & ((((vchop @ V22) @ V33) @ V42) & ((nat_card @ ((lan @ product_unit) @ V33)) = X3))) => (((ord_less_eq @ nat) @ X3) @ (nat_card @ ((lan @ product_unit) @ V2))))))).
% 2.67/1.43 thf(fact_81_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X3:A]: ((((zero_zero @ A) = X3) = (X3 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_82_view_Overtical__chop__singleton, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: ((((((vchop @ V2) @ U4) @ W3) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))) => (((nat_card @ ((lan @ product_unit) @ U4)) = (zero_zero @ nat)) | ((nat_card @ ((lan @ product_unit) @ W3)) = (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_83_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X3:A]: ((((one_one @ A) = X3) = (X3 = (one_one @ A))))))))).
% 2.67/1.43 thf(fact_84_view_Ohorizontal__chop1, axiom, (! [V2:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit),X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ U2) @ X_1)))))).
% 2.67/1.43 thf(fact_85_view_Ohorizontal__chop__assoc1, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((hchop @ V2) @ V1) @ V22) & (((hchop @ V22) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((hchop @ V2) @ V4) @ V42) & (((hchop @ V4) @ V1) @ V33)))))))).
% 2.67/1.43 thf(fact_86_view_Ohorizontal__chop__assoc2, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((hchop @ V2) @ V1) @ V22) & (((hchop @ V1) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((hchop @ V2) @ V33) @ V4) & (((hchop @ V4) @ V42) @ V22)))))))).
% 2.67/1.43 thf(fact_87_view_Ohorizontal__chop__empty__left, axiom, (! [V:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit)]: ((((hchop @ V) @ U2) @ V)))))).
% 2.67/1.43 thf(fact_88_view_Ohorizontal__chop__empty__right, axiom, (! [V:(view_ext @ product_unit)]: ((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ V) @ X_1)))))).
% 2.67/1.43 thf(fact_89_view_Overtical__chop1, axiom, (! [V:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit),X_1:(view_ext @ product_unit)]: ((((vchop @ V) @ U2) @ X_1)))))).
% 2.67/1.43 thf(fact_90_view_Overtical__chop__assoc1, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((vchop @ V2) @ V1) @ V22) & (((vchop @ V22) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((vchop @ V2) @ V4) @ V42) & (((vchop @ V4) @ V1) @ V33)))))))).
% 2.67/1.43 thf(fact_91_view_Overtical__chop__assoc2, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((vchop @ V2) @ V1) @ V22) & (((vchop @ V1) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((vchop @ V2) @ V33) @ V4) & (((vchop @ V4) @ V42) @ V22)))))))).
% 2.67/1.43 thf(fact_92_view_Overtical__chop__empty__up, axiom, (! [V:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit)]: ((((vchop @ V) @ U2) @ V)))))).
% 2.67/1.43 thf(fact_93_view_Overtical__chop__empty__down, axiom, (! [V:(view_ext @ product_unit)]: ((? [X_1:(view_ext @ product_unit)]: ((((vchop @ V) @ V) @ X_1)))))).
% 2.67/1.43 thf(fact_94_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3))))))).
% 2.67/1.43 thf(fact_95_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_96_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_97_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.67/1.43 thf(fact_98_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.67/1.43 thf(fact_99_view_Ohorizontal__chop__leq2, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V2) @ U4) @ W3) => (((ord_less_eq @ (view_ext @ product_unit)) @ W3) @ V2))))).
% 2.67/1.43 thf(fact_100_view_Ohorizontal__chop__leq1, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V2) @ U4) @ W3) => (((ord_less_eq @ (view_ext @ product_unit)) @ U4) @ V2))))).
% 2.67/1.43 thf(fact_101_view_Overtical__chop__leq2, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ (view_ext @ product_unit)) @ W3) @ V2))))).
% 2.67/1.43 thf(fact_102_view_Overtical__chop__leq1, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ (view_ext @ product_unit)) @ U4) @ V2))))).
% 2.67/1.43 thf(fact_103_view_Ohorizontal__chop__width__stable, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V2) @ U4) @ W3) => (((nat_card @ ((lan @ product_unit) @ V2)) = (nat_card @ ((lan @ product_unit) @ U4))) & ((nat_card @ ((lan @ product_unit) @ V2)) = (nat_card @ ((lan @ product_unit) @ W3)))))))).
% 2.67/1.43 thf(fact_104_view_Overtical__chop__length__stable, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((vchop @ V2) @ U4) @ W3) => (((real_length @ ((ext @ product_unit) @ V2)) = (real_length @ ((ext @ product_unit) @ U4))) & ((real_length @ ((ext @ product_unit) @ V2)) = (real_length @ ((ext @ product_unit) @ W3)))))))).
% 2.67/1.43 thf(fact_105_view_Osomewhere__leq, axiom, ((ord_less_eq @ (view_ext @ product_unit)) = (^ [V5:(view_ext @ product_unit),V6:(view_ext @ product_unit)]: ((? [V13:(view_ext @ product_unit),V24:(view_ext @ product_unit),V34:(view_ext @ product_unit),Vl:(view_ext @ product_unit),Vr:(view_ext @ product_unit),Vu:(view_ext @ product_unit),Vd:(view_ext @ product_unit)]: (((((hchop @ V6) @ Vl) @ V13) & ((((hchop @ V13) @ V24) @ Vr) & ((((vchop @ V24) @ Vd) @ V34) & (((vchop @ V34) @ V5) @ Vu)))))))))).
% 2.67/1.43 thf(fact_106_hmlsl_Oview__leq__len__leq, axiom, (! [V2:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((((ord_less_eq @ real_int) @ ((ext @ product_unit) @ V2)) @ ((ext @ product_unit) @ V3)) & ((((own @ product_unit) @ V2) = ((own @ product_unit) @ V3)) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ V2) @ Ts) @ C))))) => (((ord_less_eq @ real_int) @ ((((len @ regular_regular) @ V2) @ Ts) @ C)) @ ((((len @ regular_regular) @ V3) @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_107_restriction_Orestriction__card__somewhere__mon, axiom, (! [V2:(view_ext @ product_unit),Vl2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),Vr2:(view_ext @ product_unit),Vu2:(view_ext @ product_unit),V33:(view_ext @ product_unit),V3:(view_ext @ product_unit),Vd2:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: ((((((hchop @ V2) @ Vl2) @ V1) & ((((hchop @ V1) @ V22) @ Vr2) & ((((vchop @ V22) @ Vu2) @ V33) & ((((vchop @ V33) @ V3) @ Vd2) & ((nat_card @ (((restrict @ V3) @ F) @ C)) = (one_one @ nat)))))) => (((ord_less_eq @ nat) @ (one_one @ nat)) @ (nat_card @ (((restrict @ V2) @ F) @ C))))))).
% 2.67/1.43 thf(fact_108_hmlsl__regular_Obackwards__res__act, axiom, (! [Ts:traffic,C:cars,Ts6:traffic,V2:(view_ext @ product_unit)]: ((((((create_reservation @ Ts) @ C) @ Ts6) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts6) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts6)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat)))))) => (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (clm @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat)))))))))).
% 2.67/1.43 thf(fact_109_hmlsl__regular_Oreservation2, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((! [Ts3:traffic]: (((((create_reservation @ Ts2) @ C) @ Ts3) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts3) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts3)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))) => (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))).
% 2.67/1.43 thf(fact_110_hmlsl__regular_Oreservation1, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))) => (! [Ts5:traffic]: (((((create_reservation @ Ts2) @ C) @ Ts5) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts5) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts5)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))))).
% 2.67/1.43 thf(fact_111_hmlsl__regular_Oreservation, axiom, (! [C:cars,Ts2:traffic,V:(view_ext @ product_unit)]: (((! [Ts4:traffic]: (((((create_reservation @ Ts2) @ C) @ Ts4) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts4) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts4)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))) = (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (res @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat))))) | ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) & ((((((len @ regular_regular) @ V) @ Ts2) @ C) = ((ext @ product_unit) @ V)) & (((((restrict @ V) @ (clm @ Ts2)) @ C) = ((lan @ product_unit) @ V)) & ((nat_card @ ((lan @ product_unit) @ V)) = (one_one @ nat)))))))))).
% 2.67/1.43 thf(fact_112_hmlsl_Oext__eq__len__eq, axiom, (! [V2:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((((ext @ product_unit) @ V2) = ((ext @ product_unit) @ V3)) & (((own @ product_unit) @ V2) = ((own @ product_unit) @ V3))) => (((((len @ regular_regular) @ V2) @ Ts) @ C) = ((((len @ regular_regular) @ V3) @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_113_view_Ohorizontal__chop__own__trans, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V2) @ U4) @ W3) => (((own @ product_unit) @ U4) = ((own @ product_unit) @ W3)))))).
% 2.67/1.43 thf(fact_114_view_Overtical__chop__own__trans, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((vchop @ V2) @ U4) @ W3) => (((own @ product_unit) @ U4) = ((own @ product_unit) @ W3)))))).
% 2.67/1.43 thf(fact_115_restriction_Orestrict__subseteq, axiom, (! [V2:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: ((((ord_less_eq @ nat_int) @ (((restrict @ V2) @ F) @ C)) @ (F @ C))))).
% 2.67/1.43 thf(fact_116_restriction_Orestrict__view, axiom, (! [V2:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: ((((ord_less_eq @ nat_int) @ (((restrict @ V2) @ F) @ C)) @ ((lan @ product_unit) @ V2))))).
% 2.67/1.43 thf(fact_117_restriction_Orestrict__res, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((ord_less_eq @ nat_int) @ (((restrict @ V2) @ (res @ Ts)) @ C)) @ ((res @ Ts) @ C))))).
% 2.67/1.43 thf(fact_118_restriction_Orestriction__stable, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((hchop @ V2) @ U4) @ W3) => ((((restrict @ U4) @ F) @ C) = (((restrict @ W3) @ F) @ C)))))).
% 2.67/1.43 thf(fact_119_restriction_Orestriction__stable1, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((hchop @ V2) @ U4) @ W3) => ((((restrict @ V2) @ F) @ C) = (((restrict @ U4) @ F) @ C)))))).
% 2.67/1.43 thf(fact_120_restriction_Orestriction__stable2, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((hchop @ V2) @ U4) @ W3) => ((((restrict @ V2) @ F) @ C) = (((restrict @ W3) @ F) @ C)))))).
% 2.67/1.43 thf(fact_121_restriction_Orestrict__clm, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((ord_less_eq @ nat_int) @ (((restrict @ V2) @ (clm @ Ts)) @ C)) @ ((clm @ Ts) @ C))))).
% 2.67/1.43 thf(fact_122_restriction_Orestriction__mon2, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ nat_int) @ (((restrict @ W3) @ F) @ C)) @ (((restrict @ V2) @ F) @ C)))))).
% 2.67/1.43 thf(fact_123_restriction_Orestriction__mon1, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ nat_int) @ (((restrict @ U4) @ F) @ C)) @ (((restrict @ V2) @ F) @ C)))))).
% 2.67/1.43 thf(fact_124_restriction_Orestriction__eq__view__card, axiom, (! [V2:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: ((((((restrict @ V2) @ F) @ C) = ((lan @ product_unit) @ V2)) => ((nat_card @ (((restrict @ V2) @ F) @ C)) = (nat_card @ ((lan @ product_unit) @ V2))))))).
% 2.67/1.43 thf(fact_125_restriction_Orestrict__eq__lan__subs, axiom, (! [V2:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((nat_card @ (((restrict @ V2) @ F) @ C)) = (nat_card @ ((lan @ product_unit) @ V2))) & (((ord_less_eq @ nat_int) @ (((restrict @ V2) @ F) @ C)) @ ((lan @ product_unit) @ V2))) => ((((restrict @ V2) @ F) @ C) = ((lan @ product_unit) @ V2)))))).
% 2.67/1.43 thf(fact_126_restriction_Orestriction__card__mon1, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ nat) @ (nat_card @ (((restrict @ U4) @ F) @ C))) @ (nat_card @ (((restrict @ V2) @ F) @ C))))))).
% 2.67/1.43 thf(fact_127_restriction_Orestriction__card__mon2, axiom, (! [V2:(view_ext @ product_unit),U4:(view_ext @ product_unit),W3:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: (((((vchop @ V2) @ U4) @ W3) => (((ord_less_eq @ nat) @ (nat_card @ (((restrict @ W3) @ F) @ C))) @ (nat_card @ (((restrict @ V2) @ F) @ C))))))).
% 2.67/1.43 thf(fact_128_restriction_Orestriction__clm__leq__one, axiom, (! [V2:(view_ext @ product_unit),Ts:traffic,C:cars]: ((((ord_less_eq @ nat) @ (nat_card @ (((restrict @ V2) @ (clm @ Ts)) @ C))) @ (one_one @ nat))))).
% 2.67/1.43 thf(fact_129_restriction_Orestriction__card__mon__trans, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit),F:(cars > nat_int),C:cars]: ((((((vchop @ V2) @ V1) @ V22) & ((((vchop @ V22) @ V33) @ V42) & ((nat_card @ (((restrict @ V33) @ F) @ C)) = (one_one @ nat)))) => (((ord_less_eq @ nat) @ (one_one @ nat)) @ (nat_card @ (((restrict @ V2) @ F) @ C))))))).
% 2.67/1.43 thf(fact_130_hmlsl__regular_Obackwards__res__stab, axiom, (! [Ts:traffic,D2:cars,Ts6:traffic,C:cars,V2:(view_ext @ product_unit)]: ((((((create_reservation @ Ts) @ D2) @ Ts6) & ((D2 != C) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts6) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts6)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))))) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) & ((((((len @ regular_regular) @ V2) @ Ts) @ C) = ((ext @ product_unit) @ V2)) & (((((restrict @ V2) @ (res @ Ts)) @ C) = ((lan @ product_unit) @ V2)) & ((nat_card @ ((lan @ product_unit) @ V2)) = (one_one @ nat))))))))).
% 2.67/1.43 thf(fact_131_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_132_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.67/1.43 thf(fact_133_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.67/1.43 thf(fact_134_card__non__empty__geq__one, axiom, (! [I:nat_int]: (((I != (bot_bot @ nat_int)) = (((ord_less_eq @ nat) @ (one_one @ nat)) @ (nat_card @ I)))))).
% 2.67/1.43 thf(fact_135_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 2.67/1.43 thf(fact_136_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_137_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.67/1.43 thf(fact_138_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V7:(A > nat),X3:A]: (((! [X4:A]: (((~ ((P @ X4))) => (? [Y2:A]: (((((ord_less @ nat) @ (V7 @ Y2)) @ (V7 @ X4)) & (~ ((P @ Y2))))))))) => (P @ X3))))).
% 2.67/1.43 thf(fact_139_linorder__neqE__nat, axiom, (! [X3:nat,Y3:nat]: (((X3 != Y3) => ((~ ((((ord_less @ nat) @ X3) @ Y3))) => (((ord_less @ nat) @ Y3) @ X3)))))).
% 2.67/1.43 thf(fact_140_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.67/1.43 thf(fact_141_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.67/1.43 thf(fact_142_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.67/1.43 thf(fact_143_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.67/1.43 thf(fact_144_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.67/1.43 thf(fact_145_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.67/1.43 thf(fact_146_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.67/1.43 thf(fact_147_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y2:A]: (((((ord_less @ B) @ (F @ Y2)) @ (F @ X4)) => (P @ Y2)))) => (P @ X4)))) => (P @ A2)))))))).
% 2.67/1.43 thf(fact_148_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y2:A]: (((((ord_less @ B) @ (F @ Y2)) @ (F @ X4)) => (P @ Y2)))) => (P @ X4)))) => (P @ A2)))))))).
% 2.67/1.43 thf(fact_149_infinite__descent0__measure, axiom, (! [A:$tType,V7:(A > nat),P:(A > $o),X3:A]: (((! [X4:A]: ((((V7 @ X4) = (zero_zero @ nat)) => (P @ X4)))) => ((! [X4:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V7 @ X4)) => ((~ ((P @ X4))) => (? [Y2:A]: (((((ord_less @ nat) @ (V7 @ Y2)) @ (V7 @ X4)) & (~ ((P @ Y2)))))))))) => (P @ X3)))))).
% 2.67/1.43 thf(fact_150_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_151_infinite__descent0, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2)))))))))) => (P @ N)))))).
% 2.67/1.43 thf(fact_152_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_153_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_154_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_155_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_156_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.67/1.43 thf(fact_157_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (((ord_less @ nat) @ (F @ I2)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 2.67/1.43 thf(fact_158_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.67/1.43 thf(fact_159_Nat_Oex__has__greatest__nat, axiom, (! [P:(nat > $o),K:nat,B2:nat]: (((P @ K) => ((! [Y4:nat]: (((P @ Y4) => (((ord_less_eq @ nat) @ Y4) @ B2)))) => (? [X4:nat]: (((P @ X4) & (! [Y2:nat]: (((P @ Y2) => (((ord_less_eq @ nat) @ Y2) @ X4)))))))))))).
% 2.67/1.43 thf(fact_160_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_161_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less @ nat) @ M3) @ N3) | (M3 = N3)))))).
% 2.67/1.43 thf(fact_162_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_163_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.67/1.43 thf(fact_164_nat__less__le, axiom, ((ord_less @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less_eq @ nat) @ M3) @ N3) & (M3 != N3)))))).
% 2.67/1.43 thf(fact_165_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.67/1.43 thf(fact_166_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_167_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 2.67/1.43 thf(fact_168_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.67/1.43 thf(fact_169_card__subset__less, axiom, (! [I:nat_int,I3:nat_int]: (((((ord_less @ nat_int) @ I) @ I3) => (((ord_less @ nat) @ (nat_card @ I)) @ (nat_card @ I3)))))).
% 2.67/1.43 thf(fact_170_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_171_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_172_ex__least__nat__le, axiom, (! [P:(nat > $o),N:nat]: (((P @ N) => ((~ ((P @ (zero_zero @ nat)))) => (? [K2:nat]: (((((ord_less_eq @ nat) @ K2) @ N) & ((! [I4:nat]: (((((ord_less @ nat) @ I4) @ K2) => (~ ((P @ I4)))))) & (P @ K2)))))))))).
% 2.67/1.43 thf(fact_173_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_174_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.67/1.43 thf(fact_175_card__subset__le, axiom, (! [I:nat_int,I3:nat_int]: (((((ord_less_eq @ nat_int) @ I) @ I3) => (((ord_less_eq @ nat) @ (nat_card @ I)) @ (nat_card @ I3)))))).
% 2.67/1.43 thf(fact_176_card__empty__zero, axiom, ((nat_card @ (bot_bot @ nat_int)) = (zero_zero @ nat))).
% 2.67/1.43 thf(fact_177_local_Ohmlsl_Owidth__ge, axiom, (! [V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit)]: (((? [X_12:(view_ext @ product_unit)]: ((((vchop @ V) @ Va) @ X_12))) & ((nat_card @ ((lan @ product_unit) @ Va)) = (((plus_plus @ nat) @ (zero_zero @ nat)) @ (one_one @ nat)))))) => (((ord_less @ nat) @ (zero_zero @ nat)) @ (nat_card @ ((lan @ product_unit) @ V))))))).
% 2.67/1.43 thf(fact_178_traffic_Ocreate__res__subseteq2, axiom, (! [Ts:traffic,C:cars,Ts6:traffic]: (((((create_reservation @ Ts) @ C) @ Ts6) => (((ord_less_eq @ nat_int) @ ((clm @ Ts) @ C)) @ ((res @ Ts6) @ C)))))).
% 2.67/1.43 thf(fact_179_traffic_OatMostOneClm, axiom, (! [Ts:traffic,C:cars]: ((((ord_less_eq @ nat) @ (nat_card @ ((clm @ Ts) @ C))) @ (one_one @ nat))))).
% 2.67/1.43 thf(fact_180_traffic_OatLeastOneRes, axiom, (! [Ts:traffic,C:cars]: ((((ord_less_eq @ nat) @ (one_one @ nat)) @ (nat_card @ ((res @ Ts) @ C)))))).
% 2.67/1.43 thf(fact_181_local_Ohmlsl_Owidth__add1, axiom, (! [X3:nat,Y3:nat,Ts2:traffic,V:(view_ext @ product_unit)]: (((? [Va:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((vchop @ V) @ Va) @ U) & (((nat_card @ ((lan @ product_unit) @ Va)) = X3) & ((nat_card @ ((lan @ product_unit) @ U)) = Y3))))) => ((nat_card @ ((lan @ product_unit) @ V)) = (((plus_plus @ nat) @ X3) @ Y3)))))).
% 2.67/1.43 thf(fact_182_local_Ohmlsl_Owidth__add2, axiom, (! [X3:nat,Y3:nat,Ts2:traffic,V:(view_ext @ product_unit)]: ((((nat_card @ ((lan @ product_unit) @ V)) = (((plus_plus @ nat) @ X3) @ Y3)) => (? [Va2:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((vchop @ V) @ Va2) @ U2) & (((nat_card @ ((lan @ product_unit) @ Va2)) = X3) & ((nat_card @ ((lan @ product_unit) @ U2)) = Y3))))))))).
% 2.67/1.43 thf(fact_183_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) = (B2 = C)))))))).
% 2.67/1.43 thf(fact_184_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B2 = C)))))))).
% 2.67/1.43 thf(fact_185_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_186_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_187_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.67/1.43 thf(fact_188_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.67/1.43 thf(fact_189_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_190_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_191_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_192_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_193_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_194_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_195_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A,Y3:A]: ((((((plus_plus @ A) @ X3) @ Y3) = (zero_zero @ A)) = ((X3 = (zero_zero @ A)) & (Y3 = (zero_zero @ A)))))))))).
% 2.67/1.43 thf(fact_196_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A,Y3:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X3) @ Y3)) = ((X3 = (zero_zero @ A)) & (Y3 = (zero_zero @ A)))))))))).
% 2.67/1.43 thf(fact_197_add__less__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_198_add__less__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_199_add__is__0, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) & (N = (zero_zero @ nat))))))).
% 2.67/1.43 thf(fact_200_Nat_Oadd__0__right, axiom, (! [M:nat]: (((((plus_plus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.67/1.43 thf(fact_201_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_202_nat__add__left__cancel__le, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_203_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_204_add__le__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_205_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.67/1.43 thf(fact_206_le__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.67/1.43 thf(fact_207_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_208_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.67/1.43 thf(fact_209_add__less__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_210_add__less__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_211_less__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.67/1.43 thf(fact_212_less__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.67/1.43 thf(fact_213_double__add__less__zero__iff__single__add__less__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.67/1.43 thf(fact_214_zero__less__double__add__iff__zero__less__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.67/1.43 thf(fact_215_add__gr__0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((plus_plus @ nat) @ M) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) | (((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))).
% 2.67/1.43 thf(fact_216_add__leE, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (~ (((((ord_less_eq @ nat) @ M) @ N) => (~ ((((ord_less_eq @ nat) @ K) @ N)))))))))).
% 2.67/1.43 thf(fact_217_le__add1, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ N) @ M))))).
% 2.67/1.43 thf(fact_218_le__add2, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_219_add__leD1, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.43 thf(fact_220_add__leD2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ K) @ N))))).
% 2.67/1.43 thf(fact_221_le__Suc__ex, axiom, (! [K:nat,L:nat]: (((((ord_less_eq @ nat) @ K) @ L) => (? [N2:nat]: ((L = (((plus_plus @ nat) @ K) @ N2)))))))).
% 2.67/1.43 thf(fact_222_add__le__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.67/1.43 thf(fact_223_add__le__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.67/1.43 thf(fact_224_trans__le__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.67/1.43 thf(fact_225_trans__le__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.67/1.43 thf(fact_226_nat__le__iff__add, axiom, ((ord_less_eq @ nat) = (^ [M3:nat,N3:nat]: ((? [K3:nat]: ((N3 = (((plus_plus @ nat) @ M3) @ K3)))))))).
% 2.67/1.43 thf(fact_227_plus__nat_Oadd__0, axiom, (! [N:nat]: (((((plus_plus @ nat) @ (zero_zero @ nat)) @ N) = N)))).
% 2.67/1.43 thf(fact_228_add__eq__self__zero, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = M) => (N = (zero_zero @ nat)))))).
% 2.67/1.43 thf(fact_229_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_230_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_231_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: ((? [C3:A]: ((B3 = (((plus_plus @ A) @ A3) @ C3))))))))))).
% 2.67/1.43 thf(fact_232_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.67/1.43 thf(fact_233_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C2:A]: ((B2 != (((plus_plus @ A) @ A2) @ C2))))))))))))).
% 2.67/1.43 thf(fact_234_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 2.67/1.43 thf(fact_235_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A,D2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D2)))))))))).
% 2.67/1.43 thf(fact_236_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.43 thf(fact_237_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.43 thf(fact_238_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.43 thf(fact_239_add__less__imp__less__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_240_add__less__imp__less__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.67/1.43 thf(fact_241_add__strict__right__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.67/1.43 thf(fact_242_add__strict__left__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 2.67/1.43 thf(fact_243_add__strict__mono, axiom, (! [A:$tType]: (((strict2144017051up_add @ A) => (! [A2:A,B2:A,C:A,D2:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ D2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D2)))))))))).
% 2.67/1.43 thf(fact_244_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.43 thf(fact_245_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ 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))))))))).
% 2.67/1.43 thf(fact_246_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ 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))))))))).
% 2.67/1.43 thf(fact_247_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)))))).
% 2.67/1.43 thf(fact_248_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.67/1.43 thf(fact_249_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.67/1.43 thf(fact_250_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)))))).
% 2.67/1.43 thf(fact_251_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.67/1.43 thf(fact_252_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, (ordere516151231imp_le @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (strict2144017051up_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, (ordere223160158up_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, (monoid_add @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.67/1.43 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_1, axiom, (ordere516151231imp_le @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_2, axiom, (strict2144017051up_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_3, axiom, (ordere223160158up_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_4, axiom, (ordere236663937imp_le @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_5, axiom, (ordere779506340up_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_6, axiom, (cancel1352612707id_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_7, axiom, (cancel_semigroup_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Omonoid__add_8, axiom, (monoid_add @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Ozero_9, axiom, (zero @ real)).
% 2.67/1.43 thf(tcon_Real_Oreal___Groups_Oone_10, axiom, (one @ real)).
% 2.67/1.43 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_11, axiom, (wellorder @ product_unit)).
% 2.67/1.43 thf(conj_0, hypothesis, (! [V8:(view_ext @ product_unit)]: ((((((ord_less_eq @ (view_ext @ product_unit)) @ V8) @ (((move @ ts3) @ ts) @ v)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V8))) & ((((((len @ regular_regular) @ V8) @ ts) @ c) = ((ext @ product_unit) @ V8)) & (((((restrict @ V8) @ (res @ ts)) @ c) = ((lan @ product_unit) @ V8)) & (((nat_card @ ((lan @ product_unit) @ V8)) = (one_one @ nat)) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V8))) & ((((((len @ regular_regular) @ V8) @ ts) @ e) = ((ext @ product_unit) @ V8)) & (((((restrict @ V8) @ (res @ ts)) @ e) = ((lan @ product_unit) @ V8)) & ((nat_card @ ((lan @ product_unit) @ V8)) = (one_one @ nat)))))))))) => thesis)))).
% 2.67/1.43 thf(conj_1, conjecture, thesis).
% 2.67/1.43 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jc752Tu92v/DTF2DTF28583.p
% 2.67/1.43 ------------------------
% 2.67/1.48 ---- Cleaned THF ---
% 2.67/1.48 thf(ty_t_Views_Oview_Oview__ext,type,
% 2.67/1.48 view_ext: $tType > $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_Product__Type_Ounit,type,
% 2.67/1.48 product_unit: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_RealInt_Oreal__int,type,
% 2.67/1.48 real_int: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_Traffic_Otraffic,type,
% 2.67/1.48 traffic: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_NatInt_Onat__int,type,
% 2.67/1.48 nat_int: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_Real_Oreal,type,
% 2.67/1.48 real: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_Cars_Ocars,type,
% 2.67/1.48 cars: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(ty_t_Nat_Onat,type,
% 2.67/1.48 nat: $tType ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Oone,type,
% 2.67/1.48 one:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Ozero,type,
% 2.67/1.48 zero:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Omonoid__add,type,
% 2.67/1.48 monoid_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Orderings_Owellorder,type,
% 2.67/1.48 wellorder:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.67/1.48 cancel_semigroup_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.67/1.48 cancel1352612707id_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.67/1.48 linord219039673up_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.67/1.48 ordere779506340up_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.67/1.48 canoni770627133id_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.67/1.48 ordere236663937imp_le:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.67/1.48 ordere223160158up_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.67/1.48 strict2144017051up_add:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.67/1.48 ordere516151231imp_le:
% 2.67/1.48 !>[A: $tType] : $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.67/1.48 one_one:
% 2.67/1.48 !>[A: $tType] : A ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.67/1.48 plus_plus:
% 2.67/1.48 !>[A: $tType] : ( A > A > A ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.67/1.48 zero_zero:
% 2.67/1.48 !>[A: $tType] : A ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Length_Osensors_Olen,type,
% 2.67/1.48 len: ( cars > traffic > cars > real ) > ( view_ext @ product_unit ) > traffic > cars > real_int ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Move_Otraffic_Omove,type,
% 2.67/1.48 move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 2.67/1.48 nat_card: nat_int > nat ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.67/1.48 bot_bot:
% 2.67/1.48 !>[A: $tType] : A ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.67/1.48 ord_less:
% 2.67/1.48 !>[A: $tType] : ( A > A > $o ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.67/1.48 ord_less_eq:
% 2.67/1.48 !>[A: $tType] : ( A > A > $o ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 2.67/1.48 real_length: real_int > real ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Regular__Sensors_Oregular,type,
% 2.67/1.48 regular_regular: cars > traffic > cars > real ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Restriction_Orestriction_Orestrict,type,
% 2.67/1.48 restrict: ( view_ext @ product_unit ) > ( cars > nat_int ) > cars > nat_int ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 2.67/1.48 abstract: traffic > traffic > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 2.67/1.48 clm: traffic > cars > nat_int ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 2.67/1.48 create_claim: traffic > cars > nat > traffic > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 2.67/1.48 create_reservation: traffic > cars > traffic > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Ores,type,
% 2.67/1.48 res: traffic > cars > nat_int ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 2.67/1.48 withdraw_claim: traffic > cars > traffic > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 2.67/1.48 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Views_Oview_Oext,type,
% 2.67/1.48 ext:
% 2.67/1.48 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Views_Oview_Ohchop,type,
% 2.67/1.48 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Views_Oview_Olan,type,
% 2.67/1.48 lan:
% 2.67/1.48 !>[Z: $tType] : ( ( view_ext @ Z ) > nat_int ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Views_Oview_Oown,type,
% 2.67/1.48 own:
% 2.67/1.48 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 2.67/1.48
% 2.67/1.48 thf(sy_c_Views_Oview_Ovchop,type,
% 2.67/1.48 vchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_c____,type,
% 2.67/1.48 c: cars ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_d____,type,
% 2.67/1.48 d: cars ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_e____,type,
% 2.67/1.48 e: cars ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_thesis____,type,
% 2.67/1.48 thesis: $o ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_ts_H_H____,type,
% 2.67/1.48 ts: traffic ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_ts_H____,type,
% 2.67/1.48 ts2: traffic ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_ts_Ha____,type,
% 2.67/1.48 ts_a: traffic ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_ts____,type,
% 2.67/1.48 ts3: traffic ).
% 2.67/1.48
% 2.67/1.48 thf(sy_v_v____,type,
% 2.67/1.48 v: view_ext @ product_unit ).
% 2.67/1.48
% 2.67/1.48 thf(fact_0_neg,axiom,
% 2.67/1.48 c != e ).
% 2.67/1.48
% 2.67/1.48 thf(fact_1_local_Ohmlsl_Osensors__ge,axiom,
% 2.67/1.48 ! [E: cars,Ts: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ E @ Ts @ C ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_2_local_Ohmlsl_Olength__geq__zero,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 | ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_3_hmlsl_Olen__empty__subview,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V3: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V2 ) )
% 2.67/1.48 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,axiom,
% 2.67/1.48 ? [V4: view_ext @ product_unit] :
% 2.67/1.48 ( ( ord_less_eq @ ( view_ext @ product_unit ) @ V4 @ ( move @ ts3 @ ts @ v ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V4 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V4 @ ts @ c )
% 2.67/1.48 = ( ext @ product_unit @ V4 ) )
% 2.67/1.48 & ( ( restrict @ V4 @ ( res @ ts ) @ c )
% 2.67/1.48 = ( lan @ product_unit @ V4 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V4 ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V4 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V4 @ ts @ e )
% 2.67/1.48 = ( ext @ product_unit @ V4 ) )
% 2.67/1.48 & ( ( restrict @ V4 @ ( res @ ts ) @ e )
% 2.67/1.48 = ( lan @ product_unit @ V4 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V4 ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_5_local_Ohmlsl_Ores__ge__zero,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_6_local_Ohmlsl_Owidth__res,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_7_abs,axiom,
% 2.67/1.48 abstract @ ts3 @ ts2 ).
% 2.67/1.48
% 2.67/1.48 thf(fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 2.67/1.48 ( ( move @ ts3 @ ts_a @ v )
% 2.67/1.48 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_9_move__stab,axiom,
% 2.67/1.48 ( ( move @ ts3 @ ts_a @ v )
% 2.67/1.48 = ( move @ ts3 @ ts @ v ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_10_local_Ohmlsl_Ores__compose,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_11_local_Ohmlsl_Ores__decompose,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va2 ) )
% 2.67/1.48 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va2 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U2 ) )
% 2.67/1.48 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U2 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_12_local_Ohmlsl_Ores__dense,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ W ) )
% 2.67/1.48 & ( ( restrict @ W @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ W ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U3 ) )
% 2.67/1.48 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U3 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_13_local_Ohmlsl_Ocar__one__lane__non__empty,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X: cars] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) )
% 2.67/1.48 => ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_14_local_Ohmlsl_Oempty__no__car,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 => ~ ? [X: cars] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_15_local_Ohmlsl_Otwo__lanes__no__car,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 != ( one_one @ nat ) )
% 2.67/1.48 => ~ ? [X: cars] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_16_local_Ohmlsl_Ores__at__most__two,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ U @ Vb @ Ua )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Vb ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Vb @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Vb ) )
% 2.67/1.48 & ( ( restrict @ Vb @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Vb ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Vb ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_17_local_Ohmlsl_Otwo__res__not__res,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_18_local_Ohmlsl_Oclm__ge__zero,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_19_local_Ohmlsl_Ohchop__weaken2,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( Phi @ Ts2 @ V )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_20_local_Ohmlsl_Ohchop__weaken1,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( Phi @ Ts2 @ V )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.67/1.48 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_21_local_Ohmlsl_Ohchop__weaken,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( Phi @ Ts2 @ V )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ? [Vb2: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb2 @ X_1 )
% 2.67/1.48 & ( Phi @ Ts2 @ Vb2 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_22_local_Ohmlsl_Ohchop__neg2,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ~ ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( Phi @ Ts2 @ U2 ) )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_23_local_Ohmlsl_Ohchop__neg1,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ~ ? [Va2: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.67/1.48 & ( Phi @ Ts2 @ Va2 ) )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.67/1.48 & ~ ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_24_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 2.67/1.48 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ( Psi @ Ts2 @ W )
% 2.67/1.48 | ( Chi @ Ts2 @ W ) )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Psi @ Ts2 @ W )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) )
% 2.67/1.48 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Chi @ Ts2 @ W )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_25_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( ( Psi @ Ts2 @ U3 )
% 2.67/1.48 | ( Chi @ Ts2 @ U3 ) ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( Psi @ Ts2 @ U3 ) )
% 2.67/1.48 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_26_local_Ohmlsl_Ohchop__assoc,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ U3 @ X2 @ Y )
% 2.67/1.48 & ( Psi @ Ts2 @ X2 )
% 2.67/1.48 & ( Chi @ Ts2 @ Y ) ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ W @ X2 @ Y )
% 2.67/1.48 & ( Phi @ Ts2 @ X2 )
% 2.67/1.48 & ( Psi @ Ts2 @ Y ) )
% 2.67/1.48 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_27_local_Ohmlsl_Ovchop__disj__distr2,axiom,
% 2.67/1.48 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( ( Psi @ Ts2 @ W )
% 2.67/1.48 | ( Chi @ Ts2 @ W ) )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Psi @ Ts2 @ W )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) )
% 2.67/1.48 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Chi @ Ts2 @ W )
% 2.67/1.48 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_28_local_Ohmlsl_Ovchop__disj__distr1,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( ( Psi @ Ts2 @ U3 )
% 2.67/1.48 | ( Chi @ Ts2 @ U3 ) ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( Psi @ Ts2 @ U3 ) )
% 2.67/1.48 | ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_29_local_Ohmlsl_Ov__chop__weaken2,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( Phi @ Ts2 @ V )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_30_local_Ohmlsl_Ov__chop__weaken1,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( Phi @ Ts2 @ V )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit] :
% 2.67/1.48 ( ? [X_1: view_ext @ product_unit] : ( vchop @ V @ Va2 @ X_1 )
% 2.67/1.48 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_31_local_Ohmlsl_Ov__chop__assoc,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( Phi @ Ts2 @ W )
% 2.67/1.48 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ U3 @ X2 @ Y )
% 2.67/1.48 & ( Psi @ Ts2 @ X2 )
% 2.67/1.48 & ( Chi @ Ts2 @ Y ) ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ? [X2: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ W @ X2 @ Y )
% 2.67/1.48 & ( Phi @ Ts2 @ X2 )
% 2.67/1.48 & ( Psi @ Ts2 @ Y ) )
% 2.67/1.48 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_32_local_Ohmlsl_Oglobally__refl,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ! [Ts3: traffic] :
% 2.67/1.48 ( ( abstract @ Ts2 @ Ts3 )
% 2.67/1.48 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 2.67/1.48 => ( Phi @ Ts2 @ V ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_33_local_Ohmlsl_Oglobally__all__iff_H,axiom,
% 2.67/1.48 ! [A: $tType,B: $tType,Ts: traffic,Phi: traffic > ( view_ext @ product_unit ) > $o,V2: view_ext @ product_unit] :
% 2.67/1.48 ( ( ! [Ts4: traffic] :
% 2.67/1.48 ( ( abstract @ Ts @ Ts4 )
% 2.67/1.48 => ! [X2: A] : ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V2 ) ) ) )
% 2.67/1.48 = ( ! [X2: B,Ts4: traffic] :
% 2.67/1.48 ( ( abstract @ Ts @ Ts4 )
% 2.67/1.48 => ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V2 ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_34_local_Ohmlsl_Oglobally__all__iff,axiom,
% 2.67/1.48 ! [A: $tType,B: $tType,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ! [Ts4: traffic] :
% 2.67/1.48 ( ( abstract @ Ts2 @ Ts4 )
% 2.67/1.48 => ! [X2: A] : ( Phi @ Ts4 @ ( move @ Ts2 @ Ts4 @ V ) ) ) )
% 2.67/1.48 = ( ! [X2: B,Ts4: traffic] :
% 2.67/1.48 ( ( abstract @ Ts2 @ Ts4 )
% 2.67/1.48 => ( Phi @ Ts4 @ ( move @ Ts2 @ Ts4 @ V ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_35_local_Ohmlsl_Oglobally__4,axiom,
% 2.67/1.48 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ! [Ts3: traffic] :
% 2.67/1.48 ( ( abstract @ Ts2 @ Ts3 )
% 2.67/1.48 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 2.67/1.48 => ! [Ts5: traffic] :
% 2.67/1.48 ( ( abstract @ Ts2 @ Ts5 )
% 2.67/1.48 => ! [Ts_a: traffic] :
% 2.67/1.48 ( ( abstract @ Ts5 @ Ts_a )
% 2.67/1.48 => ( Phi @ Ts_a @ ( move @ Ts5 @ Ts_a @ ( move @ Ts2 @ Ts5 @ V ) ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_36_wd__clm_Ohyps_I1_J,axiom,
% 2.67/1.48 abstract @ ts3 @ ts_a ).
% 2.67/1.48
% 2.67/1.48 thf(fact_37_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 2.67/1.48 ! [X3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = X3 )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 2.67/1.48 = X3 )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 2.67/1.48 = X3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_38_local_Ohmlsl_Olength__vchop__stable,axiom,
% 2.67/1.48 ! [X3: real,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 2.67/1.48 = X3 )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ W @ U3 )
% 2.67/1.48 & ( ( real_length @ ( ext @ product_unit @ W ) )
% 2.67/1.48 = X3 )
% 2.67/1.48 & ( ( real_length @ ( ext @ product_unit @ U3 ) )
% 2.67/1.48 = X3 ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_39_hmlsl_Olen__stable__up,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.48 ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.48 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.48 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_40_hmlsl_Olen__stable__down,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.48 ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.48 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.48 = ( len @ regular_regular @ V1 @ Ts @ C ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_41_hmlsl_Olen__stable,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.48 ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.48 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.67/1.48 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_42_hmlsl_Olen__view__hchop__right,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V2 ) )
% 2.67/1.48 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.67/1.48 => ( ( len @ regular_regular @ V22 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V22 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_43_hmlsl_Olen__view__hchop__left,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V2 ) )
% 2.67/1.48 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.67/1.48 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V1 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_44_hmlsl_Olen__compose__hchop,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.48 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.67/1.48 & ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V1 ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V22 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V22 ) ) )
% 2.67/1.48 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V2 ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_45_ext,axiom,
% 2.67/1.48 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.67/1.48 ( ! [X4: A] :
% 2.67/1.48 ( ( F @ X4 )
% 2.67/1.48 = ( G @ X4 ) )
% 2.67/1.48 => ( F = G ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_46_wd__clm_Ohyps_I2_J,axiom,
% 2.67/1.48 ? [C2: cars] : ( withdraw_claim @ ts_a @ C2 @ ts ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_47_local_Ohmlsl_Olength__split,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_48_local_Ohmlsl_Olength__meld,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) ) )
% 2.67/1.48 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_49_local_Ohmlsl_Olength__dense,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_50_hmlsl_Olen__empty__on__subview2,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.67/1.48 => ( ( real_length @ ( len @ regular_regular @ V22 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_51_hmlsl_Olen__empty__on__subview1,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars,V1: view_ext @ product_unit,V22: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.67/1.48 => ( ( real_length @ ( len @ regular_regular @ V1 @ Ts @ C ) )
% 2.67/1.48 = ( zero_zero @ real ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_52_hmlsl_Olen__fills__subview,axiom,
% 2.67/1.48 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.48 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) )
% 2.67/1.48 => ? [V12: view_ext @ product_unit,V23: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V2 @ V12 @ V23 )
% 2.67/1.48 & ( hchop @ V23 @ V4 @ V32 )
% 2.67/1.48 & ( ( len @ regular_regular @ V4 @ Ts @ C )
% 2.67/1.48 = ( ext @ product_unit @ V4 ) )
% 2.67/1.48 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C ) )
% 2.67/1.48 = ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_53_d__def,axiom,
% 2.67/1.48 withdraw_claim @ ts_a @ d @ ts ).
% 2.67/1.48
% 2.67/1.48 thf(fact_54_local_Ohmlsl_Owidth__clm,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_55_local_Ohmlsl_Oclm__dense,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ W ) )
% 2.67/1.48 & ( ( restrict @ W @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ W ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U3 ) )
% 2.67/1.48 & ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U3 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_56_local_Ohmlsl_Oclm__decompose,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va2 ) )
% 2.67/1.48 & ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va2 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U2 ) )
% 2.67/1.48 & ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U2 ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_57_local_Ohmlsl_Oclm__compose,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_58_local_Ohmlsl_Oclm__sing__not__interrupted,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ U @ Vb @ Ua )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( restrict @ Ua @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_59_local_Ohmlsl_Oclm__sing,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_60_local_Ohmlsl_Ono__clm__before__res2,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ? [Vb: view_ext @ product_unit,Ua: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ U @ Vb @ Ua )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Ua ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Ua ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Ua ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_61_local_Ohmlsl_Ono__clm__before__res,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ~ ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_62_local_Ohmlsl_Otwo__res__no__car,axiom,
% 2.67/1.48 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.48 ( ( vchop @ V @ Va @ U )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ Va ) )
% 2.67/1.48 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ Va ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.67/1.48 = ( ext @ product_unit @ U ) )
% 2.67/1.48 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.67/1.48 = ( lan @ product_unit @ U ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 => ~ ? [X: cars] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) )
% 2.67/1.48 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.48 = ( ext @ product_unit @ V ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.67/1.48 = ( lan @ product_unit @ V ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_63__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.67/1.48 ~ ! [D: cars] :
% 2.67/1.48 ~ ( withdraw_claim @ ts_a @ D @ ts ) ).
% 2.67/1.48
% 2.67/1.48 thf(fact_64_local_Ohmlsl_Ofree__dense,axiom,
% 2.67/1.48 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.48 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ! [C3: cars] :
% 2.67/1.48 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C3 ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C3 )
% 2.67/1.48 = ( bot_bot @ nat_int ) )
% 2.67/1.48 & ( ( restrict @ V @ ( res @ Ts2 ) @ C3 )
% 2.67/1.48 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.48 = ( ? [W: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.67/1.48 ( ( hchop @ V @ W @ U3 )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ! [C3: cars] :
% 2.67/1.48 ( ( ( real_length @ ( len @ regular_regular @ W @ Ts2 @ C3 ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 | ( ( ( restrict @ W @ ( clm @ Ts2 ) @ C3 )
% 2.67/1.48 = ( bot_bot @ nat_int ) )
% 2.67/1.48 & ( ( restrict @ W @ ( res @ Ts2 ) @ C3 )
% 2.67/1.48 = ( bot_bot @ nat_int ) ) ) )
% 2.67/1.48 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) )
% 2.67/1.48 & ( ( nat_card @ ( lan @ product_unit @ U3 ) )
% 2.67/1.48 = ( one_one @ nat ) )
% 2.67/1.48 & ! [C3: cars] :
% 2.67/1.48 ( ( ( real_length @ ( len @ regular_regular @ U3 @ Ts2 @ C3 ) )
% 2.67/1.48 = ( zero_zero @ real ) )
% 2.67/1.48 | ( ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C3 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C3 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_65_local_Ohmlsl_Ofree__decompose,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C4: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ Va2 @ Ts2 @ C4 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C4: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ U2 @ Ts2 @ C4 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_66_local_Ohmlsl_Ofree__compose,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V @ Va @ U )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ Va @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ Va @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ U @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ U @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C4: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C4 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C4 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_67_local_Ohmlsl_Owidth__free,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_68_local_Ohmlsl_Ores__not__free,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ? [X4: cars] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X4 )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_69_local_Ohmlsl_Ofree__no__res,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ~ ? [X: cars] :
% 2.67/1.49 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_70_local_Ohmlsl_Ofree__no__clm,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ~ ? [X: cars] :
% 2.67/1.49 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_71_local_Ohmlsl_Ofree__ge__zero,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) )
% 2.67/1.49 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_72_local_Ohmlsl_Oclm__not__free,axiom,
% 2.67/1.49 ! [Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ? [X4: cars] :
% 2.67/1.49 ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X4 )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ! [C2: cars] :
% 2.67/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.67/1.49 = ( zero_zero @ real ) )
% 2.67/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.67/1.49 = ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_73_hmlsl__regular_Obackwards__wdc__res__stab,axiom,
% 2.67/1.49 ! [Ts: traffic,D2: cars,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 2.67/1.49 ( ( ( withdraw_claim @ Ts @ D2 @ Ts6 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_74_view_Ohorizontal__chop__non__empty,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit] :
% 2.67/1.49 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 => ? [U2: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ U2 @ W2 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W2 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_75_not__gr__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [N: A] :
% 2.67/1.49 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.67/1.49 = ( N
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_76_le__zero__eq,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [N: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.67/1.49 = ( N
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_77_hmlsl__regular_Obackwards__c__res__stab,axiom,
% 2.67/1.49 ! [Ts: traffic,D2: cars,N: nat,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 2.67/1.49 ( ( ( create_claim @ Ts @ D2 @ N @ Ts6 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_78_hmlsl__regular_Obackwards__wdr__res__stab,axiom,
% 2.67/1.49 ! [Ts: traffic,D2: cars,N: nat,Ts6: traffic,V2: view_ext @ product_unit,C: cars] :
% 2.67/1.49 ( ( ( withdraw_reservation @ Ts @ D2 @ N @ Ts6 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_79_hmlsl_Olen__sub__int,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( ext @ product_unit @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_80_view_Overtical__chop__width__mon,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit,X3: nat] :
% 2.67/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( vchop @ V22 @ V33 @ V42 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V33 ) )
% 2.67/1.49 = X3 ) )
% 2.67/1.49 => ( ord_less_eq @ nat @ X3 @ ( nat_card @ ( lan @ product_unit @ V2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_81_zero__reorient,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( zero @ A )
% 2.67/1.49 => ! [X3: A] :
% 2.67/1.49 ( ( ( zero_zero @ A )
% 2.67/1.49 = X3 )
% 2.67/1.49 = ( X3
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_82_view_Overtical__chop__singleton,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ( nat_card @ ( lan @ product_unit @ U4 ) )
% 2.67/1.49 = ( zero_zero @ nat ) )
% 2.67/1.49 | ( ( nat_card @ ( lan @ product_unit @ W3 ) )
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_83_one__reorient,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( one @ A )
% 2.67/1.49 => ! [X3: A] :
% 2.67/1.49 ( ( ( one_one @ A )
% 2.67/1.49 = X3 )
% 2.67/1.49 = ( X3
% 2.67/1.49 = ( one_one @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_84_view_Ohorizontal__chop1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit] :
% 2.67/1.49 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_85_view_Ohorizontal__chop__assoc1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( hchop @ V22 @ V33 @ V42 ) )
% 2.67/1.49 => ? [V4: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ V4 @ V42 )
% 2.67/1.49 & ( hchop @ V4 @ V1 @ V33 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_86_view_Ohorizontal__chop__assoc2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( hchop @ V1 @ V33 @ V42 ) )
% 2.67/1.49 => ? [V4: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ V33 @ V4 )
% 2.67/1.49 & ( hchop @ V4 @ V42 @ V22 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_87_view_Ohorizontal__chop__empty__left,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ? [U2: view_ext @ product_unit] : ( hchop @ V @ U2 @ V ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_88_view_Ohorizontal__chop__empty__right,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ? [X_1: view_ext @ product_unit] : ( hchop @ V @ V @ X_1 ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_89_view_Overtical__chop1,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( vchop @ V @ U2 @ X_1 ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_90_view_Overtical__chop__assoc1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( vchop @ V22 @ V33 @ V42 ) )
% 2.67/1.49 => ? [V4: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ V4 @ V42 )
% 2.67/1.49 & ( vchop @ V4 @ V1 @ V33 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_91_view_Overtical__chop__assoc2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( vchop @ V1 @ V33 @ V42 ) )
% 2.67/1.49 => ? [V4: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ V33 @ V4 )
% 2.67/1.49 & ( vchop @ V4 @ V42 @ V22 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_92_view_Overtical__chop__empty__up,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ? [U2: view_ext @ product_unit] : ( vchop @ V @ U2 @ V ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_93_view_Overtical__chop__empty__down,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ? [X_1: view_ext @ product_unit] : ( vchop @ V @ V @ X_1 ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_94_zero__le,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_95_zero__less__iff__neq__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [N: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.67/1.49 = ( N
% 2.67/1.49 != ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_96_gr__implies__not__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [M: A,N: A] :
% 2.67/1.49 ( ( ord_less @ A @ M @ N )
% 2.67/1.49 => ( N
% 2.67/1.49 != ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_97_not__less__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [N: A] :
% 2.67/1.49 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_98_gr__zeroI,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [N: A] :
% 2.67/1.49 ( ( N
% 2.67/1.49 != ( zero_zero @ A ) )
% 2.67/1.49 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_99_view_Ohorizontal__chop__leq2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W3 @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_100_view_Ohorizontal__chop__leq1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_101_view_Overtical__chop__leq2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W3 @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_102_view_Overtical__chop__leq1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_103_view_Ohorizontal__chop__width__stable,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( nat_card @ ( lan @ product_unit @ U4 ) ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( nat_card @ ( lan @ product_unit @ W3 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_104_view_Overtical__chop__length__stable,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.67/1.49 = ( real_length @ ( ext @ product_unit @ U4 ) ) )
% 2.67/1.49 & ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.67/1.49 = ( real_length @ ( ext @ product_unit @ W3 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_105_view_Osomewhere__leq,axiom,
% 2.67/1.49 ( ( ord_less_eq @ ( view_ext @ product_unit ) )
% 2.67/1.49 = ( ^ [V5: view_ext @ product_unit,V6: view_ext @ product_unit] :
% 2.67/1.49 ? [V13: view_ext @ product_unit,V24: view_ext @ product_unit,V34: view_ext @ product_unit,Vl: view_ext @ product_unit,Vr: view_ext @ product_unit,Vu: view_ext @ product_unit,Vd: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V6 @ Vl @ V13 )
% 2.67/1.49 & ( hchop @ V13 @ V24 @ Vr )
% 2.67/1.49 & ( vchop @ V24 @ Vd @ V34 )
% 2.67/1.49 & ( vchop @ V34 @ V5 @ Vu ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_106_hmlsl_Oview__leq__len__leq,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.49 ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V2 ) @ ( ext @ product_unit @ V3 ) )
% 2.67/1.49 & ( ( own @ product_unit @ V2 )
% 2.67/1.49 = ( own @ product_unit @ V3 ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) )
% 2.67/1.49 => ( ord_less_eq @ real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_107_restriction_Orestriction__card__somewhere__mon,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,Vl2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,Vr2: view_ext @ product_unit,Vu2: view_ext @ product_unit,V33: view_ext @ product_unit,V3: view_ext @ product_unit,Vd2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( ( hchop @ V2 @ Vl2 @ V1 )
% 2.67/1.49 & ( hchop @ V1 @ V22 @ Vr2 )
% 2.67/1.49 & ( vchop @ V22 @ Vu2 @ V33 )
% 2.67/1.49 & ( vchop @ V33 @ V3 @ Vd2 )
% 2.67/1.49 & ( ( nat_card @ ( restrict @ V3 @ F @ C ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_108_hmlsl__regular_Obackwards__res__act,axiom,
% 2.67/1.49 ! [Ts: traffic,C: cars,Ts6: traffic,V2: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( create_reservation @ Ts @ C @ Ts6 )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( clm @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_109_hmlsl__regular_Oreservation2,axiom,
% 2.67/1.49 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ! [Ts3: traffic] :
% 2.67/1.49 ( ( create_reservation @ Ts2 @ C @ Ts3 )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts3 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts3 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) )
% 2.67/1.49 => ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_110_hmlsl__regular_Oreservation1,axiom,
% 2.67/1.49 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) )
% 2.67/1.49 => ! [Ts5: traffic] :
% 2.67/1.49 ( ( create_reservation @ Ts2 @ C @ Ts5 )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts5 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts5 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_111_hmlsl__regular_Oreservation,axiom,
% 2.67/1.49 ! [C: cars,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ! [Ts4: traffic] :
% 2.67/1.49 ( ( create_reservation @ Ts2 @ C @ Ts4 )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts4 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts4 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) )
% 2.67/1.49 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 | ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V ) )
% 2.67/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_112_hmlsl_Oext__eq__len__eq,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C: cars] :
% 2.67/1.49 ( ( ( ( ext @ product_unit @ V2 )
% 2.67/1.49 = ( ext @ product_unit @ V3 ) )
% 2.67/1.49 & ( ( own @ product_unit @ V2 )
% 2.67/1.49 = ( own @ product_unit @ V3 ) ) )
% 2.67/1.49 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_113_view_Ohorizontal__chop__own__trans,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( own @ product_unit @ U4 )
% 2.67/1.49 = ( own @ product_unit @ W3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_114_view_Overtical__chop__own__trans,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( own @ product_unit @ U4 )
% 2.67/1.49 = ( own @ product_unit @ W3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_115_restriction_Orestrict__subseteq,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( F @ C ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_116_restriction_Orestrict__view,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan @ product_unit @ V2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_117_restriction_Orestrict__res,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ ( res @ Ts ) @ C ) @ ( res @ Ts @ C ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_118_restriction_Orestriction__stable,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( restrict @ U4 @ F @ C )
% 2.67/1.49 = ( restrict @ W3 @ F @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_119_restriction_Orestriction__stable1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.67/1.49 = ( restrict @ U4 @ F @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_120_restriction_Orestriction__stable2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.67/1.49 = ( restrict @ W3 @ F @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_121_restriction_Orestrict__clm,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) @ ( clm @ Ts @ C ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_122_restriction_Orestriction__mon2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ nat_int @ ( restrict @ W3 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_123_restriction_Orestriction__mon1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ nat_int @ ( restrict @ U4 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_124_restriction_Orestriction__eq__view__card,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( ( restrict @ V2 @ F @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 => ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 2.67/1.49 = ( nat_card @ ( lan @ product_unit @ V2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_125_restriction_Orestrict__eq__lan__subs,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 2.67/1.49 = ( nat_card @ ( lan @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ord_less_eq @ nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan @ product_unit @ V2 ) ) )
% 2.67/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_126_restriction_Orestriction__card__mon1,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ U4 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_127_restriction_Orestriction__card__mon2,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,U4: view_ext @ product_unit,W3: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ W3 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_128_restriction_Orestriction__clm__leq__one,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) ) @ ( one_one @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_129_restriction_Orestriction__card__mon__trans,axiom,
% 2.67/1.49 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit,F: cars > nat_int,C: cars] :
% 2.67/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.67/1.49 & ( vchop @ V22 @ V33 @ V42 )
% 2.67/1.49 & ( ( nat_card @ ( restrict @ V33 @ F @ C ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_130_hmlsl__regular_Obackwards__res__stab,axiom,
% 2.67/1.49 ! [Ts: traffic,D2: cars,Ts6: traffic,C: cars,V2: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( create_reservation @ Ts @ D2 @ Ts6 )
% 2.67/1.49 & ( D2 != C )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts6 @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts6 ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.67/1.49 = ( ext @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.67/1.49 = ( lan @ product_unit @ V2 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.67/1.49 = ( one_one @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_131_less__one,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.67/1.49 = ( N
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_132_le0,axiom,
% 2.67/1.49 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_133_bot__nat__0_Oextremum,axiom,
% 2.67/1.49 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_134_card__non__empty__geq__one,axiom,
% 2.67/1.49 ! [I: nat_int] :
% 2.67/1.49 ( ( I
% 2.67/1.49 != ( bot_bot @ nat_int ) )
% 2.67/1.49 = ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ I ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_135_bot__nat__0_Onot__eq__extremum,axiom,
% 2.67/1.49 ! [A2: nat] :
% 2.67/1.49 ( ( A2
% 2.67/1.49 != ( zero_zero @ nat ) )
% 2.67/1.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_136_less__nat__zero__code,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_137_neq0__conv,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( N
% 2.67/1.49 != ( zero_zero @ nat ) )
% 2.67/1.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_138_infinite__descent__measure,axiom,
% 2.67/1.49 ! [A: $tType,P: A > $o,V7: A > nat,X3: A] :
% 2.67/1.49 ( ! [X4: A] :
% 2.67/1.49 ( ~ ( P @ X4 )
% 2.67/1.49 => ? [Y2: A] :
% 2.67/1.49 ( ( ord_less @ nat @ ( V7 @ Y2 ) @ ( V7 @ X4 ) )
% 2.67/1.49 & ~ ( P @ Y2 ) ) )
% 2.67/1.49 => ( P @ X3 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_139_linorder__neqE__nat,axiom,
% 2.67/1.49 ! [X3: nat,Y3: nat] :
% 2.67/1.49 ( ( X3 != Y3 )
% 2.67/1.49 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 2.67/1.49 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_140_infinite__descent,axiom,
% 2.67/1.49 ! [P: nat > $o,N: nat] :
% 2.67/1.49 ( ! [N2: nat] :
% 2.67/1.49 ( ~ ( P @ N2 )
% 2.67/1.49 => ? [M2: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.67/1.49 & ~ ( P @ M2 ) ) )
% 2.67/1.49 => ( P @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_141_nat__less__induct,axiom,
% 2.67/1.49 ! [P: nat > $o,N: nat] :
% 2.67/1.49 ( ! [N2: nat] :
% 2.67/1.49 ( ! [M2: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.67/1.49 => ( P @ M2 ) )
% 2.67/1.49 => ( P @ N2 ) )
% 2.67/1.49 => ( P @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_142_less__irrefl__nat,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ N @ N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_143_less__not__refl3,axiom,
% 2.67/1.49 ! [S: nat,T: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ S @ T )
% 2.67/1.49 => ( S != T ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_144_less__not__refl2,axiom,
% 2.67/1.49 ! [N: nat,M: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ N @ M )
% 2.67/1.49 => ( M != N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_145_less__not__refl,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ N @ N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_146_nat__neq__iff,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( M != N )
% 2.67/1.49 = ( ( ord_less @ nat @ M @ N )
% 2.67/1.49 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_147_measure__induct__rule,axiom,
% 2.67/1.49 ! [B: $tType,A: $tType] :
% 2.67/1.49 ( ( wellorder @ B )
% 2.67/1.49 => ! [F: A > B,P: A > $o,A2: A] :
% 2.67/1.49 ( ! [X4: A] :
% 2.67/1.49 ( ! [Y2: A] :
% 2.67/1.49 ( ( ord_less @ B @ ( F @ Y2 ) @ ( F @ X4 ) )
% 2.67/1.49 => ( P @ Y2 ) )
% 2.67/1.49 => ( P @ X4 ) )
% 2.67/1.49 => ( P @ A2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_148_measure__induct,axiom,
% 2.67/1.49 ! [B: $tType,A: $tType] :
% 2.67/1.49 ( ( wellorder @ B )
% 2.67/1.49 => ! [F: A > B,P: A > $o,A2: A] :
% 2.67/1.49 ( ! [X4: A] :
% 2.67/1.49 ( ! [Y2: A] :
% 2.67/1.49 ( ( ord_less @ B @ ( F @ Y2 ) @ ( F @ X4 ) )
% 2.67/1.49 => ( P @ Y2 ) )
% 2.67/1.49 => ( P @ X4 ) )
% 2.67/1.49 => ( P @ A2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_149_infinite__descent0__measure,axiom,
% 2.67/1.49 ! [A: $tType,V7: A > nat,P: A > $o,X3: A] :
% 2.67/1.49 ( ! [X4: A] :
% 2.67/1.49 ( ( ( V7 @ X4 )
% 2.67/1.49 = ( zero_zero @ nat ) )
% 2.67/1.49 => ( P @ X4 ) )
% 2.67/1.49 => ( ! [X4: A] :
% 2.67/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V7 @ X4 ) )
% 2.67/1.49 => ( ~ ( P @ X4 )
% 2.67/1.49 => ? [Y2: A] :
% 2.67/1.49 ( ( ord_less @ nat @ ( V7 @ Y2 ) @ ( V7 @ X4 ) )
% 2.67/1.49 & ~ ( P @ Y2 ) ) ) )
% 2.67/1.49 => ( P @ X3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_150_bot__nat__0_Oextremum__strict,axiom,
% 2.67/1.49 ! [A2: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_151_infinite__descent0,axiom,
% 2.67/1.49 ! [P: nat > $o,N: nat] :
% 2.67/1.49 ( ( P @ ( zero_zero @ nat ) )
% 2.67/1.49 => ( ! [N2: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.67/1.49 => ( ~ ( P @ N2 )
% 2.67/1.49 => ? [M2: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.67/1.49 & ~ ( P @ M2 ) ) ) )
% 2.67/1.49 => ( P @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_152_gr__implies__not0,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M @ N )
% 2.67/1.49 => ( N
% 2.67/1.49 != ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_153_less__zeroE,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_154_not__less0,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_155_not__gr0,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.67/1.49 = ( N
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_156_gr0I,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( N
% 2.67/1.49 != ( zero_zero @ nat ) )
% 2.67/1.49 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_157_less__mono__imp__le__mono,axiom,
% 2.67/1.49 ! [F: nat > nat,I: nat,J: nat] :
% 2.67/1.49 ( ! [I2: nat,J2: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ I2 @ J2 )
% 2.67/1.49 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 2.67/1.49 => ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_158_le__neq__implies__less,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.49 => ( ( M != N )
% 2.67/1.49 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_159_Nat_Oex__has__greatest__nat,axiom,
% 2.67/1.49 ! [P: nat > $o,K: nat,B2: nat] :
% 2.67/1.49 ( ( P @ K )
% 2.67/1.49 => ( ! [Y4: nat] :
% 2.67/1.49 ( ( P @ Y4 )
% 2.67/1.49 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 2.67/1.49 => ? [X4: nat] :
% 2.67/1.49 ( ( P @ X4 )
% 2.67/1.49 & ! [Y2: nat] :
% 2.67/1.49 ( ( P @ Y2 )
% 2.67/1.49 => ( ord_less_eq @ nat @ Y2 @ X4 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_160_less__or__eq__imp__le,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ( ord_less @ nat @ M @ N )
% 2.67/1.49 | ( M = N ) )
% 2.67/1.49 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_161_le__eq__less__or__eq,axiom,
% 2.67/1.49 ( ( ord_less_eq @ nat )
% 2.67/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M3 @ N3 )
% 2.67/1.49 | ( M3 = N3 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_162_less__imp__le__nat,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ M @ N )
% 2.67/1.49 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_163_nat__le__linear,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.49 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_164_nat__less__le,axiom,
% 2.67/1.49 ( ( ord_less @ nat )
% 2.67/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 2.67/1.49 & ( M3 != N3 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_165_le__antisym,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.49 => ( ( ord_less_eq @ nat @ N @ M )
% 2.67/1.49 => ( M = N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_166_eq__imp__le,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( M = N )
% 2.67/1.49 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_167_le__trans,axiom,
% 2.67/1.49 ! [I: nat,J: nat,K: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ( ord_less_eq @ nat @ J @ K )
% 2.67/1.49 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_168_le__refl,axiom,
% 2.67/1.49 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_169_card__subset__less,axiom,
% 2.67/1.49 ! [I: nat_int,I3: nat_int] :
% 2.67/1.49 ( ( ord_less @ nat_int @ I @ I3 )
% 2.67/1.49 => ( ord_less @ nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_170_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.67/1.49 ! [A2: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.67/1.49 => ( A2
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_171_bot__nat__0_Oextremum__unique,axiom,
% 2.67/1.49 ! [A2: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.67/1.49 = ( A2
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_172_ex__least__nat__le,axiom,
% 2.67/1.49 ! [P: nat > $o,N: nat] :
% 2.67/1.49 ( ( P @ N )
% 2.67/1.49 => ( ~ ( P @ ( zero_zero @ nat ) )
% 2.67/1.49 => ? [K2: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ K2 @ N )
% 2.67/1.49 & ! [I4: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ I4 @ K2 )
% 2.67/1.49 => ~ ( P @ I4 ) )
% 2.67/1.49 & ( P @ K2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_173_le__0__eq,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.67/1.49 = ( N
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_174_less__eq__nat_Osimps_I1_J,axiom,
% 2.67/1.49 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_175_card__subset__le,axiom,
% 2.67/1.49 ! [I: nat_int,I3: nat_int] :
% 2.67/1.49 ( ( ord_less_eq @ nat_int @ I @ I3 )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_176_card__empty__zero,axiom,
% 2.67/1.49 ( ( nat_card @ ( bot_bot @ nat_int ) )
% 2.67/1.49 = ( zero_zero @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_177_local_Ohmlsl_Owidth__ge,axiom,
% 2.67/1.49 ! [V: view_ext @ product_unit] :
% 2.67/1.49 ( ? [Va: view_ext @ product_unit] :
% 2.67/1.49 ( ? [X_12: view_ext @ product_unit] : ( vchop @ V @ Va @ X_12 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.49 = ( plus_plus @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) )
% 2.67/1.49 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat_card @ ( lan @ product_unit @ V ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_178_traffic_Ocreate__res__subseteq2,axiom,
% 2.67/1.49 ! [Ts: traffic,C: cars,Ts6: traffic] :
% 2.67/1.49 ( ( create_reservation @ Ts @ C @ Ts6 )
% 2.67/1.49 => ( ord_less_eq @ nat_int @ ( clm @ Ts @ C ) @ ( res @ Ts6 @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_179_traffic_OatMostOneClm,axiom,
% 2.67/1.49 ! [Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( clm @ Ts @ C ) ) @ ( one_one @ nat ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_180_traffic_OatLeastOneRes,axiom,
% 2.67/1.49 ! [Ts: traffic,C: cars] : ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( res @ Ts @ C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_181_local_Ohmlsl_Owidth__add1,axiom,
% 2.67/1.49 ! [X3: nat,Y3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ? [Va: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V @ Va @ U )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ Va ) )
% 2.67/1.49 = X3 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.67/1.49 = Y3 ) )
% 2.67/1.49 => ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( plus_plus @ nat @ X3 @ Y3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_182_local_Ohmlsl_Owidth__add2,axiom,
% 2.67/1.49 ! [X3: nat,Y3: nat,Ts2: traffic,V: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.67/1.49 = ( plus_plus @ nat @ X3 @ Y3 ) )
% 2.67/1.49 => ? [Va2: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.67/1.49 ( ( vchop @ V @ Va2 @ U2 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ Va2 ) )
% 2.67/1.49 = X3 )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ U2 ) )
% 2.67/1.49 = Y3 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_183_add__left__cancel,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel_semigroup_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.67/1.49 = ( plus_plus @ A @ A2 @ C ) )
% 2.67/1.49 = ( B2 = C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_184_add__right__cancel,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel_semigroup_add @ A )
% 2.67/1.49 => ! [B2: A,A2: A,C: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.67/1.49 = ( plus_plus @ A @ C @ A2 ) )
% 2.67/1.49 = ( B2 = C ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_185_add__le__cancel__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [C: A,A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.67/1.49 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_186_add__le__cancel__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [A2: A,C: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.67/1.49 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_187_add_Oleft__neutral,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( monoid_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.67/1.49 = A2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_188_add_Oright__neutral,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( monoid_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.67/1.49 = A2 ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_189_double__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.67/1.49 = ( zero_zero @ A ) )
% 2.67/1.49 = ( A2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_190_double__zero__sym,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ( zero_zero @ A )
% 2.67/1.49 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.67/1.49 = ( A2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_191_add__cancel__left__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel1352612707id_add @ A )
% 2.67/1.49 => ! [B2: A,A2: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.67/1.49 = A2 )
% 2.67/1.49 = ( B2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_192_add__cancel__left__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel1352612707id_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.67/1.49 = A2 )
% 2.67/1.49 = ( B2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_193_add__cancel__right__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel1352612707id_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( A2
% 2.67/1.49 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.67/1.49 = ( B2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_194_add__cancel__right__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( cancel1352612707id_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( A2
% 2.67/1.49 = ( plus_plus @ A @ A2 @ B2 ) )
% 2.67/1.49 = ( B2
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_195_add__eq__0__iff__both__eq__0,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [X3: A,Y3: A] :
% 2.67/1.49 ( ( ( plus_plus @ A @ X3 @ Y3 )
% 2.67/1.49 = ( zero_zero @ A ) )
% 2.67/1.49 = ( ( X3
% 2.67/1.49 = ( zero_zero @ A ) )
% 2.67/1.49 & ( Y3
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_196_zero__eq__add__iff__both__eq__0,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [X3: A,Y3: A] :
% 2.67/1.49 ( ( ( zero_zero @ A )
% 2.67/1.49 = ( plus_plus @ A @ X3 @ Y3 ) )
% 2.67/1.49 = ( ( X3
% 2.67/1.49 = ( zero_zero @ A ) )
% 2.67/1.49 & ( Y3
% 2.67/1.49 = ( zero_zero @ A ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_197_add__less__cancel__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [C: A,A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.67/1.49 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_198_add__less__cancel__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [A2: A,C: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.67/1.49 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_199_add__is__0,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ( plus_plus @ nat @ M @ N )
% 2.67/1.49 = ( zero_zero @ nat ) )
% 2.67/1.49 = ( ( M
% 2.67/1.49 = ( zero_zero @ nat ) )
% 2.67/1.49 & ( N
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_200_Nat_Oadd__0__right,axiom,
% 2.67/1.49 ! [M: nat] :
% 2.67/1.49 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 2.67/1.49 = M ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_201_nat__add__left__cancel__less,axiom,
% 2.67/1.49 ! [K: nat,M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.67/1.49 = ( ord_less @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_202_nat__add__left__cancel__le,axiom,
% 2.67/1.49 ! [K: nat,M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.67/1.49 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_203_add__le__same__cancel1,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [B2: A,A2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.67/1.49 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_204_add__le__same__cancel2,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.67/1.49 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_205_le__add__same__cancel1,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.67/1.49 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_206_le__add__same__cancel2,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.67/1.49 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_207_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.67/1.49 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_208_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.67/1.49 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_209_add__less__same__cancel1,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [B2: A,A2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.67/1.49 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_210_add__less__same__cancel2,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.67/1.49 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_211_less__add__same__cancel1,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.67/1.49 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_212_less__add__same__cancel2,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere516151231imp_le @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.67/1.49 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_213_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.67/1.49 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_214_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( linord219039673up_add @ A )
% 2.67/1.49 => ! [A2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.67/1.49 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_215_add__gr__0,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ M @ N ) )
% 2.67/1.49 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.67/1.49 | ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_216_add__leE,axiom,
% 2.67/1.49 ! [M: nat,K: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.49 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.49 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_217_le__add1,axiom,
% 2.67/1.49 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_218_le__add2,axiom,
% 2.67/1.49 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_219_add__leD1,axiom,
% 2.67/1.49 ! [M: nat,K: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.49 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_220_add__leD2,axiom,
% 2.67/1.49 ! [M: nat,K: nat,N: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.49 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_221_le__Suc__ex,axiom,
% 2.67/1.49 ! [K: nat,L: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ K @ L )
% 2.67/1.49 => ? [N2: nat] :
% 2.67/1.49 ( L
% 2.67/1.49 = ( plus_plus @ nat @ K @ N2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_222_add__le__mono,axiom,
% 2.67/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ( ord_less_eq @ nat @ K @ L )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_223_add__le__mono1,axiom,
% 2.67/1.49 ! [I: nat,J: nat,K: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_224_trans__le__add1,axiom,
% 2.67/1.49 ! [I: nat,J: nat,M: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_225_trans__le__add2,axiom,
% 2.67/1.49 ! [I: nat,J: nat,M: nat] :
% 2.67/1.49 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.49 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_226_nat__le__iff__add,axiom,
% 2.67/1.49 ( ( ord_less_eq @ nat )
% 2.67/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.67/1.49 ? [K3: nat] :
% 2.67/1.49 ( N3
% 2.67/1.49 = ( plus_plus @ nat @ M3 @ K3 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_227_plus__nat_Oadd__0,axiom,
% 2.67/1.49 ! [N: nat] :
% 2.67/1.49 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 2.67/1.49 = N ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_228_add__eq__self__zero,axiom,
% 2.67/1.49 ! [M: nat,N: nat] :
% 2.67/1.49 ( ( ( plus_plus @ nat @ M @ N )
% 2.67/1.49 = M )
% 2.67/1.49 => ( N
% 2.67/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_229_add__le__imp__le__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [A2: A,C: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.67/1.49 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_230_add__le__imp__le__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [C: A,A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.67/1.49 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_231_le__iff__add,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ( ( ord_less_eq @ A )
% 2.67/1.49 = ( ^ [A3: A,B3: A] :
% 2.67/1.49 ? [C3: A] :
% 2.67/1.49 ( B3
% 2.67/1.49 = ( plus_plus @ A @ A3 @ C3 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_232_add__right__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_233_less__eqE,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( canoni770627133id_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.67/1.49 => ~ ! [C2: A] :
% 2.67/1.49 ( B2
% 2.67/1.49 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_234_add__left__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_235_add__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A,D2: A] :
% 2.67/1.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.67/1.49 => ( ( ord_less_eq @ A @ C @ D2 )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_236_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( ord_less_eq @ A @ I @ J )
% 2.67/1.49 & ( ord_less_eq @ A @ K @ L ) )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_237_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( I = J )
% 2.67/1.49 & ( ord_less_eq @ A @ K @ L ) )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_238_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere779506340up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( ord_less_eq @ A @ I @ J )
% 2.67/1.49 & ( K = L ) )
% 2.67/1.49 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_239_add__less__imp__less__right,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [A2: A,C: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.67/1.49 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_240_add__less__imp__less__left,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere236663937imp_le @ A )
% 2.67/1.49 => ! [C: A,A2: A,B2: A] :
% 2.67/1.49 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.67/1.49 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_241_add__strict__right__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere223160158up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A] :
% 2.67/1.49 ( ( ord_less @ A @ A2 @ B2 )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_242_add__strict__left__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere223160158up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A] :
% 2.67/1.49 ( ( ord_less @ A @ A2 @ B2 )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_243_add__strict__mono,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( strict2144017051up_add @ A )
% 2.67/1.49 => ! [A2: A,B2: A,C: A,D2: A] :
% 2.67/1.49 ( ( ord_less @ A @ A2 @ B2 )
% 2.67/1.49 => ( ( ord_less @ A @ C @ D2 )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_244_add__mono__thms__linordered__field_I1_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere223160158up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( ord_less @ A @ I @ J )
% 2.67/1.49 & ( K = L ) )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_245_add__mono__thms__linordered__field_I2_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere223160158up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( I = J )
% 2.67/1.49 & ( ord_less @ A @ K @ L ) )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_246_add__mono__thms__linordered__field_I5_J,axiom,
% 2.67/1.49 ! [A: $tType] :
% 2.67/1.49 ( ( ordere223160158up_add @ A )
% 2.67/1.49 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.49 ( ( ( ord_less @ A @ I @ J )
% 2.67/1.49 & ( ord_less @ A @ K @ L ) )
% 2.67/1.49 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_247_less__add__eq__less,axiom,
% 2.67/1.49 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ K @ L )
% 2.67/1.49 => ( ( ( plus_plus @ nat @ M @ L )
% 2.67/1.49 = ( plus_plus @ nat @ K @ N ) )
% 2.67/1.49 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_248_trans__less__add2,axiom,
% 2.67/1.49 ! [I: nat,J: nat,M: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ I @ J )
% 2.67/1.49 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_249_trans__less__add1,axiom,
% 2.67/1.49 ! [I: nat,J: nat,M: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ I @ J )
% 2.67/1.49 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_250_add__less__mono1,axiom,
% 2.67/1.49 ! [I: nat,J: nat,K: nat] :
% 2.67/1.49 ( ( ord_less @ nat @ I @ J )
% 2.67/1.49 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_251_not__add__less2,axiom,
% 2.67/1.49 ! [J: nat,I: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.67/1.49
% 2.67/1.49 thf(fact_252_not__add__less1,axiom,
% 2.67/1.49 ! [I: nat,J: nat] :
% 2.67/1.49 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.67/1.49 ordere516151231imp_le @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.67/1.49 strict2144017051up_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.67/1.49 ordere223160158up_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.67/1.49 ordere236663937imp_le @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.67/1.49 canoni770627133id_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.67/1.49 ordere779506340up_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.67/1.49 cancel1352612707id_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.67/1.49 cancel_semigroup_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.67/1.49 wellorder @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.67/1.49 monoid_add @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.67/1.49 zero @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.67/1.49 one @ nat ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_1,axiom,
% 2.67/1.49 ordere516151231imp_le @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_2,axiom,
% 2.67/1.49 strict2144017051up_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_3,axiom,
% 2.67/1.49 ordere223160158up_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_4,axiom,
% 2.67/1.49 ordere236663937imp_le @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_5,axiom,
% 2.67/1.49 ordere779506340up_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 2.67/1.49 linord219039673up_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_6,axiom,
% 2.67/1.49 cancel1352612707id_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_7,axiom,
% 2.67/1.49 cancel_semigroup_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Omonoid__add_8,axiom,
% 2.67/1.49 monoid_add @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Ozero_9,axiom,
% 2.67/1.49 zero @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Real_Oreal___Groups_Oone_10,axiom,
% 2.67/1.49 one @ real ).
% 2.67/1.49
% 2.67/1.49 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_11,axiom,
% 2.67/1.49 wellorder @ product_unit ).
% 2.67/1.49
% 2.67/1.49 thf(conj_0,hypothesis,
% 2.67/1.49 ! [V8: view_ext @ product_unit] :
% 2.67/1.49 ( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ V8 @ ( move @ ts3 @ ts @ v ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V8 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V8 @ ts @ c )
% 2.67/1.49 = ( ext @ product_unit @ V8 ) )
% 2.67/1.49 & ( ( restrict @ V8 @ ( res @ ts ) @ c )
% 2.67/1.49 = ( lan @ product_unit @ V8 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V8 ) )
% 2.67/1.49 = ( one_one @ nat ) )
% 2.67/1.49 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V8 ) ) )
% 2.67/1.49 & ( ( len @ regular_regular @ V8 @ ts @ e )
% 2.67/1.49 = ( ext @ product_unit @ V8 ) )
% 2.67/1.49 & ( ( restrict @ V8 @ ( res @ ts ) @ e )
% 2.67/1.49 = ( lan @ product_unit @ V8 ) )
% 2.67/1.49 & ( ( nat_card @ ( lan @ product_unit @ V8 ) )
% 2.67/1.49 = ( one_one @ nat ) ) )
% 2.67/1.49 => thesis ) ).
% 2.67/1.49
% 2.67/1.49 thf(conj_1,conjecture,
% 2.67/1.49 thesis ).
% 2.67/1.49 ------------------------
% 2.79/1.51 % (28685)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/183Mi)
% 2.79/1.52 % (28690)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_28583 for (2999ds/275Mi)
% 2.79/1.52 % (28688)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/2Mi)
% 2.79/1.52 % (28687)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_28583 for (2999ds/27Mi)
% 2.79/1.52 % (28689)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_28583 for (2999ds/2Mi)
% 2.79/1.52 % (28686)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_28583 for (2999ds/4Mi)
% 2.79/1.52 % (28691)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/18Mi)
% 2.79/1.52 % (28688)Instruction limit reached!
% 2.79/1.52 % (28688)------------------------------
% 2.79/1.52 % (28688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (28688)Termination reason: Unknown
% 2.79/1.52 % (28689)Instruction limit reached!
% 2.79/1.52 % (28689)------------------------------
% 2.79/1.52 % (28689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (28689)Termination reason: Unknown
% 2.79/1.52 % (28689)Termination phase: shuffling
% 2.79/1.52
% 2.79/1.52 % (28689)Memory used [KB]: 1407
% 2.79/1.52 % (28689)Time elapsed: 0.003 s
% 2.79/1.52 % (28689)Instructions burned: 3 (million)
% 2.79/1.52 % (28689)------------------------------
% 2.79/1.52 % (28689)------------------------------
% 2.79/1.52 % (28688)Termination phase: shuffling
% 2.79/1.52
% 2.79/1.52 % (28688)Memory used [KB]: 1407
% 2.79/1.52 % (28688)Time elapsed: 0.003 s
% 2.79/1.52 % (28688)Instructions burned: 3 (million)
% 2.79/1.52 % (28688)------------------------------
% 2.79/1.52 % (28688)------------------------------
% 2.79/1.52 % (28686)Instruction limit reached!
% 2.79/1.52 % (28686)------------------------------
% 2.79/1.52 % (28686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (28686)Termination reason: Unknown
% 2.79/1.52 % (28686)Termination phase: shuffling
% 2.79/1.52
% 2.79/1.52 % (28686)Memory used [KB]: 1407
% 2.79/1.52 % (28686)Time elapsed: 0.004 s
% 2.79/1.52 % (28686)Instructions burned: 5 (million)
% 2.79/1.52 % (28686)------------------------------
% 2.79/1.52 % (28686)------------------------------
% 2.79/1.53 % (28691)Instruction limit reached!
% 2.79/1.53 % (28691)------------------------------
% 2.79/1.53 % (28691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.53 % (28691)Termination reason: Unknown
% 2.79/1.53 % (28691)Termination phase: shuffling
% 2.79/1.53
% 2.79/1.53 % (28691)Memory used [KB]: 1535
% 2.79/1.53 % (28691)Time elapsed: 0.011 s
% 2.79/1.53 % (28691)Instructions burned: 18 (million)
% 2.79/1.53 % (28691)------------------------------
% 2.79/1.53 % (28691)------------------------------
% 2.79/1.53 % (28687)Instruction limit reached!
% 2.79/1.53 % (28687)------------------------------
% 2.79/1.53 % (28687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.53 % (28687)Termination reason: Unknown
% 2.79/1.53 % (28687)Termination phase: shuffling
% 2.79/1.53
% 2.79/1.53 % (28687)Memory used [KB]: 1791
% 2.79/1.53 % (28687)Time elapsed: 0.015 s
% 2.79/1.53 % (28687)Instructions burned: 27 (million)
% 2.79/1.53 % (28687)------------------------------
% 2.79/1.53 % (28687)------------------------------
% 2.79/1.54 % (28693)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_28583 for (2999ds/37Mi)
% 2.79/1.54 % (28692)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/3Mi)
% 2.79/1.54 % (28694)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_28583 for (2999ds/15Mi)
% 2.79/1.54 % (28692)Instruction limit reached!
% 2.79/1.54 % (28692)------------------------------
% 2.79/1.54 % (28692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (28692)Termination reason: Unknown
% 2.79/1.54 % (28692)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (28692)Memory used [KB]: 1407
% 2.79/1.54 % (28692)Time elapsed: 0.003 s
% 2.79/1.54 % (28692)Instructions burned: 3 (million)
% 2.79/1.54 % (28692)------------------------------
% 2.79/1.54 % (28692)------------------------------
% 2.79/1.54 % (28695)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_28583 for (2999ds/3Mi)
% 2.79/1.54 % (28694)Instruction limit reached!
% 2.79/1.54 % (28694)------------------------------
% 2.79/1.54 % (28694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (28694)Termination reason: Unknown
% 2.79/1.54 % (28694)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (28694)Memory used [KB]: 1535
% 2.79/1.54 % (28694)Time elapsed: 0.009 s
% 2.79/1.54 % (28694)Instructions burned: 15 (million)
% 2.79/1.54 % (28694)------------------------------
% 2.79/1.54 % (28694)------------------------------
% 2.79/1.55 % (28695)Instruction limit reached!
% 2.79/1.55 % (28695)------------------------------
% 2.79/1.55 % (28695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.55 % (28695)Termination reason: Unknown
% 2.79/1.55 % (28695)Termination phase: shuffling
% 2.79/1.55
% 2.79/1.55 % (28695)Memory used [KB]: 1407
% 2.79/1.55 % (28695)Time elapsed: 0.003 s
% 2.79/1.55 % (28695)Instructions burned: 3 (million)
% 2.79/1.55 % (28695)------------------------------
% 2.79/1.55 % (28695)------------------------------
% 2.79/1.55 % (28696)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_28583 for (2999ds/1041Mi)
% 2.79/1.55 % (28693)Instruction limit reached!
% 2.79/1.55 % (28693)------------------------------
% 2.79/1.55 % (28693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.55 % (28693)Termination reason: Unknown
% 2.79/1.55 % (28693)Termination phase: shuffling
% 2.79/1.55
% 2.79/1.55 % (28693)Memory used [KB]: 2046
% 2.79/1.55 % (28693)Time elapsed: 0.018 s
% 2.79/1.55 % (28693)Instructions burned: 37 (million)
% 2.79/1.55 % (28693)------------------------------
% 2.79/1.55 % (28693)------------------------------
% 2.79/1.56 % (28697)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/7Mi)
% 2.79/1.56 % (28697)Instruction limit reached!
% 2.79/1.56 % (28697)------------------------------
% 2.79/1.56 % (28697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.56 % (28697)Termination reason: Unknown
% 2.79/1.56 % (28697)Termination phase: shuffling
% 2.79/1.56
% 2.79/1.56 % (28697)Memory used [KB]: 1407
% 2.79/1.56 % (28697)Time elapsed: 0.005 s
% 2.79/1.56 % (28697)Instructions burned: 7 (million)
% 2.79/1.56 % (28697)------------------------------
% 2.79/1.56 % (28697)------------------------------
% 2.79/1.56 % (28698)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/16Mi)
% 2.79/1.56 % (28699)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_28583 for (2999ds/3Mi)
% 2.79/1.56 % (28685)Instruction limit reached!
% 2.79/1.56 % (28685)------------------------------
% 2.79/1.56 % (28685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.56 % (28685)Termination reason: Unknown
% 2.79/1.56 % (28685)Termination phase: Saturation
% 2.79/1.56
% 2.79/1.56 % (28685)Memory used [KB]: 7036
% 2.79/1.56 % (28685)Time elapsed: 0.053 s
% 2.79/1.56 % (28685)Instructions burned: 186 (million)
% 2.79/1.56 % (28685)------------------------------
% 2.79/1.56 % (28685)------------------------------
% 2.79/1.57 % (28699)Instruction limit reached!
% 2.79/1.57 % (28699)------------------------------
% 2.79/1.57 % (28699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (28699)Termination reason: Unknown
% 2.79/1.57 % (28699)Termination phase: shuffling
% 2.79/1.57
% 2.79/1.57 % (28699)Memory used [KB]: 1407
% 2.79/1.57 % (28699)Time elapsed: 0.003 s
% 2.79/1.57 % (28699)Instructions burned: 3 (million)
% 2.79/1.57 % (28699)------------------------------
% 2.79/1.57 % (28699)------------------------------
% 2.79/1.57 % (28698)Instruction limit reached!
% 2.79/1.57 % (28698)------------------------------
% 2.79/1.57 % (28698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (28698)Termination reason: Unknown
% 2.79/1.57 % (28698)Termination phase: shuffling
% 2.79/1.57
% 2.79/1.57 % (28698)Memory used [KB]: 1535
% 2.79/1.57 % (28698)Time elapsed: 0.009 s
% 2.79/1.57 % (28698)Instructions burned: 16 (million)
% 2.79/1.57 % (28698)------------------------------
% 2.79/1.57 % (28698)------------------------------
% 2.79/1.57 % (28700)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/3Mi)
% 2.79/1.57 % (28700)Instruction limit reached!
% 2.79/1.57 % (28700)------------------------------
% 2.79/1.57 % (28700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (28700)Termination reason: Unknown
% 2.79/1.57 % (28700)Termination phase: shuffling
% 2.79/1.57
% 2.79/1.57 % (28700)Memory used [KB]: 1407
% 2.79/1.57 % (28700)Time elapsed: 0.003 s
% 2.79/1.57 % (28700)Instructions burned: 3 (million)
% 2.79/1.57 % (28700)------------------------------
% 2.79/1.57 % (28700)------------------------------
% 2.79/1.57 % (28702)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/3Mi)
% 2.79/1.57 % (28702)Instruction limit reached!
% 2.79/1.57 % (28702)------------------------------
% 2.79/1.57 % (28702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (28702)Termination reason: Unknown
% 2.79/1.57 % (28702)Termination phase: shuffling
% 2.79/1.57
% 2.79/1.57 % (28702)Memory used [KB]: 1407
% 2.79/1.57 % (28702)Time elapsed: 0.002 s
% 2.79/1.57 % (28702)Instructions burned: 3 (million)
% 2.79/1.57 % (28702)------------------------------
% 2.79/1.57 % (28702)------------------------------
% 2.79/1.58 % (28701)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/7Mi)
% 2.79/1.58 % (28701)Instruction limit reached!
% 2.79/1.58 % (28701)------------------------------
% 2.79/1.58 % (28701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.58 % (28701)Termination reason: Unknown
% 2.79/1.58 % (28701)Termination phase: shuffling
% 2.79/1.58
% 2.79/1.58 % (28701)Memory used [KB]: 1407
% 2.79/1.58 % (28701)Time elapsed: 0.005 s
% 2.79/1.58 % (28701)Instructions burned: 7 (million)
% 2.79/1.58 % (28701)------------------------------
% 2.79/1.58 % (28701)------------------------------
% 2.79/1.58 % (28703)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/4Mi)
% 2.79/1.58 % (28704)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/18Mi)
% 2.79/1.58 % (28706)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/6Mi)
% 2.79/1.58 % (28703)Instruction limit reached!
% 2.79/1.58 % (28703)------------------------------
% 2.79/1.58 % (28703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.58 % (28703)Termination reason: Unknown
% 2.79/1.58 % (28703)Termination phase: shuffling
% 2.79/1.58
% 2.79/1.58 % (28703)Memory used [KB]: 1407
% 2.79/1.58 % (28703)Time elapsed: 0.003 s
% 2.79/1.58 % (28703)Instructions burned: 4 (million)
% 2.79/1.58 % (28703)------------------------------
% 2.79/1.58 % (28703)------------------------------
% 2.79/1.59 % (28706)Instruction limit reached!
% 2.79/1.59 % (28706)------------------------------
% 2.79/1.59 % (28706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.59 % (28706)Termination reason: Unknown
% 2.79/1.59 % (28706)Termination phase: shuffling
% 2.79/1.59
% 2.79/1.59 % (28706)Memory used [KB]: 1407
% 2.79/1.59 % (28706)Time elapsed: 0.003 s
% 2.79/1.59 % (28706)Instructions burned: 6 (million)
% 2.79/1.59 % (28706)------------------------------
% 2.79/1.59 % (28706)------------------------------
% 2.79/1.59 % (28705)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/710Mi)
% 2.79/1.59 % (28704)Instruction limit reached!
% 2.79/1.59 % (28704)------------------------------
% 2.79/1.59 % (28704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.59 % (28704)Termination reason: Unknown
% 2.79/1.59 % (28704)Termination phase: shuffling
% 2.79/1.59
% 2.79/1.59 % (28704)Memory used [KB]: 1535
% 2.79/1.59 % (28704)Time elapsed: 0.010 s
% 2.79/1.59 % (28704)Instructions burned: 18 (million)
% 2.79/1.59 % (28704)------------------------------
% 2.79/1.59 % (28704)------------------------------
% 2.79/1.59 % (28707)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/902Mi)
% 2.79/1.60 % (28709)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/5Mi)
% 2.79/1.60 % (28709)Instruction limit reached!
% 2.79/1.60 % (28709)------------------------------
% 2.79/1.60 % (28709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.60 % (28709)Termination reason: Unknown
% 2.79/1.60 % (28709)Termination phase: shuffling
% 2.79/1.60
% 2.79/1.60 % (28709)Memory used [KB]: 1407
% 2.79/1.60 % (28709)Time elapsed: 0.003 s
% 2.79/1.60 % (28709)Instructions burned: 7 (million)
% 2.79/1.60 % (28709)------------------------------
% 2.79/1.60 % (28709)------------------------------
% 2.79/1.60 % (28708)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/21Mi)
% 2.79/1.61 % (28710)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/6Mi)
% 2.79/1.61 % (28710)Instruction limit reached!
% 2.79/1.61 % (28710)------------------------------
% 2.79/1.61 % (28710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.61 % (28710)Termination reason: Unknown
% 2.79/1.61 % (28710)Termination phase: shuffling
% 2.79/1.61
% 2.79/1.61 % (28710)Memory used [KB]: 1407
% 2.79/1.61 % (28710)Time elapsed: 0.003 s
% 2.79/1.61 % (28710)Instructions burned: 7 (million)
% 2.79/1.61 % (28710)------------------------------
% 2.79/1.61 % (28710)------------------------------
% 2.79/1.61 % (28708)Instruction limit reached!
% 2.79/1.61 % (28708)------------------------------
% 2.79/1.61 % (28708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.61 % (28708)Termination reason: Unknown
% 2.79/1.61 % (28708)Termination phase: shuffling
% 2.79/1.61
% 2.79/1.61 % (28708)Memory used [KB]: 1663
% 2.79/1.61 % (28708)Time elapsed: 0.012 s
% 2.79/1.61 % (28708)Instructions burned: 21 (million)
% 2.79/1.61 % (28708)------------------------------
% 2.79/1.61 % (28708)------------------------------
% 2.79/1.61 % (28690)First to succeed.
% 2.79/1.61 % (28711)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28583 for (2999ds/377Mi)
% 2.79/1.62 % (28690)Refutation found. Thanks to Tanya!
% 2.79/1.62 % SZS status Theorem for DTF2THF_28583
% 2.79/1.62 % SZS output start Proof for DTF2THF_28583
% 2.79/1.62 thf(type_def_6, type, cars: $tType).
% 2.79/1.62 thf(type_def_7, type, traffic: $tType).
% 2.79/1.62 thf(type_def_8, type, real: $tType).
% 2.79/1.62 thf(type_def_9, type, product_unit: $tType).
% 2.79/1.62 thf(type_def_10, type, view_ext: ($tType) > $tType).
% 2.79/1.62 thf(type_def_11, type, real_int: $tType).
% 2.79/1.62 thf(type_def_12, type, nat_int: $tType).
% 2.79/1.62 thf(type_def_13, type, nat: $tType).
% 2.79/1.62 thf(func_def_0, type, view_ext: ($tType) > $tType).
% 2.79/1.62 thf(func_def_1, type, product_unit: $tType).
% 2.79/1.62 thf(func_def_2, type, real_int: $tType).
% 2.79/1.62 thf(func_def_3, type, traffic: $tType).
% 2.79/1.62 thf(func_def_4, type, nat_int: $tType).
% 2.79/1.62 thf(func_def_5, type, real: $tType).
% 2.79/1.62 thf(func_def_6, type, cars: $tType).
% 2.79/1.62 thf(func_def_7, type, nat: $tType).
% 2.79/1.62 thf(func_def_8, type, one: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_9, type, zero: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_10, type, monoid_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_12, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_13, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_14, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_15, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_16, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_17, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_18, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_19, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_20, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 2.79/1.62 thf(func_def_21, type, one_one: !>[X0: $tType]:(X0)).
% 2.79/1.62 thf(func_def_22, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.79/1.62 thf(func_def_23, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.79/1.62 thf(func_def_24, type, len: (cars > traffic > cars > real) > view_ext @ product_unit > traffic > cars > real_int).
% 2.79/1.62 thf(func_def_25, type, move: traffic > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_26, type, nat_card: nat_int > nat).
% 2.79/1.62 thf(func_def_27, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.79/1.62 thf(func_def_28, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.79/1.62 thf(func_def_29, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.79/1.62 thf(func_def_30, type, real_length: real_int > real).
% 2.79/1.62 thf(func_def_31, type, regular_regular: cars > traffic > cars > real).
% 2.79/1.62 thf(func_def_32, type, restrict: view_ext @ product_unit > (cars > nat_int) > cars > nat_int).
% 2.79/1.62 thf(func_def_33, type, abstract: traffic > traffic > $o).
% 2.79/1.62 thf(func_def_34, type, clm: traffic > cars > nat_int).
% 2.79/1.62 thf(func_def_35, type, create_claim: traffic > cars > nat > traffic > $o).
% 2.79/1.62 thf(func_def_36, type, create_reservation: traffic > cars > traffic > $o).
% 2.79/1.62 thf(func_def_37, type, res: traffic > cars > nat_int).
% 2.79/1.62 thf(func_def_38, type, withdraw_claim: traffic > cars > traffic > $o).
% 2.79/1.62 thf(func_def_39, type, withdraw_reservation: traffic > cars > nat > traffic > $o).
% 2.79/1.62 thf(func_def_40, type, ext: !>[X0: $tType]:(view_ext @ X0 > real_int)).
% 2.79/1.62 thf(func_def_41, type, hchop: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > $o).
% 2.79/1.62 thf(func_def_42, type, lan: !>[X0: $tType]:(view_ext @ X0 > nat_int)).
% 2.79/1.62 thf(func_def_43, type, own: !>[X0: $tType]:(view_ext @ X0 > cars)).
% 2.79/1.62 thf(func_def_44, type, vchop: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > $o).
% 2.79/1.62 thf(func_def_45, type, c: cars).
% 2.79/1.62 thf(func_def_46, type, d: cars).
% 2.79/1.62 thf(func_def_47, type, e: cars).
% 2.79/1.62 thf(func_def_49, type, ts: traffic).
% 2.79/1.62 thf(func_def_50, type, ts2: traffic).
% 2.79/1.62 thf(func_def_51, type, ts_a: traffic).
% 2.79/1.62 thf(func_def_52, type, ts3: traffic).
% 2.79/1.62 thf(func_def_53, type, v: view_ext @ product_unit).
% 2.79/1.62 thf(func_def_72, type, sP0: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > $o).
% 2.79/1.62 thf(func_def_73, type, sP1: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 2.79/1.62 thf(func_def_74, type, sP2: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 2.79/1.62 thf(func_def_75, type, sP3: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 2.79/1.62 thf(func_def_76, type, sP4: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > $o).
% 2.79/1.62 thf(func_def_77, type, sP5: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 2.79/1.62 thf(func_def_78, type, sP6: view_ext @ product_unit > traffic > cars > $o).
% 2.79/1.62 thf(func_def_79, type, sP7: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > $o).
% 2.79/1.62 thf(func_def_80, type, sP8: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 2.79/1.62 thf(func_def_81, type, sK9: (nat > $o) > nat).
% 2.79/1.62 thf(func_def_82, type, sK10: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_83, type, sK11: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_84, type, sK12: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_85, type, sK13: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_86, type, sK14: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_87, type, sK15: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_88, type, sK16: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_89, type, sK17: nat > (nat > $o) > nat).
% 2.79/1.62 thf(func_def_90, type, sK18: (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_91, type, sK19: (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_92, type, sK20: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_93, type, sK21: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_94, type, sK22: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_95, type, sK23: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_96, type, sK24: (nat > nat) > nat).
% 2.79/1.62 thf(func_def_97, type, sK25: (nat > nat) > nat).
% 2.79/1.62 thf(func_def_98, type, sK26: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_99, type, sK27: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 2.79/1.62 thf(func_def_100, type, sK28: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_101, type, sK29: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_102, type, sK30: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_103, type, sK31: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_104, type, sK32: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_105, type, sK33: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_106, type, sK34: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_107, type, sK35: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_108, type, sK36: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_109, type, sK37: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_110, type, sK38: (nat > $o) > nat).
% 2.79/1.62 thf(func_def_111, type, sK39: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_112, type, sK40: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_113, type, sK41: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_114, type, sK42: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_115, type, sK43: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_116, type, sK44: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_117, type, sK45: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_118, type, sK46: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_119, type, sK47: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_120, type, sK48: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_121, type, sK49: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 2.79/1.62 thf(func_def_122, type, sK50: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 2.79/1.62 thf(func_def_123, type, sK51: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_124, type, sK52: view_ext @ product_unit).
% 2.79/1.62 thf(func_def_125, type, sK53: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_126, type, sK54: view_ext @ product_unit > nat > nat > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_127, type, sK55: view_ext @ product_unit > nat > nat > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_128, type, sK56: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_129, type, sK57: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_130, type, sK58: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_131, type, sK59: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_132, type, sK60: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.79/1.62 thf(func_def_133, type, sK61: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.79/1.62 thf(func_def_134, type, sK62: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_135, type, sK63: (nat > $o) > nat).
% 2.79/1.62 thf(func_def_136, type, sK64: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_137, type, sK65: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_138, type, sK66: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_139, type, sK67: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_140, type, sK68: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_141, type, sK69: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_142, type, sK70: (nat > $o) > nat).
% 2.79/1.62 thf(func_def_143, type, sK71: nat > (nat > $o) > nat).
% 2.79/1.62 thf(func_def_144, type, sK72: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_145, type, sK73: view_ext @ product_unit > traffic > cars > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_146, type, sK74: view_ext @ product_unit > traffic > cars > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_147, type, sK75: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_148, type, sK76: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_149, type, sK77: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_150, type, sK78: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_151, type, sK79: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_152, type, sK80: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_153, type, sK81: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_154, type, sK82: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > traffic).
% 2.79/1.62 thf(func_def_155, type, sK83: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > traffic).
% 2.79/1.62 thf(func_def_156, type, sK84: view_ext @ product_unit > nat > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_157, type, sK85: view_ext @ product_unit > nat > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_158, type, sK86: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.79/1.62 thf(func_def_159, type, sK87: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_160, type, sK88: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_161, type, sK89: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 2.79/1.62 thf(func_def_162, type, sK90: view_ext @ product_unit > traffic > cars > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_163, type, sK91: view_ext @ product_unit > traffic > cars > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_164, type, sK92: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_165, type, sK93: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_166, type, sK94: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_167, type, sK95: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_168, type, sK96: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_169, type, sK97: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_170, type, sK98: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_171, type, sK99: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_172, type, sK100: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 2.79/1.62 thf(func_def_173, type, sK101: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_174, type, sK102: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_175, type, sK103: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_176, type, sK104: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_177, type, sK105: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_178, type, sK106: view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_179, type, sK107: view_ext @ product_unit > real > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_180, type, sK108: view_ext @ product_unit > real > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_181, type, sK109: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_182, type, sK110: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_183, type, sK111: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_184, type, sK112: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_185, type, sK113: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_186, type, sK114: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_187, type, sK115: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_188, type, sK116: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_189, type, sK117: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_190, type, sK118: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_191, type, sK119: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 2.79/1.62 thf(func_def_193, type, ph121: !>[X0: $tType]:(X0)).
% 2.79/1.62 thf(f1518,plain,(
% 2.79/1.62 $false),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1517,f1258])).
% 2.79/1.62 thf(f1258,plain,(
% 2.79/1.62 ((len @ regular_regular @ sK52 @ ts @ c) = (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1046,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ e) = (lan @ product_unit @ sK52)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ sK52))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ sK52))) & ((len @ regular_regular @ sK52 @ ts @ e) = (ext @ product_unit @ sK52)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) & ($true = (ord_less_eq @ view_ext @ product_unit @ sK52 @ (move @ ts3 @ ts @ v))) & ((len @ regular_regular @ sK52 @ ts @ c) = (ext @ product_unit @ sK52)) & ((restrict @ sK52 @ (res @ ts) @ c) = (lan @ product_unit @ sK52))),
% 2.79/1.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f771,f1045])).
% 2.79/1.62 thf(f1045,plain,(
% 2.79/1.62 ? [X0 : view_ext @ product_unit] : (((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & ((ext @ product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) = $true) & ((len @ regular_regular @ X0 @ ts @ c) = (ext @ product_unit @ X0)) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ c))) => (((restrict @ sK52 @ (res @ ts) @ e) = (lan @ product_unit @ sK52)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ sK52))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ sK52))) & ((len @ regular_regular @ sK52 @ ts @ e) = (ext @ product_unit @ sK52)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) & ($true = (ord_less_eq @ view_ext @ product_unit @ sK52 @ (move @ ts3 @ ts @ v))) & ((len @ regular_regular @ sK52 @ ts @ c) = (ext @ product_unit @ sK52)) & ((restrict @ sK52 @ (res @ ts) @ c) = (lan @ product_unit @ sK52)))),
% 2.79/1.62 introduced(definition,[],[choice_axiom])).
% 2.79/1.62 thf(f771,plain,(
% 2.79/1.62 ? [X0 : view_ext @ product_unit] : (((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & ((ext @ product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) = $true) & ((len @ regular_regular @ X0 @ ts @ c) = (ext @ product_unit @ X0)) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ c)))),
% 2.79/1.62 inference(fool_elimination,[status(thm)],[f770])).
% 2.79/1.62 thf(f770,plain,(
% 2.79/1.62 ? [X0 : view_ext @ product_unit] : ((one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & (ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ c)) & ((ext @ product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0))) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & ((len @ regular_regular @ X0 @ ts @ c) = (ext @ product_unit @ X0)) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)))),
% 2.79/1.62 inference(rectify,[status(thm)],[f5])).
% 2.79/1.62 thf(f5,axiom,(
% 2.79/1.62 ? [X9 : view_ext @ product_unit] : (((nat_card @ (lan @ product_unit @ X9)) = one_one @ nat) & (ord_less_eq @ view_ext @ product_unit @ X9 @ (move @ ts3 @ ts @ v)) & ((restrict @ X9 @ (res @ ts) @ c) = (lan @ product_unit @ X9)) & ((ext @ product_unit @ X9) = (len @ regular_regular @ X9 @ ts @ e)) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X9))) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X9))) & ((nat_card @ (lan @ product_unit @ X9)) = one_one @ nat) & ((ext @ product_unit @ X9) = (len @ regular_regular @ X9 @ ts @ c)) & ((lan @ product_unit @ X9) = (restrict @ X9 @ (res @ ts) @ e)))),
% 2.79/1.62 file('/export/starexec/sandbox2/tmp/tmp.jc752Tu92v/DTF2THF_28583.p',fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062)).
% 2.79/1.62 thf(f1517,plain,(
% 2.79/1.62 ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1516,f1264])).
% 2.79/1.62 thf(f1264,plain,(
% 2.79/1.62 ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52))))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1516,plain,(
% 2.79/1.62 ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1515,f1265])).
% 2.79/1.62 thf(f1265,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ e) = (lan @ product_unit @ sK52))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1515,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ e) != (lan @ product_unit @ sK52)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1514,f1257])).
% 2.79/1.62 thf(f1257,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ c) = (lan @ product_unit @ sK52))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1514,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ c) != (lan @ product_unit @ sK52)) | ((restrict @ sK52 @ (res @ ts) @ e) != (lan @ product_unit @ sK52)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52)))) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1513,f1263])).
% 2.79/1.62 thf(f1263,plain,(
% 2.79/1.62 (one_one @ nat = (nat_card @ (lan @ product_unit @ sK52)))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1513,plain,(
% 2.79/1.62 (one_one @ nat != (nat_card @ (lan @ product_unit @ sK52))) | ((restrict @ sK52 @ (res @ ts) @ e) != (lan @ product_unit @ sK52)) | ((restrict @ sK52 @ (res @ ts) @ c) != (lan @ product_unit @ sK52)) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52))))),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1499,f1259])).
% 2.79/1.62 thf(f1259,plain,(
% 2.79/1.62 ($true = (ord_less_eq @ view_ext @ product_unit @ sK52 @ (move @ ts3 @ ts @ v)))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1499,plain,(
% 2.79/1.62 ($true != (ord_less_eq @ view_ext @ product_unit @ sK52 @ (move @ ts3 @ ts @ v))) | ((restrict @ sK52 @ (res @ ts) @ e) != (lan @ product_unit @ sK52)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ sK52))) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52)) | ((restrict @ sK52 @ (res @ ts) @ c) != (lan @ product_unit @ sK52)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52))))),
% 2.79/1.62 inference(trivial_inequality_removal,[status(thm)],[f1476])).
% 2.79/1.62 thf(f1476,plain,(
% 2.79/1.62 ((restrict @ sK52 @ (res @ ts) @ c) != (lan @ product_unit @ sK52)) | ((ext @ product_unit @ sK52) != (ext @ product_unit @ sK52)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ sK52))) | ((len @ regular_regular @ sK52 @ ts @ c) != (ext @ product_unit @ sK52)) | ((restrict @ sK52 @ (res @ ts) @ e) != (lan @ product_unit @ sK52)) | ($true != (ord_less_eq @ view_ext @ product_unit @ sK52 @ (move @ ts3 @ ts @ v))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ sK52))))),
% 2.79/1.62 inference(superposition,[status(thm)],[f1475,f1261])).
% 2.79/1.62 thf(f1261,plain,(
% 2.79/1.62 ((len @ regular_regular @ sK52 @ ts @ e) = (ext @ product_unit @ sK52))),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f1046])).
% 2.79/1.62 thf(f1475,plain,(
% 2.79/1.62 ( ! [X0 : view_ext @ product_unit] : (((ext @ product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ c)) | ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) != $true) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((len @ regular_regular @ X0 @ ts @ c) != (ext @ product_unit @ X0))) )),
% 2.79/1.62 inference(subsumption_resolution,[status(thm)],[f1474,f1152])).
% 2.79/1.62 thf(f1152,plain,(
% 2.79/1.62 (thesis != $true)),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f816])).
% 2.79/1.62 thf(f816,plain,(
% 2.79/1.62 (thesis != $true)),
% 2.79/1.62 inference(flattening,[status(thm)],[f469])).
% 2.79/1.62 thf(f469,plain,(
% 2.79/1.62 ~(thesis = $true)),
% 2.79/1.62 inference(fool_elimination,[status(thm)],[f468])).
% 2.79/1.62 thf(f468,plain,(
% 2.79/1.62 ~thesis),
% 2.79/1.62 inference(rectify,[status(thm)],[f280])).
% 2.79/1.62 thf(f280,negated_conjecture,(
% 2.79/1.62 ~thesis),
% 2.79/1.62 inference(negated_conjecture,[status(cth)],[f279])).
% 2.79/1.62 thf(f279,conjecture,(
% 2.79/1.62 thesis),
% 2.79/1.62 file('/export/starexec/sandbox2/tmp/tmp.jc752Tu92v/DTF2THF_28583.p',conj_1)).
% 2.79/1.62 thf(f1474,plain,(
% 2.79/1.62 ( ! [X0 : view_ext @ product_unit] : (((len @ regular_regular @ X0 @ ts @ c) != (ext @ product_unit @ X0)) | ((ext @ product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) != $true) | (thesis = $true) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ c))) )),
% 2.79/1.62 inference(duplicate_literal_removal,[status(thm)],[f1235])).
% 2.79/1.62 thf(f1235,plain,(
% 2.79/1.62 ( ! [X0 : view_ext @ product_unit] : ((thesis = $true) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ c)) | ((ext @ product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((len @ regular_regular @ X0 @ ts @ c) != (ext @ product_unit @ X0)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) != $true)) )),
% 2.79/1.62 inference(cnf_transformation,[status(thm)],[f926])).
% 2.79/1.62 thf(f926,plain,(
% 2.79/1.62 ! [X0 : view_ext @ product_unit] : ((thesis = $true) | ((len @ regular_regular @ X0 @ ts @ c) != (ext @ product_unit @ X0)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ c)) | ((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) != $true) | ((ext @ product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)))),
% 2.79/1.62 inference(flattening,[status(thm)],[f925])).
% 2.79/1.62 thf(f925,plain,(
% 2.79/1.62 ! [X0 : view_ext @ product_unit] : ((thesis = $true) | (((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) != $true) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) | ((ext @ product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((lan @ product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ c)) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | (one_one @ nat != (nat_card @ (lan @ product_unit @ X0))) | ((len @ regular_regular @ X0 @ ts @ c) != (ext @ product_unit @ X0))))),
% 2.79/1.62 inference(ennf_transformation,[status(thm)],[f567])).
% 2.79/1.62 thf(f567,plain,(
% 2.79/1.62 ! [X0 : view_ext @ product_unit] : ((((ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) = $true) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & ($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0)))) & ((ext @ product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ c)) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & ((len @ regular_regular @ X0 @ ts @ c) = (ext @ product_unit @ X0))) => (thesis = $true))),
% 2.79/1.62 inference(fool_elimination,[status(thm)],[f566])).
% 2.79/1.62 thf(f566,plain,(
% 2.79/1.62 ! [X0 : view_ext @ product_unit] : (((one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0))) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ c)) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X0))) & (ord_less_eq @ view_ext @ product_unit @ X0 @ (move @ ts3 @ ts @ v)) & ((ext @ product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ((len @ regular_regular @ X0 @ ts @ c) = (ext @ product_unit @ X0)) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X0))) & ((lan @ product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e))) => thesis)),
% 2.79/1.62 inference(rectify,[status(thm)],[f278])).
% 2.79/1.62 thf(f278,axiom,(
% 2.79/1.62 ! [X92 : view_ext @ product_unit] : (((one_one @ nat = (nat_card @ (lan @ product_unit @ X92))) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X92))) & ((restrict @ X92 @ (res @ ts) @ c) = (lan @ product_unit @ X92)) & (ord_less @ real @ zero_zero @ real @ (real_length @ (ext @ product_unit @ X92))) & (ord_less_eq @ view_ext @ product_unit @ X92 @ (move @ ts3 @ ts @ v)) & ((ext @ product_unit @ X92) = (len @ regular_regular @ X92 @ ts @ e)) & ((ext @ product_unit @ X92) = (len @ regular_regular @ X92 @ ts @ c)) & (one_one @ nat = (nat_card @ (lan @ product_unit @ X92))) & ((lan @ product_unit @ X92) = (restrict @ X92 @ (res @ ts) @ e))) => thesis)),
% 2.79/1.62 file('/export/starexec/sandbox2/tmp/tmp.jc752Tu92v/DTF2THF_28583.p',conj_0)).
% 2.79/1.62 % SZS output end Proof for DTF2THF_28583
% 2.79/1.62 % (28690)------------------------------
% 2.79/1.62 % (28690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.62 % (28690)Termination reason: Refutation
% 2.79/1.62
% 2.79/1.62 % (28690)Memory used [KB]: 7547
% 2.79/1.62 % (28690)Time elapsed: 0.099 s
% 2.79/1.62 % (28690)Instructions burned: 203 (million)
% 2.79/1.62 % (28690)------------------------------
% 2.79/1.62 % (28690)------------------------------
% 2.79/1.62 % (28684)Success in time 0.116 s
%------------------------------------------------------------------------------