%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP170^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 3.05s 1.68s
% Output : Refutation 3.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP170^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:28:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP170^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer Safety_Regular problem prob_415__3354378_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : Safety_Regular/prob_415__3354378_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.33 v9.1.0, 0.00 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 377 ( 97 unt; 75 typ; 0 def)
% 0.29/0.46 % Number of atoms : 820 ( 246 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.29/0.46 % Number of connectives : 3738 ( 36 ~; 7 |; 112 &;3252 @)
% 0.29/0.46 % ( 0 <=>; 331 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 17 ( 7 avg)
% 0.29/0.46 % Number of types : 7 ( 6 usr)
% 0.29/0.46 % Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 70 ( 69 usr; 6 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 909 ( 25 ^; 772 !; 69 ?; 909 :)
% 0.29/0.46 % ( 43 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:23:21.183
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (8)
% 0.29/0.46 thf(ty_t_Views_Oview_Oview__ext,type,
% 0.29/0.46 view_ext: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.29/0.46 product_unit: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.46 product_prod: $tType > $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_RealInt_Oreal__int,type,
% 0.29/0.46 real_int: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Traffic_Otraffic,type,
% 0.29/0.46 traffic: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_NatInt_Onat__int,type,
% 0.29/0.46 nat_int: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Real_Oreal,type,
% 0.29/0.46 real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Cars_Ocars,type,
% 0.29/0.46 cars: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (67)
% 0.29/0.46 thf(sy_cl_HOL_Otype,type,
% 0.29/0.46 type:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oone,type,
% 0.29/0.46 one:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.46 zero:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.46 ord:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.29/0.46 neg_numeral:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.46 order:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.46 group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.29/0.46 monoid_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.46 linorder:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.29/0.46 preorder:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.29/0.46 zero_neq_one:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.29/0.46 zero_less_one:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.29/0.46 semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.29/0.46 linordered_idom:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.29/0.46 comm_monoid_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Fields_Olinordered__field,type,
% 0.29/0.46 linordered_field:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.29/0.46 ab_semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.29/0.46 linordered_semidom:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.29/0.46 cancel_semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.29/0.46 cancel1352612707id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.29/0.46 linord219039673up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.29/0.46 ordere216010020id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.29/0.46 ordere779506340up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.29/0.46 linord1659791738miring:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.46 canoni770627133id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 0.29/0.46 ordere1818651114id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.29/0.46 strict797366125id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.29/0.46 ordere236663937imp_le:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.29/0.46 ordere223160158up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.29/0.46 strict2144017051up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.29/0.46 unique1598680935umeral:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.29/0.46 ordere516151231imp_le:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 0.29/0.46 unique455577585es_aux:
% 0.29/0.46 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.29/0.46 one_one:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.29/0.46 plus_plus:
% 0.29/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.46 zero_zero:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Length_Osensors_Olen,type,
% 0.29/0.46 len: ( cars > traffic > cars > real ) > ( view_ext @ product_unit ) > traffic > cars > real_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.29/0.46 bot_bot:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.46 ord_less:
% 0.29/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.46 ord_less_eq:
% 0.29/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.29/0.46 product_Pair:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_RealInt_Oleft,type,
% 0.29/0.46 left: real_int > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_RealInt_Oreal__int_OAbs__real__int,type,
% 0.29/0.46 real_Abs_real_int: ( product_prod @ real @ real ) > real_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 0.29/0.46 real_length: real_int > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 0.29/0.46 real_shift: real_int > real > real_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_RealInt_Oright,type,
% 0.29/0.46 right: real_int > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Regular__Sensors_Oregular,type,
% 0.29/0.46 regular_regular: cars > traffic > cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sensors_Osensors,type,
% 0.29/0.46 sensors: ( cars > traffic > cars > real ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sensors_Osensors_Ospace,type,
% 0.29/0.46 space: ( cars > traffic > cars > real ) > traffic > ( view_ext @ product_unit ) > cars > real_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Traffic_Otraffic_OAbs__traffic,type,
% 0.29/0.46 abs_traffic: ( product_prod @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) ) > traffic ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 0.29/0.46 physical_size: traffic > cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Traffic_Otraffic_Opos,type,
% 0.29/0.46 pos: traffic > cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Views_Oview_Oext,type,
% 0.29/0.46 ext:
% 0.29/0.46 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Views_Oview_Ohchop,type,
% 0.29/0.46 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Views_Oview_Oown,type,
% 0.29/0.46 own:
% 0.29/0.46 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_c____,type,
% 0.29/0.46 c: cars ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_cl____,type,
% 0.29/0.46 cl: cars > nat_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_d____,type,
% 0.29/0.46 d: cars ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_dy____,type,
% 0.29/0.46 dy: cars > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_po____,type,
% 0.29/0.46 po: cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_ps____,type,
% 0.29/0.46 ps: cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_re____,type,
% 0.29/0.46 re: cars > nat_int ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_sd____,type,
% 0.29/0.46 sd: cars > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_ts____,type,
% 0.29/0.46 ts: traffic ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_ts__rep____,type,
% 0.29/0.46 ts_rep: product_prod @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_v_H____,type,
% 0.29/0.46 v: view_ext @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_v____,type,
% 0.29/0.46 v2: view_ext @ product_unit ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (252)
% 0.29/0.46 thf(fact_0__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062dy_O_A_092_060forall_062c_Ax_O_Ady_Ac_Ax_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.46 ~ ! [Dy: cars > real > real] :
% 0.29/0.46 ~ ! [C: cars,X: real] :
% 0.29/0.46 ( ( Dy @ C @ X )
% 0.29/0.46 = ( zero_zero @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>thesis. (\<And>dy. \<forall>c x. dy c x = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.46 thf(fact_1_dyn__def,axiom,
% 0.29/0.46 ! [C: cars,X: real] :
% 0.29/0.46 ( ( dy @ C @ X )
% 0.29/0.46 = ( zero_zero @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % dyn_def
% 0.29/0.46 thf(fact_2_local_Ohmlsl_Osensors__ge,axiom,
% 0.29/0.46 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ E @ Ts @ C2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.sensors_ge
% 0.29/0.46 thf(fact_3_hmlsl_Olen__non__empty__inside,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 0.29/0.46 => ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_non_empty_inside
% 0.29/0.46 thf(fact_4_v_H__d,axiom,
% 0.29/0.46 ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ v @ ts @ d ) ) ).
% 0.29/0.46
% 0.29/0.46 % v'_d
% 0.29/0.46 thf(fact_5_hmlsl_Ospace__nonempty,axiom,
% 0.29/0.46 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] : ( ord_less @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.space_nonempty
% 0.29/0.46 thf(fact_6_ts__def,axiom,
% 0.29/0.46 ( ts
% 0.29/0.46 = ( abs_traffic @ ts_rep ) ) ).
% 0.29/0.46
% 0.29/0.46 % ts_def
% 0.29/0.46 thf(fact_7_assumption,axiom,
% 0.29/0.46 d != c ).
% 0.29/0.46
% 0.29/0.46 % assumption
% 0.29/0.46 thf(fact_8_local_Ohmlsl_Olength__geq__zero,axiom,
% 0.29/0.46 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 | ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_geq_zero
% 0.29/0.46 thf(fact_9_v_H__rel__c,axiom,
% 0.29/0.46 ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext @ product_unit @ v ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % v'_rel_c
% 0.29/0.46 thf(fact_10_hmlsl_Oleft__space,axiom,
% 0.29/0.46 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 0.29/0.46 = ( pos @ Ts @ C2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.left_space
% 0.29/0.46 thf(fact_11_len__eq,axiom,
% 0.29/0.46 ( ( len @ regular_regular @ v @ ts @ c )
% 0.29/0.46 = ( len @ regular_regular @ v @ ts @ d ) ) ).
% 0.29/0.46
% 0.29/0.46 % len_eq
% 0.29/0.46 thf(fact_12_hmlsl_Olen__space__left,axiom,
% 0.29/0.46 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( ord_less_eq @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 0.29/0.46 => ( ord_less_eq @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_space_left
% 0.29/0.46 thf(fact_13_hmlsl_Olen__space__right,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) )
% 0.29/0.46 => ( ord_less_eq @ real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_space_right
% 0.29/0.46 thf(fact_14_regular__sensors_Osensors__le,axiom,
% 0.29/0.46 ! [E: cars,C2: cars,Ts: traffic] :
% 0.29/0.46 ( ( E != C2 )
% 0.29/0.46 => ( ord_less @ real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % regular_sensors.sensors_le
% 0.29/0.46 thf(fact_15_ps__ge__zero,axiom,
% 0.29/0.46 ! [C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( ps @ C ) ) ).
% 0.29/0.46
% 0.29/0.46 % ps_ge_zero
% 0.29/0.46 thf(fact_16_sd__ge__zero,axiom,
% 0.29/0.46 ! [C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( sd @ C ) ) ).
% 0.29/0.46
% 0.29/0.46 % sd_ge_zero
% 0.29/0.46 thf(fact_17_hmlsl_Olen__left,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_left
% 0.29/0.46 thf(fact_18_hmlsl_Olen__right,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_right
% 0.29/0.46 thf(fact_19_v_H__c,axiom,
% 0.29/0.46 ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) ).
% 0.29/0.46
% 0.29/0.46 % v'_c
% 0.29/0.46 thf(fact_20_hmlsl_Osensors__axioms,axiom,
% 0.29/0.46 sensors @ regular_regular ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.sensors_axioms
% 0.29/0.46 thf(fact_21_dyn__geq__zero,axiom,
% 0.29/0.46 ! [C: cars,X: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( dy @ C @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % dyn_geq_zero
% 0.29/0.46 thf(fact_22_ps__def,axiom,
% 0.29/0.46 ! [C: cars] :
% 0.29/0.46 ( ( ps @ C )
% 0.29/0.46 = ( one_one @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % ps_def
% 0.29/0.46 thf(fact_23_regular__sensors_Osensors__leq,axiom,
% 0.29/0.46 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % regular_sensors.sensors_leq
% 0.29/0.46 thf(fact_24_sensors_Olen__non__empty__inside,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 0.29/0.46 => ( ( ord_less @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_non_empty_inside
% 0.29/0.46 thf(fact_25_other__len__zero,axiom,
% 0.29/0.46 ! [E2: cars] :
% 0.29/0.46 ( ( ( E2 != c )
% 0.29/0.46 & ( E2 != d ) )
% 0.29/0.46 => ( ( real_length @ ( len @ regular_regular @ v2 @ ts @ E2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % other_len_zero
% 0.29/0.46 thf(fact_26_sensors_Olen__space__right,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) )
% 0.29/0.46 => ( ord_less_eq @ real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_space_right
% 0.29/0.46 thf(fact_27_sensors_Olen__space__left,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ord_less_eq @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 0.29/0.46 => ( ord_less_eq @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_space_left
% 0.29/0.46 thf(fact_28_lc,axiom,
% 0.29/0.46 ( ( left @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % lc
% 0.29/0.46 thf(fact_29_sensors_Ospace__nonempty,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ord_less @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.space_nonempty
% 0.29/0.46 thf(fact_30_sensors_Olen__right,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ord_less_eq @ real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_right
% 0.29/0.46 thf(fact_31_sensors_Olen__left,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_left
% 0.29/0.46 thf(fact_32_not__gr__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N: A] :
% 0.29/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.29/0.46 = ( N
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_gr_zero
% 0.29/0.46 thf(fact_33_le__zero__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.29/0.46 = ( N
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_zero_eq
% 0.29/0.46 thf(fact_34__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.46 ~ ! [Ps: cars > real] :
% 0.29/0.46 ~ ! [C: cars] :
% 0.29/0.46 ( ( Ps @ C )
% 0.29/0.46 = ( one_one @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>thesis. (\<And>ps. \<forall>c. ps c = 1 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.46 thf(fact_35_hmlsl_Olen__sub__int,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( ext @ product_unit @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_sub_int
% 0.29/0.46 thf(fact_36_hmlsl_Olen__empty__subview,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V3: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V ) )
% 0.29/0.46 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_empty_subview
% 0.29/0.46 thf(fact_37_lv,axiom,
% 0.29/0.46 ( ( left @ ( ext @ product_unit @ v2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % lv
% 0.29/0.46 thf(fact_38_rc,axiom,
% 0.29/0.46 ( ( right @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 0.29/0.46 = ( one_one @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % rc
% 0.29/0.46 thf(fact_39_one__reorient,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( one @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( ( one_one @ A )
% 0.29/0.46 = X2 )
% 0.29/0.46 = ( X2
% 0.29/0.46 = ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_reorient
% 0.29/0.46 thf(fact_40_sensors_Olen__sub__int,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ord_less_eq @ real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( ext @ product_unit @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_sub_int
% 0.29/0.46 thf(fact_41_sensors_Olen__empty__subview,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V3: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V ) )
% 0.29/0.46 => ( ( real_length @ ( len @ Sensors @ V3 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_empty_subview
% 0.29/0.46 thf(fact_42_ext,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) )
% 0.29/0.46 => ( F = G ) ) ).
% 0.29/0.46
% 0.29/0.46 % ext
% 0.29/0.46 thf(fact_43_zero__reorient,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = X2 )
% 0.29/0.46 = ( X2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_reorient
% 0.29/0.46 thf(fact_44_sensors_Olen_Ocong,axiom,
% 0.29/0.46 len = len ).
% 0.29/0.46
% 0.29/0.46 % sensors.len.cong
% 0.29/0.46 thf(fact_45_sensors_Ospace_Ocong,axiom,
% 0.29/0.46 space = space ).
% 0.29/0.46
% 0.29/0.46 % sensors.space.cong
% 0.29/0.46 thf(fact_46_zero__le,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_le
% 0.29/0.46 thf(fact_47_gr__zeroI,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N: A] :
% 0.29/0.46 ( ( N
% 0.29/0.46 != ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr_zeroI
% 0.29/0.46 thf(fact_48_not__less__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N: A] :
% 0.29/0.46 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_less_zero
% 0.29/0.46 thf(fact_49_gr__implies__not__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [M: A,N: A] :
% 0.29/0.46 ( ( ord_less @ A @ M @ N )
% 0.29/0.46 => ( N
% 0.29/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr_implies_not_zero
% 0.29/0.46 thf(fact_50_zero__less__iff__neq__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.29/0.46 = ( N
% 0.29/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_iff_neq_zero
% 0.29/0.46 thf(fact_51_sensors__def,axiom,
% 0.29/0.46 ( sensors
% 0.29/0.46 = ( ^ [Sensors2: cars > traffic > cars > real] :
% 0.29/0.46 ! [E3: cars,Ts3: traffic,C3: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors2 @ E3 @ Ts3 @ C3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors_def
% 0.29/0.46 thf(fact_52_sensors_Ointro,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real] :
% 0.29/0.46 ( ! [E4: cars,Ts4: traffic,C4: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors @ E4 @ Ts4 @ C4 ) )
% 0.29/0.46 => ( sensors @ Sensors ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.intro
% 0.29/0.46 thf(fact_53_sensors_Osensors__ge,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,E: cars,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors @ E @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.sensors_ge
% 0.29/0.46 thf(fact_54_sensors_Oleft__space,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( left @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 0.29/0.46 = ( pos @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.left_space
% 0.29/0.46 thf(fact_55_size,axiom,
% 0.29/0.46 ! [C: cars] :
% 0.29/0.46 ( ( physical_size @ ts @ C )
% 0.29/0.46 = ( one_one @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % size
% 0.29/0.46 thf(fact_56_sensors__c,axiom,
% 0.29/0.46 ( ( regular_regular @ ( own @ product_unit @ v2 ) @ ts @ c )
% 0.29/0.46 = ( one_one @ real ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors_c
% 0.29/0.46 thf(fact_57_hmlsl_Oview__leq__len__leq,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V ) @ ( ext @ product_unit @ V3 ) )
% 0.29/0.46 & ( ( own @ product_unit @ V )
% 0.29/0.46 = ( own @ product_unit @ V3 ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) )
% 0.29/0.46 => ( ord_less_eq @ real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.view_leq_len_leq
% 0.29/0.46 thf(fact_58_length__zero__iff__borders__eq,axiom,
% 0.29/0.46 ! [R: real_int] :
% 0.29/0.46 ( ( ( real_length @ R )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 = ( ( left @ R )
% 0.29/0.46 = ( right @ R ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % length_zero_iff_borders_eq
% 0.29/0.46 thf(fact_59_hmlsl_Olen__fills__subview,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 0.29/0.46 => ? [V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ V1 @ V22 )
% 0.29/0.46 & ( hchop @ V22 @ V4 @ V32 )
% 0.29/0.46 & ( ( len @ regular_regular @ V4 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V4 ) )
% 0.29/0.46 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C2 ) )
% 0.29/0.46 = ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_fills_subview
% 0.29/0.46 thf(fact_60_less__real__int__def,axiom,
% 0.29/0.46 ( ( ord_less @ real_int )
% 0.29/0.46 = ( ^ [R2: real_int,S: real_int] :
% 0.29/0.46 ( ( ord_less_eq @ real @ ( left @ S ) @ ( left @ R2 ) )
% 0.29/0.46 & ( ord_less_eq @ real @ ( right @ R2 ) @ ( right @ S ) )
% 0.29/0.46 & ~ ( ( ord_less_eq @ real @ ( left @ R2 ) @ ( left @ S ) )
% 0.29/0.46 & ( ord_less_eq @ real @ ( right @ S ) @ ( right @ R2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_real_int_def
% 0.29/0.46 thf(fact_61_less__eq__real__int__def,axiom,
% 0.29/0.46 ( ( ord_less_eq @ real_int )
% 0.29/0.46 = ( ^ [R2: real_int,S: real_int] :
% 0.29/0.46 ( ( ord_less_eq @ real @ ( left @ S ) @ ( left @ R2 ) )
% 0.29/0.46 & ( ord_less_eq @ real @ ( right @ R2 ) @ ( right @ S ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eq_real_int_def
% 0.29/0.46 thf(fact_62_left__leq__right,axiom,
% 0.29/0.46 ! [R: real_int] : ( ord_less_eq @ real @ ( left @ R ) @ ( right @ R ) ) ).
% 0.29/0.46
% 0.29/0.46 % left_leq_right
% 0.29/0.46 thf(fact_63_length__ge__zero,axiom,
% 0.29/0.46 ! [R: real_int] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( real_length @ R ) ) ).
% 0.29/0.46
% 0.29/0.46 % length_ge_zero
% 0.29/0.46 thf(fact_64_local_Ohmlsl_Ohchop__assoc,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Phi @ Ts2 @ W )
% 0.29/0.46 & ? [X4: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ U @ X4 @ Y )
% 0.29/0.46 & ( Psi @ Ts2 @ X4 )
% 0.29/0.46 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.29/0.46 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ? [X4: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ W @ X4 @ Y )
% 0.29/0.46 & ( Phi @ Ts2 @ X4 )
% 0.29/0.46 & ( Psi @ Ts2 @ Y ) )
% 0.29/0.46 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_assoc
% 0.29/0.46 thf(fact_65_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Phi @ Ts2 @ W )
% 0.29/0.46 & ( ( Psi @ Ts2 @ U )
% 0.29/0.46 | ( Chi @ Ts2 @ U ) ) ) )
% 0.29/0.46 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Phi @ Ts2 @ W )
% 0.29/0.46 & ( Psi @ Ts2 @ U ) )
% 0.29/0.46 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Phi @ Ts2 @ W )
% 0.29/0.46 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_disj_distr1
% 0.29/0.46 thf(fact_66_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 0.29/0.46 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( ( Psi @ Ts2 @ W )
% 0.29/0.46 | ( Chi @ Ts2 @ W ) )
% 0.29/0.46 & ( Phi @ Ts2 @ U ) ) )
% 0.29/0.46 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Psi @ Ts2 @ W )
% 0.29/0.46 & ( Phi @ Ts2 @ U ) )
% 0.29/0.46 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( Chi @ Ts2 @ W )
% 0.29/0.46 & ( Phi @ Ts2 @ U ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_disj_distr2
% 0.29/0.46 thf(fact_67_local_Ohmlsl_Ohchop__neg1,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ~ ? [Va: view_ext @ product_unit] :
% 0.29/0.46 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.29/0.46 & ( Phi @ Ts2 @ Va ) )
% 0.29/0.46 => ? [Va: view_ext @ product_unit] :
% 0.29/0.46 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.29/0.46 & ~ ( Phi @ Ts2 @ Va ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_neg1
% 0.29/0.46 thf(fact_68_local_Ohmlsl_Ohchop__neg2,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ~ ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ( Phi @ Ts2 @ U2 ) )
% 0.29/0.46 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_neg2
% 0.29/0.46 thf(fact_69_local_Ohmlsl_Ohchop__weaken,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( Phi @ Ts2 @ V2 )
% 0.29/0.46 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ? [Vb: view_ext @ product_unit] :
% 0.29/0.46 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 0.29/0.46 & ( Phi @ Ts2 @ Vb ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_weaken
% 0.29/0.46 thf(fact_70_local_Ohmlsl_Ohchop__weaken1,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( Phi @ Ts2 @ V2 )
% 0.29/0.46 => ? [Va: view_ext @ product_unit] :
% 0.29/0.46 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.29/0.46 & ( Phi @ Ts2 @ Va ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_weaken1
% 0.29/0.46 thf(fact_71_local_Ohmlsl_Ohchop__weaken2,axiom,
% 0.29/0.46 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( Phi @ Ts2 @ V2 )
% 0.29/0.46 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.hchop_weaken2
% 0.29/0.46 thf(fact_72_hmlsl_Olen__view__hchop__right,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_view_hchop_right
% 0.29/0.46 thf(fact_73_hmlsl_Olen__view__hchop__left,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V12 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_view_hchop_left
% 0.29/0.46 thf(fact_74_hmlsl_Olen__compose__hchop,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 & ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V12 ) )
% 0.29/0.46 & ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V23 ) ) )
% 0.29/0.46 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_compose_hchop
% 0.29/0.46 thf(fact_75_hmlsl_Oext__eq__len__eq,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ( ( ext @ product_unit @ V )
% 0.29/0.46 = ( ext @ product_unit @ V3 ) )
% 0.29/0.46 & ( ( own @ product_unit @ V )
% 0.29/0.46 = ( own @ product_unit @ V3 ) ) )
% 0.29/0.46 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.ext_eq_len_eq
% 0.29/0.46 thf(fact_76_local_Ohmlsl_Olength__split,axiom,
% 0.29/0.46 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.29/0.46 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_split
% 0.29/0.46 thf(fact_77_local_Ohmlsl_Olength__meld,axiom,
% 0.29/0.46 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ? [Va2: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va2 @ U3 )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) ) )
% 0.29/0.46 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_meld
% 0.29/0.46 thf(fact_78_local_Ohmlsl_Olength__dense,axiom,
% 0.29/0.46 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 0.29/0.46 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_dense
% 0.29/0.46 thf(fact_79_hmlsl_Olen__empty__on__subview2,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_empty_on_subview2
% 0.29/0.46 thf(fact_80_hmlsl_Olen__empty__on__subview1,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_empty_on_subview1
% 0.29/0.46 thf(fact_81_hmlsl_Olen__hchop__right__right__border,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( right @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( right @ ( ext @ product_unit @ V23 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_hchop_right_right_border
% 0.29/0.46 thf(fact_82_hmlsl_Olen__hchop__right__left__border,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( left @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( left @ ( ext @ product_unit @ V23 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_hchop_right_left_border
% 0.29/0.46 thf(fact_83_hmlsl_Olen__hchop__left__right__border,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( right @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( right @ ( ext @ product_unit @ V12 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_hchop_left_right_border
% 0.29/0.46 thf(fact_84_hmlsl_Olen__hchop__left__left__border,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( left @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( left @ ( ext @ product_unit @ V12 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_hchop_left_left_border
% 0.29/0.46 thf(fact_85_regular__sensors_Ospace__eq,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( ( own @ product_unit @ V )
% 0.29/0.46 = ( own @ product_unit @ V3 ) )
% 0.29/0.46 => ( ( space @ regular_regular @ Ts @ V @ C2 )
% 0.29/0.46 = ( space @ regular_regular @ Ts @ V3 @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % regular_sensors.space_eq
% 0.29/0.46 thf(fact_86_sensors_Olen__compose__hchop,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 & ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V12 ) )
% 0.29/0.46 & ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V23 ) ) )
% 0.29/0.46 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_compose_hchop
% 0.29/0.46 thf(fact_87_sensors_Olen__view__hchop__left,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V12 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_view_hchop_left
% 0.29/0.46 thf(fact_88_sensors_Olen__view__hchop__right,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V23 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_view_hchop_right
% 0.29/0.46 thf(fact_89_sensors_Oext__eq__len__eq,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( ext @ product_unit @ V )
% 0.29/0.46 = ( ext @ product_unit @ V3 ) )
% 0.29/0.46 & ( ( own @ product_unit @ V )
% 0.29/0.46 = ( own @ product_unit @ V3 ) ) )
% 0.29/0.46 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.ext_eq_len_eq
% 0.29/0.46 thf(fact_90_sensors_Olen__empty__on__subview1,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_empty_on_subview1
% 0.29/0.46 thf(fact_91_sensors_Olen__empty__on__subview2,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( zero_zero @ real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_empty_on_subview2
% 0.29/0.46 thf(fact_92_sensors_Olen__hchop__right__right__border,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( right @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( right @ ( ext @ product_unit @ V23 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_hchop_right_right_border
% 0.29/0.46 thf(fact_93_sensors_Olen__hchop__right__left__border,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( left @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.29/0.46 = ( left @ ( ext @ product_unit @ V23 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_hchop_right_left_border
% 0.29/0.46 thf(fact_94_sensors_Olen__hchop__left__right__border,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( right @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( right @ ( ext @ product_unit @ V12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_hchop_left_right_border
% 0.29/0.46 thf(fact_95_sensors_Olen__hchop__left__left__border,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V ) )
% 0.29/0.46 & ( hchop @ V @ V12 @ V23 ) )
% 0.29/0.46 => ( ( left @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.29/0.46 = ( left @ ( ext @ product_unit @ V12 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_hchop_left_left_border
% 0.29/0.46 thf(fact_96_sensors_Olen__fills__subview,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 0.29/0.46 => ? [V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ V1 @ V22 )
% 0.29/0.46 & ( hchop @ V22 @ V4 @ V32 )
% 0.29/0.46 & ( ( len @ Sensors @ V4 @ Ts @ C2 )
% 0.29/0.46 = ( ext @ product_unit @ V4 ) )
% 0.29/0.46 & ( ( real_length @ ( len @ Sensors @ V4 @ Ts @ C2 ) )
% 0.29/0.46 = ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_fills_subview
% 0.29/0.46 thf(fact_97_sensors_Oview__leq__len__leq,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V ) @ ( ext @ product_unit @ V3 ) )
% 0.29/0.46 & ( ( own @ product_unit @ V )
% 0.29/0.46 = ( own @ product_unit @ V3 ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) )
% 0.29/0.46 => ( ord_less_eq @ real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.view_leq_len_leq
% 0.29/0.46 thf(fact_98_view_Oh__chop__middle2,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U4 @ W2 )
% 0.29/0.46 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ W2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.h_chop_middle2
% 0.29/0.46 thf(fact_99_view_Oh__chop__middle1,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U4 @ W2 )
% 0.29/0.46 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( ext @ product_unit @ U4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.h_chop_middle1
% 0.29/0.46 thf(fact_100_view_Ohorizontal__chop__non__empty,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit] :
% 0.29/0.46 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 0.29/0.46 => ? [U2: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U2 @ W3 )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_non_empty
% 0.29/0.46 thf(fact_101_hmlsl_Oright__space,axiom,
% 0.29/0.46 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 0.29/0.46 = ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.right_space
% 0.29/0.46 thf(fact_102_local_Ohmlsl_Olength__add,axiom,
% 0.29/0.46 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 0.29/0.46 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 0.29/0.46 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.29/0.46 = ( plus_plus @ real @ X2 @ Y2 ) )
% 0.29/0.46 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ W @ U )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ W ) )
% 0.29/0.46 = X2 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ U ) )
% 0.29/0.46 = Y2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_add
% 0.29/0.46 thf(fact_103_local_Ohmlsl_Olength__add2,axiom,
% 0.29/0.46 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 0.29/0.46 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 0.29/0.46 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.29/0.46 = ( plus_plus @ real @ X2 @ Y2 ) )
% 0.29/0.46 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va @ U2 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ Va ) )
% 0.29/0.46 = X2 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ U2 ) )
% 0.29/0.46 = Y2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_add2
% 0.29/0.46 thf(fact_104_traffic_OpsGeZero,axiom,
% 0.29/0.46 ! [Ts: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( physical_size @ Ts @ C ) ) ).
% 0.29/0.46
% 0.29/0.46 % traffic.psGeZero
% 0.29/0.46 thf(fact_105_local_Ohmlsl_Olength__add1,axiom,
% 0.29/0.46 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 0.29/0.46 ( ? [Va2: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V2 @ Va2 @ U3 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ Va2 ) )
% 0.29/0.46 = X2 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ U3 ) )
% 0.29/0.46 = Y2 ) )
% 0.29/0.46 => ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 0.29/0.46 = ( plus_plus @ real @ X2 @ Y2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % local.hmlsl.length_add1
% 0.29/0.46 thf(fact_106_add__left__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_cancel
% 0.29/0.46 thf(fact_107_add__right__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_cancel
% 0.29/0.46 thf(fact_108_hmlsl_Olen__hchop__add,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 => ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( plus_plus @ real @ ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.len_hchop_add
% 0.29/0.46 thf(fact_109_add__le__cancel__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_right
% 0.29/0.46 thf(fact_110_add__le__cancel__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_left
% 0.29/0.46 thf(fact_111_zero__eq__add__iff__both__eq__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = ( plus_plus @ A @ X2 @ Y2 ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_eq_add_iff_both_eq_0
% 0.29/0.46 thf(fact_112_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ X2 @ Y2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_eq_0_iff_both_eq_0
% 0.29/0.46 thf(fact_113_add__cancel__right__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_right_right
% 0.29/0.46 thf(fact_114_add__cancel__right__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_right_left
% 0.29/0.46 thf(fact_115_add__cancel__left__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = A2 )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_left_right
% 0.29/0.46 thf(fact_116_add__cancel__left__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = A2 )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_left_left
% 0.29/0.46 thf(fact_117_double__zero__sym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_zero_sym
% 0.29/0.46 thf(fact_118_double__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_zero
% 0.29/0.46 thf(fact_119_add_Oright__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.right_neutral
% 0.29/0.46 thf(fact_120_add_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_neutral
% 0.29/0.46 thf(fact_121_add__less__cancel__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_cancel_left
% 0.29/0.46 thf(fact_122_add__less__cancel__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_cancel_right
% 0.29/0.46 thf(fact_123_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.46 thf(fact_124_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.46 thf(fact_125_le__add__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_same_cancel2
% 0.29/0.46 thf(fact_126_le__add__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_same_cancel1
% 0.29/0.46 thf(fact_127_add__le__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_same_cancel2
% 0.29/0.46 thf(fact_128_add__le__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_same_cancel1
% 0.29/0.46 thf(fact_129_add__less__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.29/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_same_cancel1
% 0.29/0.46 thf(fact_130_add__less__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_same_cancel2
% 0.29/0.46 thf(fact_131_less__add__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_add_same_cancel1
% 0.29/0.46 thf(fact_132_less__add__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_add_same_cancel2
% 0.29/0.46 thf(fact_133_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.29/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_add_less_zero_iff_single_add_less_zero
% 0.29/0.46 thf(fact_134_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_double_add_iff_zero_less_single_add
% 0.29/0.46 thf(fact_135_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.46 thf(fact_136_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( I = J )
% 0.29/0.46 & ( K = L ) )
% 0.29/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.29/0.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_semiring(4)
% 0.29/0.46 thf(fact_137_group__cancel_Oadd1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A3: A,K: A,A2: A,B2: A] :
% 0.29/0.46 ( ( A3
% 0.29/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.29/0.46 => ( ( plus_plus @ A @ A3 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % group_cancel.add1
% 0.29/0.46 thf(fact_138_group__cancel_Oadd2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [B3: A,K: A,B2: A,A2: A] :
% 0.29/0.46 ( ( B3
% 0.29/0.46 = ( plus_plus @ A @ K @ B2 ) )
% 0.29/0.46 => ( ( plus_plus @ A @ A2 @ B3 )
% 0.29/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % group_cancel.add2
% 0.29/0.46 thf(fact_139_add_Oassoc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.assoc
% 0.29/0.46 thf(fact_140_add_Oleft__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_cancel
% 0.29/0.46 thf(fact_141_add_Oright__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.right_cancel
% 0.29/0.46 thf(fact_142_add_Ocommute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ( ( plus_plus @ A )
% 0.29/0.46 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.commute
% 0.29/0.46 thf(fact_143_add_Oleft__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_commute
% 0.29/0.46 thf(fact_144_add__left__imp__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 => ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_imp_eq
% 0.29/0.46 thf(fact_145_add__right__imp__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 => ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_imp_eq
% 0.29/0.46 thf(fact_146_add__le__imp__le__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_imp_le_right
% 0.29/0.46 thf(fact_147_add__le__imp__le__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_imp_le_left
% 0.29/0.46 thf(fact_148_le__iff__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ( ( ord_less_eq @ A )
% 0.29/0.46 = ( ^ [A4: A,B4: A] :
% 0.29/0.46 ? [C3: A] :
% 0.29/0.46 ( B4
% 0.29/0.46 = ( plus_plus @ A @ A4 @ C3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_iff_add
% 0.29/0.46 thf(fact_149_add__right__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_mono
% 0.29/0.46 thf(fact_150_less__eqE,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ~ ! [C4: A] :
% 0.29/0.46 ( B2
% 0.29/0.46 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_eqE
% 0.29/0.46 thf(fact_151_add__left__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_mono
% 0.29/0.46 thf(fact_152_add__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ C2 @ D )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono
% 0.29/0.46 thf(fact_153_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.29/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_semiring(1)
% 0.29/0.46 thf(fact_154_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( I = J )
% 0.29/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_semiring(2)
% 0.29/0.46 thf(fact_155_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.29/0.46 & ( K = L ) )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_semiring(3)
% 0.29/0.46 thf(fact_156_add_Ogroup__left__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.group_left_neutral
% 0.29/0.46 thf(fact_157_add_Ocomm__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.comm_neutral
% 0.29/0.46 thf(fact_158_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % comm_monoid_add_class.add_0
% 0.29/0.46 thf(fact_159_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.29/0.46 & ( ord_less @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_field(5)
% 0.29/0.46 thf(fact_160_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( I = J )
% 0.29/0.46 & ( ord_less @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_field(2)
% 0.29/0.46 thf(fact_161_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.29/0.46 & ( K = L ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_field(1)
% 0.29/0.46 thf(fact_162_add__strict__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( strict2144017051up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less @ A @ C2 @ D )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_strict_mono
% 0.29/0.46 thf(fact_163_add__strict__left__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_strict_left_mono
% 0.29/0.46 thf(fact_164_add__strict__right__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_strict_right_mono
% 0.29/0.46 thf(fact_165_add__less__imp__less__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_imp_less_left
% 0.29/0.46 thf(fact_166_add__less__imp__less__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_imp_less_right
% 0.29/0.46 thf(fact_167_add__nonpos__eq__0__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less_eq @ A @ Y2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ( plus_plus @ A @ X2 @ Y2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonpos_eq_0_iff
% 0.29/0.46 thf(fact_168_add__nonneg__eq__0__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y2 )
% 0.29/0.46 => ( ( ( plus_plus @ A @ X2 @ Y2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonneg_eq_0_iff
% 0.29/0.46 thf(fact_169_add__nonpos__nonpos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonpos_nonpos
% 0.29/0.46 thf(fact_170_add__nonneg__nonneg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonneg_nonneg
% 0.29/0.46 thf(fact_171_add__increasing2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [C2: A,B2: A,A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.46 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_increasing2
% 0.29/0.46 thf(fact_172_add__decreasing2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_decreasing2
% 0.29/0.46 thf(fact_173_add__increasing,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_increasing
% 0.29/0.46 thf(fact_174_add__decreasing,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_decreasing
% 0.29/0.46 thf(fact_175_add__less__le__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ C2 @ D )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_le_mono
% 0.29/0.46 thf(fact_176_add__le__less__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A,D: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less @ A @ C2 @ D )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_less_mono
% 0.29/0.46 thf(fact_177_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.29/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_field(3)
% 0.29/0.46 thf(fact_178_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere223160158up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.29/0.46 & ( ord_less @ A @ K @ L ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_field(4)
% 0.29/0.46 thf(fact_179_add__neg__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_neg_neg
% 0.29/0.46 thf(fact_180_add__pos__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_pos_pos
% 0.29/0.46 thf(fact_181_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ~ ! [C4: A] :
% 0.29/0.46 ( ( B2
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C4 ) )
% 0.29/0.46 => ( C4
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % canonically_ordered_monoid_add_class.lessE
% 0.29/0.46 thf(fact_182_pos__add__strict,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( strict797366125id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % pos_add_strict
% 0.29/0.46 thf(fact_183_add__strict__increasing2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere1818651114id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_strict_increasing2
% 0.29/0.46 thf(fact_184_add__strict__increasing,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere1818651114id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_strict_increasing
% 0.29/0.46 thf(fact_185_add__pos__nonneg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_pos_nonneg
% 0.29/0.46 thf(fact_186_add__nonpos__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonpos_neg
% 0.29/0.46 thf(fact_187_add__nonneg__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_nonneg_pos
% 0.29/0.46 thf(fact_188_add__neg__nonpos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere216010020id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_neg_nonpos
% 0.29/0.46 thf(fact_189_consec__add,axiom,
% 0.29/0.46 ! [R: real_int,S2: real_int,T: real_int] :
% 0.29/0.46 ( ( ( ( left @ R )
% 0.29/0.46 = ( left @ S2 ) )
% 0.29/0.46 & ( ( right @ R )
% 0.29/0.46 = ( right @ T ) )
% 0.29/0.46 & ( ( right @ S2 )
% 0.29/0.46 = ( left @ T ) ) )
% 0.29/0.46 => ( ( real_length @ R )
% 0.29/0.46 = ( plus_plus @ real @ ( real_length @ S2 ) @ ( real_length @ T ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % consec_add
% 0.29/0.46 thf(fact_190_view_Ohorizontal__chop__empty__right,axiom,
% 0.29/0.46 ! [V2: view_ext @ product_unit] :
% 0.29/0.46 ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ V2 @ X_1 ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_empty_right
% 0.29/0.46 thf(fact_191_view_Ohorizontal__chop__empty__left,axiom,
% 0.29/0.46 ! [V2: view_ext @ product_unit] :
% 0.29/0.46 ? [U2: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ V2 ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_empty_left
% 0.29/0.46 thf(fact_192_view_Ohorizontal__chop__assoc2,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 & ( hchop @ V12 @ V33 @ V42 ) )
% 0.29/0.46 => ? [V4: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ V33 @ V4 )
% 0.29/0.46 & ( hchop @ V4 @ V42 @ V23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_assoc2
% 0.29/0.46 thf(fact_193_view_Ohorizontal__chop__assoc1,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 & ( hchop @ V23 @ V33 @ V42 ) )
% 0.29/0.46 => ? [V4: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ V4 @ V42 )
% 0.29/0.46 & ( hchop @ V4 @ V12 @ V33 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_assoc1
% 0.29/0.46 thf(fact_194_view_Ohorizontal__chop1,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit] :
% 0.29/0.46 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V @ U2 @ X_1 ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop1
% 0.29/0.46 thf(fact_195_view_Ohorizontal__chop__split__add,axiom,
% 0.29/0.46 ! [X2: real,Y2: real,V: view_ext @ product_unit] :
% 0.29/0.46 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 0.29/0.46 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 0.29/0.46 => ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 0.29/0.46 = ( plus_plus @ real @ X2 @ Y2 ) )
% 0.29/0.46 => ? [U2: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U2 @ W3 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ U2 ) )
% 0.29/0.46 = X2 )
% 0.29/0.46 & ( ( real_length @ ( ext @ product_unit @ W3 ) )
% 0.29/0.46 = Y2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_split_add
% 0.29/0.46 thf(fact_196_sensors_Olen__hchop__add,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( hchop @ V @ V12 @ V23 )
% 0.29/0.46 => ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.29/0.46 = ( plus_plus @ real @ ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.len_hchop_add
% 0.29/0.46 thf(fact_197_sensors_Oright__space,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( right @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 0.29/0.46 = ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.right_space
% 0.29/0.46 thf(fact_198_view_Ohorizontal__chop__own__trans,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U4 @ W2 )
% 0.29/0.46 => ( ( own @ product_unit @ U4 )
% 0.29/0.46 = ( own @ product_unit @ W2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_own_trans
% 0.29/0.46 thf(fact_199_view_Ohorizontal__chop__leq2,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U4 @ W2 )
% 0.29/0.46 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W2 @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_leq2
% 0.29/0.46 thf(fact_200_view_Ohorizontal__chop__leq1,axiom,
% 0.29/0.46 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.29/0.46 ( ( hchop @ V @ U4 @ W2 )
% 0.29/0.46 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % view.horizontal_chop_leq1
% 0.29/0.46 thf(fact_201_zero__less__two,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_two
% 0.29/0.46 thf(fact_202_discrete,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( unique1598680935umeral @ A )
% 0.29/0.46 => ( ( ord_less @ A )
% 0.29/0.46 = ( ^ [A4: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % discrete
% 0.29/0.46 thf(fact_203_field__le__epsilon,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ! [E4: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ E4 )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ ( plus_plus @ A @ Y2 @ E4 ) ) )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % field_le_epsilon
% 0.29/0.46 thf(fact_204_add__mono1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) @ ( plus_plus @ A @ B2 @ ( one_one @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono1
% 0.29/0.46 thf(fact_205_less__add__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_semidom @ A )
% 0.29/0.46 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_add_one
% 0.29/0.46 thf(fact_206_linorder__neqE__linordered__idom,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( X2 != Y2 )
% 0.29/0.46 => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.29/0.46 => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linorder_neqE_linordered_idom
% 0.29/0.46 thf(fact_207_linordered__field__no__ub,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A )
% 0.29/0.46 => ! [X: A] :
% 0.29/0.46 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.29/0.46
% 0.29/0.46 % linordered_field_no_ub
% 0.29/0.46 thf(fact_208_linordered__field__no__lb,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_field @ A )
% 0.29/0.46 => ! [X: A] :
% 0.29/0.46 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % linordered_field_no_lb
% 0.29/0.46 thf(fact_209_zero__neq__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero_neq_one @ A )
% 0.29/0.46 => ( ( zero_zero @ A )
% 0.29/0.46 != ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_neq_one
% 0.29/0.46 thf(fact_210_zero__le__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_le_one
% 0.29/0.46 thf(fact_211_not__one__le__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_one_le_zero
% 0.29/0.46 thf(fact_212_not__one__less__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_one_less_zero
% 0.29/0.46 thf(fact_213_zero__less__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero_less_one @ A )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_one
% 0.29/0.46 thf(fact_214_add__less__zeroD,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ X2 @ Y2 ) @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 0.29/0.46 | ( ord_less @ A @ Y2 @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_less_zeroD
% 0.29/0.46 thf(fact_215_less__numeral__extra_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_numeral_extra(1)
% 0.29/0.46 thf(fact_216_space__c,axiom,
% 0.29/0.46 ( ( space @ regular_regular @ ts @ v2 @ c )
% 0.29/0.46 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( zero_zero @ real ) @ ( one_one @ real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_c
% 0.29/0.46 thf(fact_217_hmlsl_Ospace__def,axiom,
% 0.29/0.46 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( space @ regular_regular @ Ts @ V @ C2 )
% 0.29/0.46 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( pos @ Ts @ C2 ) @ ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % hmlsl.space_def
% 0.29/0.46 thf(fact_218_len__c,axiom,
% 0.29/0.46 ( ( len @ regular_regular @ v2 @ ts @ c )
% 0.29/0.46 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( zero_zero @ real ) @ ( one_one @ real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % len_c
% 0.29/0.46 thf(fact_219_sensors_Ospace__def,axiom,
% 0.29/0.46 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 0.29/0.46 ( ( sensors @ Sensors )
% 0.29/0.46 => ( ( space @ Sensors @ Ts @ V @ C2 )
% 0.29/0.46 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( pos @ Ts @ C2 ) @ ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sensors.space_def
% 0.29/0.46 thf(fact_220_is__num__normalize_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( neg_numeral @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_num_normalize(1)
% 0.29/0.46 thf(fact_221_le__numeral__extra_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_numeral_extra(3)
% 0.29/0.46 thf(fact_222_less__numeral__extra_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_numeral_extra(3)
% 0.29/0.46 thf(fact_223_le__numeral__extra_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_numeral_extra(4)
% 0.29/0.46 thf(fact_224_less__numeral__extra_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_numeral_extra(4)
% 0.29/0.46 thf(fact_225_divides__aux__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( unique1598680935umeral @ A )
% 0.29/0.46 => ! [Q: A,R: A] :
% 0.29/0.46 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q @ R ) )
% 0.29/0.46 = ( R
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % divides_aux_eq
% 0.29/0.46 thf(fact_226_real__int__class_Oshift__def,axiom,
% 0.29/0.46 ( real_shift
% 0.29/0.46 = ( ^ [R2: real_int,X4: real] : ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( plus_plus @ real @ ( left @ R2 ) @ X4 ) @ ( plus_plus @ real @ ( right @ R2 ) @ X4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % real_int_class.shift_def
% 0.29/0.46 thf(fact_227_shift__additivity,axiom,
% 0.29/0.46 ! [R: real_int,X2: real,Y2: real] :
% 0.29/0.46 ( ( real_shift @ R @ ( plus_plus @ real @ X2 @ Y2 ) )
% 0.29/0.46 = ( real_shift @ ( real_shift @ R @ X2 ) @ Y2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % shift_additivity
% 0.29/0.46 thf(fact_228_shift__keeps__length,axiom,
% 0.29/0.46 ! [X2: real] :
% 0.29/0.46 ( real_length
% 0.29/0.46 = ( ^ [R2: real_int] : ( real_length @ ( real_shift @ R2 @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % shift_keeps_length
% 0.29/0.46 thf(fact_229_shift__zero,axiom,
% 0.29/0.46 ! [R: real_int] :
% 0.29/0.46 ( ( real_shift @ R @ ( zero_zero @ real ) )
% 0.29/0.46 = R ) ).
% 0.29/0.46
% 0.29/0.46 % shift_zero
% 0.29/0.46 thf(fact_230_shift__left__eq__right,axiom,
% 0.29/0.46 ! [R: real_int,X2: real] : ( ord_less_eq @ real @ ( left @ ( real_shift @ R @ X2 ) ) @ ( right @ ( real_shift @ R @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % shift_left_eq_right
% 0.29/0.46 thf(fact_231_ts__rep__def,axiom,
% 0.29/0.46 ( ts_rep
% 0.29/0.46 = ( product_Pair @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) @ po @ ( product_Pair @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) @ re @ ( product_Pair @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) @ cl @ ( product_Pair @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) @ dy @ ( product_Pair @ ( cars > real ) @ ( cars > real ) @ ps @ sd ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ts_rep_def
% 0.29/0.46 thf(fact_232_order__refl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( preorder @ A )
% 0.29/0.46 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_refl
% 0.29/0.46 thf(fact_233_clm__def,axiom,
% 0.29/0.46 ! [C: cars] :
% 0.29/0.46 ( ( cl @ C )
% 0.29/0.46 = ( bot_bot @ nat_int ) ) ).
% 0.29/0.46
% 0.29/0.46 % clm_def
% 0.29/0.46 thf(fact_234_dual__order_Oantisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.antisym
% 0.29/0.46 thf(fact_235_dual__order_Oeq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.29/0.46 = ( ^ [A4: A,B4: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.29/0.46 & ( ord_less_eq @ A @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.eq_iff
% 0.29/0.46 thf(fact_236_dual__order_Otrans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.29/0.46 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.trans
% 0.29/0.46 thf(fact_237_linorder__wlog,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.29/0.46 ( ! [A5: A,B5: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.29/0.46 => ( P @ A5 @ B5 ) )
% 0.29/0.46 => ( ! [A5: A,B5: A] :
% 0.29/0.46 ( ( P @ B5 @ A5 )
% 0.29/0.46 => ( P @ A5 @ B5 ) )
% 0.29/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linorder_wlog
% 0.29/0.46 thf(fact_238_dual__order_Orefl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % dual_order.refl
% 0.29/0.46 thf(fact_239_order__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( preorder @ A )
% 0.29/0.46 => ! [X2: A,Y2: A,Z3: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_trans
% 0.29/0.46 thf(fact_240_order__class_Oorder_Oantisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_class.order.antisym
% 0.29/0.46 thf(fact_241_ord__le__eq__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( B2 = C2 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_le_eq_trans
% 0.29/0.46 thf(fact_242_ord__eq__le__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( A2 = B2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ord_eq_le_trans
% 0.29/0.46 thf(fact_243_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.29/0.46 = ( ^ [A4: A,B4: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.29/0.46 & ( ord_less_eq @ A @ B4 @ A4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order_class.order.eq_iff
% 0.29/0.46 thf(fact_244_antisym__conv,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [Y2: A,X2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 = ( X2 = Y2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % antisym_conv
% 0.29/0.46 thf(fact_245_le__cases3,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y2: A,Z3: A] :
% 0.29/0.46 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.29/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 0.29/0.46 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.29/0.46 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_cases3
% 0.29/0.46 thf(fact_246_order_Otrans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.29/0.46 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % order.trans
% 0.29/0.46 thf(fact_247_le__cases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_cases
% 0.29/0.46 thf(fact_248_eq__refl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( preorder @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( X2 = Y2 )
% 0.29/0.46 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_refl
% 0.29/0.46 thf(fact_249_linear,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linear
% 0.29/0.46 thf(fact_250_antisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ! [X2: A,Y2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.29/0.46 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.29/0.46 => ( X2 = Y2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % antisym
% 0.29/0.46 thf(fact_251_eq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( order @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.29/0.46 = ( ^ [X4: A,Y: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X4 @ Y )
% 0.29/0.46 & ( ord_less_eq @ A @ Y @ X4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_iff
% 0.29/0.46
% 0.29/0.46 % Type constructors (49)
% 0.29/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( preorder @ A7 )
% 0.29/0.46 => ( preorder @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( order @ A7 )
% 0.29/0.46 => ( order @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ord @ A7 )
% 0.29/0.46 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 0.29/0.46 preorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.29/0.46 linorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.29/0.46 order @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oord_3,axiom,
% 0.29/0.46 ord @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.29/0.46 ordere516151231imp_le @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.29/0.46 strict2144017051up_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.29/0.46 ordere223160158up_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.29/0.46 ordere236663937imp_le @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.29/0.46 strict797366125id_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 0.29/0.46 ordere1818651114id_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring,axiom,
% 0.29/0.46 linord1659791738miring @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add,axiom,
% 0.29/0.46 ordere779506340up_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add,axiom,
% 0.29/0.46 ordere216010020id_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.29/0.46 linord219039673up_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add,axiom,
% 0.29/0.46 cancel1352612707id_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add,axiom,
% 0.29/0.46 cancel_semigroup_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Rings_Olinordered__semidom,axiom,
% 0.29/0.46 linordered_semidom @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add,axiom,
% 0.29/0.46 ab_semigroup_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 0.29/0.46 linordered_field @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add,axiom,
% 0.29/0.46 comm_monoid_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.29/0.46 linordered_idom @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Osemigroup__add,axiom,
% 0.29/0.46 semigroup_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Rings_Ozero__less__one,axiom,
% 0.29/0.46 zero_less_one @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Rings_Ozero__neq__one,axiom,
% 0.29/0.46 zero_neq_one @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Opreorder_4,axiom,
% 0.29/0.46 preorder @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Olinorder_5,axiom,
% 0.29/0.46 linorder @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Omonoid__add,axiom,
% 0.29/0.46 monoid_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.29/0.46 group_add @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Oorder_6,axiom,
% 0.29/0.46 order @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.29/0.46 neg_numeral @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Orderings_Oord_7,axiom,
% 0.29/0.46 ord @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Ozero,axiom,
% 0.29/0.46 zero @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Groups_Oone,axiom,
% 0.29/0.46 one @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_8,axiom,
% 0.29/0.46 preorder @ nat_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_NatInt_Onat__int___Orderings_Oorder_9,axiom,
% 0.29/0.46 order @ nat_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_NatInt_Onat__int___Orderings_Oord_10,axiom,
% 0.29/0.46 ord @ nat_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_11,axiom,
% 0.29/0.46 preorder @ real_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_12,axiom,
% 0.29/0.46 order @ real_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_RealInt_Oreal__int___Orderings_Oord_13,axiom,
% 0.29/0.46 ord @ real_int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_14,axiom,
% 0.29/0.46 preorder @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_15,axiom,
% 0.29/0.46 linorder @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder_16,axiom,
% 0.29/0.46 order @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oord_17,axiom,
% 0.29/0.46 ord @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_18,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( order @ A6 )
% 0.29/0.46 => ( preorder @ ( view_ext @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_19,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( order @ A6 )
% 0.29/0.46 => ( order @ ( view_ext @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_20,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( order @ A6 )
% 0.29/0.46 => ( ord @ ( view_ext @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext @ product_unit @ v ) ) )
% 0.29/0.46 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.85/1.55 ---- Embedded in THF ---
% 2.85/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.56 %%% Generated on Tue Feb 24 08:28:43 EST 2026
% 2.85/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.56 %%% Logic specification used:
% 2.85/1.56 %%% thf(spec, logic, $$dhol).
% 2.85/1.56
% 2.85/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2DTF15185.p
% 2.85/1.56 thf(ty_t_Views_Oview_Oview__ext, type, view_ext: ($tType > $tType)).
% 2.85/1.56 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.85/1.56 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.85/1.56 thf(ty_t_RealInt_Oreal__int, type, real_int: $tType).
% 2.85/1.56 thf(ty_t_Traffic_Otraffic, type, traffic: $tType).
% 2.85/1.56 thf(ty_t_NatInt_Onat__int, type, nat_int: $tType).
% 2.85/1.56 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.85/1.56 thf(ty_t_Cars_Ocars, type, cars: $tType).
% 2.85/1.56 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add, type, ordere1818651114id_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add, type, strict797366125id_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral, type, unique1598680935umeral: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 2.85/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux, type, unique455577585es_aux: (!> [A:$tType]: ((((product_prod @ A) @ A) > $o)))).
% 2.85/1.56 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.85/1.56 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.85/1.56 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.85/1.56 thf(sy_c_Length_Osensors_Olen, type, len: ((cars > (traffic > (cars > real))) > ((view_ext @ product_unit) > (traffic > (cars > real_int))))).
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.85/1.56 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.85/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.85/1.56 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.85/1.56 thf(sy_c_RealInt_Oleft, type, left: (real_int > real)).
% 2.85/1.56 thf(sy_c_RealInt_Oreal__int_OAbs__real__int, type, real_Abs_real_int: (((product_prod @ real) @ real) > real_int)).
% 2.85/1.56 thf(sy_c_RealInt_Oreal__int_Olength, type, real_length: (real_int > real)).
% 2.85/1.56 thf(sy_c_RealInt_Oreal__int_Oshift, type, real_shift: (real_int > (real > real_int))).
% 2.85/1.56 thf(sy_c_RealInt_Oright, type, right: (real_int > real)).
% 2.85/1.56 thf(sy_c_Regular__Sensors_Oregular, type, regular_regular: (cars > (traffic > (cars > real)))).
% 2.85/1.56 thf(sy_c_Sensors_Osensors, type, sensors: ((cars > (traffic > (cars > real))) > $o)).
% 2.85/1.56 thf(sy_c_Sensors_Osensors_Ospace, type, space: ((cars > (traffic > (cars > real))) > (traffic > ((view_ext @ product_unit) > (cars > real_int))))).
% 2.85/1.56 thf(sy_c_Traffic_Otraffic_OAbs__traffic, type, abs_traffic: (((product_prod @ (cars > real)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real)))))) > traffic)).
% 2.85/1.56 thf(sy_c_Traffic_Otraffic_Ophysical__size, type, physical_size: (traffic > (cars > real))).
% 2.85/1.56 thf(sy_c_Traffic_Otraffic_Opos, type, pos: (traffic > (cars > real))).
% 2.85/1.56 thf(sy_c_Views_Oview_Oext, type, ext: (!> [Z:$tType]: (((view_ext @ Z) > real_int)))).
% 2.85/1.56 thf(sy_c_Views_Oview_Ohchop, type, hchop: ((view_ext @ product_unit) > ((view_ext @ product_unit) > ((view_ext @ product_unit) > $o)))).
% 2.85/1.56 thf(sy_c_Views_Oview_Oown, type, own: (!> [Z:$tType]: (((view_ext @ Z) > cars)))).
% 2.85/1.56 thf(sy_v_c____, type, c: cars).
% 2.85/1.56 thf(sy_v_cl____, type, cl: (cars > nat_int)).
% 2.85/1.56 thf(sy_v_d____, type, d: cars).
% 2.85/1.56 thf(sy_v_dy____, type, dy: (cars > (real > real))).
% 2.85/1.56 thf(sy_v_po____, type, po: (cars > real)).
% 2.85/1.56 thf(sy_v_ps____, type, ps: (cars > real)).
% 2.85/1.56 thf(sy_v_re____, type, re: (cars > nat_int)).
% 2.85/1.56 thf(sy_v_sd____, type, sd: (cars > real)).
% 2.85/1.56 thf(sy_v_ts____, type, ts: traffic).
% 2.85/1.56 thf(sy_v_ts__rep____, type, ts_rep: ((product_prod @ (cars > real)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real))))))).
% 2.85/1.56 thf(sy_v_v_H____, type, v: (view_ext @ product_unit)).
% 2.85/1.56 thf(sy_v_v____, type, v2: (view_ext @ product_unit)).
% 2.85/1.56 thf(fact_0__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062dy_O_A_092_060forall_062c_Ax_O_Ady_Ac_Ax_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Dy:(cars > (real > real))]: ((~ ((! [C:cars,X:real]: ((((Dy @ C) @ X) = (zero_zero @ real))))))))))).
% 2.85/1.56 thf(fact_1_dyn__def, axiom, (! [C:cars,X:real]: ((((dy @ C) @ X) = (zero_zero @ real))))).
% 2.85/1.56 thf(fact_2_local_Ohmlsl_Osensors__ge, axiom, (! [E:cars,Ts:traffic,C2:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (((regular_regular @ E) @ Ts) @ C2))))).
% 2.85/1.56 thf(fact_3_hmlsl_Olen__non__empty__inside, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2))) => ((((ord_less @ real) @ (left @ ((((space @ regular_regular) @ Ts) @ V) @ C2))) @ (right @ ((ext @ product_unit) @ V))) & (((ord_less @ real) @ (left @ ((ext @ product_unit) @ V))) @ (right @ ((((space @ regular_regular) @ Ts) @ V) @ C2)))))))).
% 2.85/1.56 thf(fact_4_v_H__d, axiom, (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ v) @ ts) @ d)))).
% 2.85/1.56 thf(fact_5_hmlsl_Ospace__nonempty, axiom, (! [Ts:traffic,V:(view_ext @ product_unit),C2:cars]: ((((ord_less @ real) @ (left @ ((((space @ regular_regular) @ Ts) @ V) @ C2))) @ (right @ ((((space @ regular_regular) @ Ts) @ V) @ C2)))))).
% 2.85/1.56 thf(fact_6_ts__def, axiom, (ts = (abs_traffic @ ts_rep))).
% 2.85/1.56 thf(fact_7_assumption, axiom, (d != c)).
% 2.85/1.56 thf(fact_8_local_Ohmlsl_Olength__geq__zero, axiom, (! [Ts2:traffic,V2:(view_ext @ product_unit)]: ((((real_length @ ((ext @ product_unit) @ V2)) = (zero_zero @ real)) | (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))))))).
% 2.85/1.56 thf(fact_9_v_H__rel__c, axiom, ((((ord_less @ real) @ (left @ ((((space @ regular_regular) @ ts) @ v) @ c))) @ (right @ ((ext @ product_unit) @ v))) & (((ord_less @ real) @ (left @ ((ext @ product_unit) @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ c))))).
% 2.85/1.56 thf(fact_10_hmlsl_Oleft__space, axiom, (! [Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((left @ ((((space @ regular_regular) @ Ts) @ V) @ C2)) = ((pos @ Ts) @ C2))))).
% 2.85/1.56 thf(fact_11_len__eq, axiom, (((((len @ regular_regular) @ v) @ ts) @ c) = ((((len @ regular_regular) @ v) @ ts) @ d))).
% 2.85/1.56 thf(fact_12_hmlsl_Olen__space__left, axiom, (! [Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((((ord_less_eq @ real) @ (left @ ((((space @ regular_regular) @ Ts) @ V) @ C2))) @ (right @ ((ext @ product_unit) @ V))) => (((ord_less_eq @ real) @ (left @ ((((space @ regular_regular) @ Ts) @ V) @ C2))) @ (left @ ((((len @ regular_regular) @ V) @ Ts) @ C2))))))).
% 2.85/1.56 thf(fact_13_hmlsl_Olen__space__right, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ V))) @ (right @ ((((space @ regular_regular) @ Ts) @ V) @ C2))) => (((ord_less_eq @ real) @ (right @ ((((len @ regular_regular) @ V) @ Ts) @ C2))) @ (right @ ((((space @ regular_regular) @ Ts) @ V) @ C2))))))).
% 2.85/1.56 thf(fact_14_regular__sensors_Osensors__le, axiom, (! [E:cars,C2:cars,Ts:traffic]: (((E != C2) => (((ord_less @ real) @ (((regular_regular @ E) @ Ts) @ C2)) @ (((regular_regular @ C2) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_15_ps__ge__zero, axiom, (! [C:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (ps @ C))))).
% 2.85/1.56 thf(fact_16_sd__ge__zero, axiom, (! [C:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (sd @ C))))).
% 2.85/1.56 thf(fact_17_hmlsl_Olen__left, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ V))) @ (left @ ((((len @ regular_regular) @ V) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_18_hmlsl_Olen__right, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((ord_less_eq @ real) @ (right @ ((((len @ regular_regular) @ V) @ Ts) @ C2))) @ (right @ ((ext @ product_unit) @ V)))))).
% 2.85/1.56 thf(fact_19_v_H__c, axiom, (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ v) @ ts) @ c)))).
% 2.85/1.56 thf(fact_20_hmlsl_Osensors__axioms, axiom, (sensors @ regular_regular)).
% 2.85/1.56 thf(fact_21_dyn__geq__zero, axiom, (! [C:cars,X:real]: ((((ord_less_eq @ real) @ (zero_zero @ real)) @ ((dy @ C) @ X))))).
% 2.85/1.56 thf(fact_22_ps__def, axiom, (! [C:cars]: (((ps @ C) = (one_one @ real))))).
% 2.85/1.56 thf(fact_23_regular__sensors_Osensors__leq, axiom, (! [E:cars,Ts:traffic,C2:cars]: ((((ord_less_eq @ real) @ (((regular_regular @ E) @ Ts) @ C2)) @ (((regular_regular @ C2) @ Ts) @ C2))))).
% 2.85/1.56 thf(fact_24_sensors_Olen__non__empty__inside, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2))) => ((((ord_less @ real) @ (left @ ((((space @ Sensors) @ Ts) @ V) @ C2))) @ (right @ ((ext @ product_unit) @ V))) & (((ord_less @ real) @ (left @ ((ext @ product_unit) @ V))) @ (right @ ((((space @ Sensors) @ Ts) @ V) @ C2))))))))).
% 2.85/1.56 thf(fact_25_other__len__zero, axiom, (! [E2:cars]: ((((E2 != c) & (E2 != d)) => ((real_length @ ((((len @ regular_regular) @ v2) @ ts) @ E2)) = (zero_zero @ real)))))).
% 2.85/1.56 thf(fact_26_sensors_Olen__space__right, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => ((((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ V))) @ (right @ ((((space @ Sensors) @ Ts) @ V) @ C2))) => (((ord_less_eq @ real) @ (right @ ((((len @ Sensors) @ V) @ Ts) @ C2))) @ (right @ ((((space @ Sensors) @ Ts) @ V) @ C2)))))))).
% 2.85/1.56 thf(fact_27_sensors_Olen__space__left, axiom, (! [Sensors:(cars > (traffic > (cars > real))),Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((sensors @ Sensors) => ((((ord_less_eq @ real) @ (left @ ((((space @ Sensors) @ Ts) @ V) @ C2))) @ (right @ ((ext @ product_unit) @ V))) => (((ord_less_eq @ real) @ (left @ ((((space @ Sensors) @ Ts) @ V) @ C2))) @ (left @ ((((len @ Sensors) @ V) @ Ts) @ C2)))))))).
% 2.85/1.56 thf(fact_28_lc, axiom, ((left @ ((((space @ regular_regular) @ ts) @ v2) @ c)) = (zero_zero @ real))).
% 2.85/1.56 thf(fact_29_sensors_Ospace__nonempty, axiom, (! [Sensors:(cars > (traffic > (cars > real))),Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((sensors @ Sensors) => (((ord_less @ real) @ (left @ ((((space @ Sensors) @ Ts) @ V) @ C2))) @ (right @ ((((space @ Sensors) @ Ts) @ V) @ C2))))))).
% 2.85/1.56 thf(fact_30_sensors_Olen__right, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((ord_less_eq @ real) @ (right @ ((((len @ Sensors) @ V) @ Ts) @ C2))) @ (right @ ((ext @ product_unit) @ V))))))).
% 2.85/1.56 thf(fact_31_sensors_Olen__left, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ V))) @ (left @ ((((len @ Sensors) @ V) @ Ts) @ C2))))))).
% 2.85/1.56 thf(fact_32_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_33_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_34__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Ps:(cars > real)]: ((~ ((! [C:cars]: (((Ps @ C) = (one_one @ real))))))))))).
% 2.85/1.56 thf(fact_35_hmlsl_Olen__sub__int, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((ord_less_eq @ real_int) @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) @ ((ext @ product_unit) @ V))))).
% 2.85/1.56 thf(fact_36_hmlsl_Olen__empty__subview, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V3:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((ord_less_eq @ (view_ext @ product_unit)) @ V3) @ V)) => ((real_length @ ((((len @ regular_regular) @ V3) @ Ts) @ C2)) = (zero_zero @ real)))))).
% 2.85/1.56 thf(fact_37_lv, axiom, ((left @ ((ext @ product_unit) @ v2)) = (zero_zero @ real))).
% 2.85/1.56 thf(fact_38_rc, axiom, ((right @ ((((space @ regular_regular) @ ts) @ v2) @ c)) = (one_one @ real))).
% 2.85/1.56 thf(fact_39_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X2:A]: ((((one_one @ A) = X2) = (X2 = (one_one @ A))))))))).
% 2.85/1.56 thf(fact_40_sensors_Olen__sub__int, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((ord_less_eq @ real_int) @ ((((len @ Sensors) @ V) @ Ts) @ C2)) @ ((ext @ product_unit) @ V)))))).
% 2.85/1.56 thf(fact_41_sensors_Olen__empty__subview, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V3:(view_ext @ product_unit)]: (((sensors @ Sensors) => ((((real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((ord_less_eq @ (view_ext @ product_unit)) @ V3) @ V)) => ((real_length @ ((((len @ Sensors) @ V3) @ Ts) @ C2)) = (zero_zero @ real))))))).
% 2.85/1.56 thf(fact_42_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.85/1.56 thf(fact_43_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X2:A]: ((((zero_zero @ A) = X2) = (X2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_44_sensors_Olen_Ocong, axiom, (len = len)).
% 2.85/1.56 thf(fact_45_sensors_Ospace_Ocong, axiom, (space = space)).
% 2.85/1.56 thf(fact_46_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2))))))).
% 2.85/1.56 thf(fact_47_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.85/1.56 thf(fact_48_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_49_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_50_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_51_sensors__def, axiom, (sensors = (^ [Sensors2:(cars > (traffic > (cars > real)))]: ((! [E3:cars,Ts3:traffic,C3:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (((Sensors2 @ E3) @ Ts3) @ C3)))))))).
% 2.85/1.56 thf(fact_52_sensors_Ointro, axiom, (! [Sensors:(cars > (traffic > (cars > real)))]: (((! [E4:cars,Ts4:traffic,C4:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ (((Sensors @ E4) @ Ts4) @ C4)))) => (sensors @ Sensors))))).
% 2.85/1.56 thf(fact_53_sensors_Osensors__ge, axiom, (! [Sensors:(cars > (traffic > (cars > real))),E:cars,Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((ord_less @ real) @ (zero_zero @ real)) @ (((Sensors @ E) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_54_sensors_Oleft__space, axiom, (! [Sensors:(cars > (traffic > (cars > real))),Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((sensors @ Sensors) => ((left @ ((((space @ Sensors) @ Ts) @ V) @ C2)) = ((pos @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_55_size, axiom, (! [C:cars]: ((((physical_size @ ts) @ C) = (one_one @ real))))).
% 2.85/1.56 thf(fact_56_sensors__c, axiom, ((((regular_regular @ ((own @ product_unit) @ v2)) @ ts) @ c) = (one_one @ real))).
% 2.85/1.56 thf(fact_57_hmlsl_Oview__leq__len__leq, axiom, (! [V:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((((ord_less_eq @ real_int) @ ((ext @ product_unit) @ V)) @ ((ext @ product_unit) @ V3)) & ((((own @ product_unit) @ V) = ((own @ product_unit) @ V3)) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2))))) => (((ord_less_eq @ real_int) @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) @ ((((len @ regular_regular) @ V3) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_58_length__zero__iff__borders__eq, axiom, (! [R:real_int]: ((((real_length @ R) = (zero_zero @ real)) = ((left @ R) = (right @ R)))))).
% 2.85/1.56 thf(fact_59_hmlsl_Olen__fills__subview, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2))) => (? [V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V32:(view_ext @ product_unit),V4:(view_ext @ product_unit)]: (((((hchop @ V) @ V1) @ V22) & ((((hchop @ V22) @ V4) @ V32) & ((((((len @ regular_regular) @ V4) @ Ts) @ C2) = ((ext @ product_unit) @ V4)) & ((real_length @ ((((len @ regular_regular) @ V4) @ Ts) @ C2)) = (real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2)))))))))))).
% 2.85/1.56 thf(fact_60_less__real__int__def, axiom, ((ord_less @ real_int) = (^ [R2:real_int,S:real_int]: (((((ord_less_eq @ real) @ (left @ S)) @ (left @ R2)) & ((((ord_less_eq @ real) @ (right @ R2)) @ (right @ S)) & (~ (((((ord_less_eq @ real) @ (left @ R2)) @ (left @ S)) & (((ord_less_eq @ real) @ (right @ S)) @ (right @ R2))))))))))).
% 2.85/1.56 thf(fact_61_less__eq__real__int__def, axiom, ((ord_less_eq @ real_int) = (^ [R2:real_int,S:real_int]: (((((ord_less_eq @ real) @ (left @ S)) @ (left @ R2)) & (((ord_less_eq @ real) @ (right @ R2)) @ (right @ S))))))).
% 2.85/1.56 thf(fact_62_left__leq__right, axiom, (! [R:real_int]: ((((ord_less_eq @ real) @ (left @ R)) @ (right @ R))))).
% 2.85/1.56 thf(fact_63_length__ge__zero, axiom, (! [R:real_int]: ((((ord_less_eq @ real) @ (zero_zero @ real)) @ (real_length @ R))))).
% 2.85/1.56 thf(fact_64_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,V2:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Phi @ Ts2) @ W) & (? [X4:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ U) @ X4) @ Y) & (((Psi @ Ts2) @ X4) & ((Chi @ Ts2) @ Y))))))))) = (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & ((? [X4:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ W) @ X4) @ Y) & (((Phi @ Ts2) @ X4) & ((Psi @ Ts2) @ Y))))) & ((Chi @ Ts2) @ U))))))))).
% 2.85/1.56 thf(fact_65_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,V2:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Phi @ Ts2) @ W) & (((Psi @ Ts2) @ U) | ((Chi @ Ts2) @ U)))))) = ((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Phi @ Ts2) @ W) & ((Psi @ Ts2) @ U))))) | (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Phi @ Ts2) @ W) & ((Chi @ Ts2) @ U)))))))))).
% 2.85/1.56 thf(fact_66_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,V2:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & ((((Psi @ Ts2) @ W) | ((Chi @ Ts2) @ W)) & ((Phi @ Ts2) @ U))))) = ((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Psi @ Ts2) @ W) & ((Phi @ Ts2) @ U))))) | (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((Chi @ Ts2) @ W) & ((Phi @ Ts2) @ U)))))))))).
% 2.85/1.56 thf(fact_67_local_Ohmlsl_Ohchop__neg1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V2:(view_ext @ product_unit)]: (((~ ((? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ Va) @ X_1))) & ((Phi @ Ts2) @ Va)))))) => (? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ Va) @ X_1))) & (~ (((Phi @ Ts2) @ Va)))))))))).
% 2.85/1.56 thf(fact_68_local_Ohmlsl_Ohchop__neg2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V2:(view_ext @ product_unit)]: (((~ ((? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & ((Phi @ Ts2) @ U2)))))) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & (~ (((Phi @ Ts2) @ U2)))))))))).
% 2.85/1.56 thf(fact_69_local_Ohmlsl_Ohchop__weaken, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V2:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V2) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & (? [Vb:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ U2) @ Vb) @ X_1))) & ((Phi @ Ts2) @ Vb))))))))))).
% 2.85/1.56 thf(fact_70_local_Ohmlsl_Ohchop__weaken1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V2:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V2) => (? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ Va) @ X_1))) & ((Phi @ Ts2) @ Va)))))))).
% 2.85/1.56 thf(fact_71_local_Ohmlsl_Ohchop__weaken2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts2:traffic,V2:(view_ext @ product_unit)]: ((((Phi @ Ts2) @ V2) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & ((Phi @ Ts2) @ U2)))))))).
% 2.85/1.56 thf(fact_72_hmlsl_Olen__view__hchop__right, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => (((((len @ regular_regular) @ V23) @ Ts) @ C2) = ((ext @ product_unit) @ V23)))))).
% 2.85/1.56 thf(fact_73_hmlsl_Olen__view__hchop__left, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => (((((len @ regular_regular) @ V12) @ Ts) @ C2) = ((ext @ product_unit) @ V12)))))).
% 2.85/1.56 thf(fact_74_hmlsl_Olen__compose__hchop, axiom, (! [V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((((hchop @ V) @ V12) @ V23) & ((((((len @ regular_regular) @ V12) @ Ts) @ C2) = ((ext @ product_unit) @ V12)) & (((((len @ regular_regular) @ V23) @ Ts) @ C2) = ((ext @ product_unit) @ V23)))) => (((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)))))).
% 2.85/1.56 thf(fact_75_hmlsl_Oext__eq__len__eq, axiom, (! [V:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C2:cars]: ((((((ext @ product_unit) @ V) = ((ext @ product_unit) @ V3)) & (((own @ product_unit) @ V) = ((own @ product_unit) @ V3))) => (((((len @ regular_regular) @ V) @ Ts) @ C2) = ((((len @ regular_regular) @ V3) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_76_local_Ohmlsl_Olength__split, axiom, (! [Ts2:traffic,V2:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))))))))))).
% 2.85/1.56 thf(fact_77_local_Ohmlsl_Olength__meld, axiom, (! [Ts2:traffic,V2:(view_ext @ product_unit)]: (((? [Va2:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va2) @ U3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ Va2))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U3))))))) => (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))))))).
% 2.85/1.56 thf(fact_78_local_Ohmlsl_Olength__dense, axiom, (! [Ts2:traffic,V2:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V2))) = (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U))))))))))).
% 2.85/1.56 thf(fact_79_hmlsl_Olen__empty__on__subview2, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((hchop @ V) @ V12) @ V23)) => ((real_length @ ((((len @ regular_regular) @ V23) @ Ts) @ C2)) = (zero_zero @ real)))))).
% 2.85/1.56 thf(fact_80_hmlsl_Olen__empty__on__subview1, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((((real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((hchop @ V) @ V12) @ V23)) => ((real_length @ ((((len @ regular_regular) @ V12) @ Ts) @ C2)) = (zero_zero @ real)))))).
% 2.85/1.56 thf(fact_81_hmlsl_Olen__hchop__right__right__border, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((right @ ((((len @ regular_regular) @ V23) @ Ts) @ C2)) = (right @ ((ext @ product_unit) @ V23))))))).
% 2.85/1.56 thf(fact_82_hmlsl_Olen__hchop__right__left__border, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((left @ ((((len @ regular_regular) @ V23) @ Ts) @ C2)) = (left @ ((ext @ product_unit) @ V23))))))).
% 2.85/1.56 thf(fact_83_hmlsl_Olen__hchop__left__right__border, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((right @ ((((len @ regular_regular) @ V12) @ Ts) @ C2)) = (right @ ((ext @ product_unit) @ V12))))))).
% 2.85/1.56 thf(fact_84_hmlsl_Olen__hchop__left__left__border, axiom, (! [V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: ((((((((len @ regular_regular) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((left @ ((((len @ regular_regular) @ V12) @ Ts) @ C2)) = (left @ ((ext @ product_unit) @ V12))))))).
% 2.85/1.56 thf(fact_85_regular__sensors_Ospace__eq, axiom, (! [V:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((((own @ product_unit) @ V) = ((own @ product_unit) @ V3)) => (((((space @ regular_regular) @ Ts) @ V) @ C2) = ((((space @ regular_regular) @ Ts) @ V3) @ C2)))))).
% 2.85/1.56 thf(fact_86_sensors_Olen__compose__hchop, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((((hchop @ V) @ V12) @ V23) & ((((((len @ Sensors) @ V12) @ Ts) @ C2) = ((ext @ product_unit) @ V12)) & (((((len @ Sensors) @ V23) @ Ts) @ C2) = ((ext @ product_unit) @ V23)))) => (((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V))))))).
% 2.85/1.56 thf(fact_87_sensors_Olen__view__hchop__left, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => (((((len @ Sensors) @ V12) @ Ts) @ C2) = ((ext @ product_unit) @ V12))))))).
% 2.85/1.56 thf(fact_88_sensors_Olen__view__hchop__right, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => (((((len @ Sensors) @ V23) @ Ts) @ C2) = ((ext @ product_unit) @ V23))))))).
% 2.85/1.56 thf(fact_89_sensors_Oext__eq__len__eq, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((((ext @ product_unit) @ V) = ((ext @ product_unit) @ V3)) & (((own @ product_unit) @ V) = ((own @ product_unit) @ V3))) => (((((len @ Sensors) @ V) @ Ts) @ C2) = ((((len @ Sensors) @ V3) @ Ts) @ C2))))))).
% 2.85/1.56 thf(fact_90_sensors_Olen__empty__on__subview1, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => ((((real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((hchop @ V) @ V12) @ V23)) => ((real_length @ ((((len @ Sensors) @ V12) @ Ts) @ C2)) = (zero_zero @ real))))))).
% 2.85/1.56 thf(fact_91_sensors_Olen__empty__on__subview2, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => ((((real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2)) = (zero_zero @ real)) & (((hchop @ V) @ V12) @ V23)) => ((real_length @ ((((len @ Sensors) @ V23) @ Ts) @ C2)) = (zero_zero @ real))))))).
% 2.85/1.56 thf(fact_92_sensors_Olen__hchop__right__right__border, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((right @ ((((len @ Sensors) @ V23) @ Ts) @ C2)) = (right @ ((ext @ product_unit) @ V23)))))))).
% 2.85/1.56 thf(fact_93_sensors_Olen__hchop__right__left__border, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((left @ ((((len @ Sensors) @ V23) @ Ts) @ C2)) = (left @ ((ext @ product_unit) @ V23)))))))).
% 2.85/1.56 thf(fact_94_sensors_Olen__hchop__left__right__border, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((right @ ((((len @ Sensors) @ V12) @ Ts) @ C2)) = (right @ ((ext @ product_unit) @ V12)))))))).
% 2.85/1.56 thf(fact_95_sensors_Olen__hchop__left__left__border, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars,V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((sensors @ Sensors) => (((((((len @ Sensors) @ V) @ Ts) @ C2) = ((ext @ product_unit) @ V)) & (((hchop @ V) @ V12) @ V23)) => ((left @ ((((len @ Sensors) @ V12) @ Ts) @ C2)) = (left @ ((ext @ product_unit) @ V12)))))))).
% 2.85/1.56 thf(fact_96_sensors_Olen__fills__subview, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2))) => (? [V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V32:(view_ext @ product_unit),V4:(view_ext @ product_unit)]: (((((hchop @ V) @ V1) @ V22) & ((((hchop @ V22) @ V4) @ V32) & ((((((len @ Sensors) @ V4) @ Ts) @ C2) = ((ext @ product_unit) @ V4)) & ((real_length @ ((((len @ Sensors) @ V4) @ Ts) @ C2)) = (real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2))))))))))))).
% 2.85/1.56 thf(fact_97_sensors_Oview__leq__len__leq, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),V3:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => (((((ord_less_eq @ real_int) @ ((ext @ product_unit) @ V)) @ ((ext @ product_unit) @ V3)) & ((((own @ product_unit) @ V) = ((own @ product_unit) @ V3)) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2))))) => (((ord_less_eq @ real_int) @ ((((len @ Sensors) @ V) @ Ts) @ C2)) @ ((((len @ Sensors) @ V3) @ Ts) @ C2))))))).
% 2.85/1.56 thf(fact_98_view_Oh__chop__middle2, axiom, (! [V:(view_ext @ product_unit),U4:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V) @ U4) @ W2) => (((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ W2))) @ (right @ ((ext @ product_unit) @ V))))))).
% 2.85/1.56 thf(fact_99_view_Oh__chop__middle1, axiom, (! [V:(view_ext @ product_unit),U4:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V) @ U4) @ W2) => (((ord_less_eq @ real) @ (left @ ((ext @ product_unit) @ V))) @ (right @ ((ext @ product_unit) @ U4))))))).
% 2.85/1.56 thf(fact_100_view_Ohorizontal__chop__non__empty, axiom, (! [V:(view_ext @ product_unit)]: (((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ V))) => (? [U2:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V) @ U2) @ W3) & ((((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ U2))) & (((ord_less @ real) @ (zero_zero @ real)) @ (real_length @ ((ext @ product_unit) @ W3))))))))))).
% 2.85/1.56 thf(fact_101_hmlsl_Oright__space, axiom, (! [Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((right @ ((((space @ regular_regular) @ Ts) @ V) @ C2)) = (((plus_plus @ real) @ ((pos @ Ts) @ C2)) @ (((regular_regular @ ((own @ product_unit) @ V)) @ Ts) @ C2)))))).
% 2.85/1.56 thf(fact_102_local_Ohmlsl_Olength__add, axiom, (! [X2:real,Y2:real,Ts2:traffic,V2:(view_ext @ product_unit)]: ((((((ord_less_eq @ real) @ (zero_zero @ real)) @ X2) & (((ord_less_eq @ real) @ (zero_zero @ real)) @ Y2)) => (((real_length @ ((ext @ product_unit) @ V2)) = (((plus_plus @ real) @ X2) @ Y2)) = (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V2) @ W) @ U) & (((real_length @ ((ext @ product_unit) @ W)) = X2) & ((real_length @ ((ext @ product_unit) @ U)) = Y2)))))))))).
% 2.85/1.56 thf(fact_103_local_Ohmlsl_Olength__add2, axiom, (! [X2:real,Y2:real,Ts2:traffic,V2:(view_ext @ product_unit)]: ((((((ord_less_eq @ real) @ (zero_zero @ real)) @ X2) & (((ord_less_eq @ real) @ (zero_zero @ real)) @ Y2)) => (((real_length @ ((ext @ product_unit) @ V2)) = (((plus_plus @ real) @ X2) @ Y2)) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va) @ U2) & (((real_length @ ((ext @ product_unit) @ Va)) = X2) & ((real_length @ ((ext @ product_unit) @ U2)) = Y2)))))))))).
% 2.85/1.56 thf(fact_104_traffic_OpsGeZero, axiom, (! [Ts:traffic,C:cars]: ((((ord_less @ real) @ (zero_zero @ real)) @ ((physical_size @ Ts) @ C))))).
% 2.85/1.56 thf(fact_105_local_Ohmlsl_Olength__add1, axiom, (! [X2:real,Y2:real,Ts2:traffic,V2:(view_ext @ product_unit)]: (((? [Va2:(view_ext @ product_unit),U3:(view_ext @ product_unit)]: (((((hchop @ V2) @ Va2) @ U3) & (((real_length @ ((ext @ product_unit) @ Va2)) = X2) & ((real_length @ ((ext @ product_unit) @ U3)) = Y2))))) => ((real_length @ ((ext @ product_unit) @ V2)) = (((plus_plus @ real) @ X2) @ Y2)))))).
% 2.85/1.56 thf(fact_106_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.85/1.56 thf(fact_107_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.85/1.56 thf(fact_108_hmlsl_Olen__hchop__add, axiom, (! [V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((((hchop @ V) @ V12) @ V23) => ((real_length @ ((((len @ regular_regular) @ V) @ Ts) @ C2)) = (((plus_plus @ real) @ (real_length @ ((((len @ regular_regular) @ V12) @ Ts) @ C2))) @ (real_length @ ((((len @ regular_regular) @ V23) @ Ts) @ C2)))))))).
% 2.85/1.56 thf(fact_109_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_110_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_111_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A,Y2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X2) @ Y2)) = ((X2 = (zero_zero @ A)) & (Y2 = (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_112_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A,Y2:A]: ((((((plus_plus @ A) @ X2) @ Y2) = (zero_zero @ A)) = ((X2 = (zero_zero @ A)) & (Y2 = (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_113_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_114_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_115_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_116_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_117_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_118_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_119_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.85/1.56 thf(fact_120_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.85/1.56 thf(fact_121_add__less__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_122_add__less__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_123_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$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)))))))).
% 2.85/1.56 thf(fact_124_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_125_le__add__same__cancel2, axiom, (! [A:$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)))))))).
% 2.85/1.56 thf(fact_126_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.85/1.56 thf(fact_127_add__le__same__cancel2, axiom, (! [A:$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))))))))).
% 2.85/1.56 thf(fact_128_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_129_add__less__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_130_add__less__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_131_less__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.85/1.56 thf(fact_132_less__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.85/1.56 thf(fact_133_double__add__less__zero__iff__single__add__less__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_134_zero__less__double__add__iff__zero__less__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.85/1.56 thf(fact_135_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_136_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.85/1.56 thf(fact_137_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A3:A,K:A,A2:A,B2:A]: (((A3 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A3) @ B2) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_138_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B3:A,K:A,B2:A,A2:A]: (((B3 = (((plus_plus @ A) @ K) @ B2)) => ((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_139_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_140_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.85/1.56 thf(fact_141_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.85/1.56 thf(fact_142_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A4:A,B4:A]: ((((plus_plus @ A) @ B4) @ A4)))))))).
% 2.85/1.56 thf(fact_143_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_144_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) => (B2 = C2)))))))).
% 2.85/1.56 thf(fact_145_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) => (B2 = C2)))))))).
% 2.85/1.56 thf(fact_146_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_147_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_148_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A4:A,B4:A]: ((? [C3:A]: ((B4 = (((plus_plus @ A) @ A4) @ C3))))))))))).
% 2.85/1.56 thf(fact_149_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_150_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C4:A]: ((B2 != (((plus_plus @ A) @ A2) @ C4))))))))))))).
% 2.85/1.56 thf(fact_151_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2))))))))).
% 2.85/1.56 thf(fact_152_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C2) @ D) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.85/1.56 thf(fact_153_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$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))))))))).
% 2.85/1.56 thf(fact_154_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.85/1.56 thf(fact_155_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$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))))))))).
% 2.85/1.56 thf(fact_156_add_Ogroup__left__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.85/1.56 thf(fact_157_add_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.85/1.56 thf(fact_158_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.85/1.56 thf(fact_159_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$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))))))))).
% 2.85/1.56 thf(fact_160_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.85/1.56 thf(fact_161_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$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))))))))).
% 2.85/1.56 thf(fact_162_add__strict__mono, axiom, (! [A:$tType]: (((strict2144017051up_add @ A) => (! [A2:A,B2:A,C2:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C2) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.85/1.56 thf(fact_163_add__strict__left__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2))))))))).
% 2.85/1.56 thf(fact_164_add__strict__right__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_165_add__less__imp__less__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_166_add__less__imp__less__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.85/1.56 thf(fact_167_add__nonpos__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ Y2) @ (zero_zero @ A)) => (((((plus_plus @ A) @ X2) @ Y2) = (zero_zero @ A)) = ((X2 = (zero_zero @ A)) & (Y2 = (zero_zero @ A)))))))))))).
% 2.85/1.56 thf(fact_168_add__nonneg__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y2) => (((((plus_plus @ A) @ X2) @ Y2) = (zero_zero @ A)) = ((X2 = (zero_zero @ A)) & (Y2 = (zero_zero @ A)))))))))))).
% 2.85/1.56 thf(fact_169_add__nonpos__nonpos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_170_add__nonneg__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_171_add__increasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C2:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => ((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.85/1.56 thf(fact_172_add__decreasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2))))))))).
% 2.85/1.56 thf(fact_173_add__increasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.85/1.56 thf(fact_174_add__decreasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2))))))))).
% 2.85/1.56 thf(fact_175_add__less__le__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C2:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C2) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.85/1.56 thf(fact_176_add__le__less__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ C2) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.85/1.56 thf(fact_177_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.85/1.56 thf(fact_178_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.85/1.56 thf(fact_179_add__neg__neg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_180_add__pos__pos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_181_canonically__ordered__monoid__add__class_OlessE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((! [C4:A]: (((B2 = (((plus_plus @ A) @ A2) @ C4)) => (C4 = (zero_zero @ A)))))))))))))).
% 2.85/1.56 thf(fact_182_pos__add__strict, axiom, (! [A:$tType]: (((strict797366125id_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ C2) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.85/1.56 thf(fact_183_add__strict__increasing2, axiom, (! [A:$tType]: (((ordere1818651114id_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ C2) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.85/1.56 thf(fact_184_add__strict__increasing, axiom, (! [A:$tType]: (((ordere1818651114id_add @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 2.85/1.56 thf(fact_185_add__pos__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_186_add__nonpos__neg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_187_add__nonneg__pos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.85/1.56 thf(fact_188_add__neg__nonpos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_189_consec__add, axiom, (! [R:real_int,S2:real_int,T:real_int]: (((((left @ R) = (left @ S2)) & (((right @ R) = (right @ T)) & ((right @ S2) = (left @ T)))) => ((real_length @ R) = (((plus_plus @ real) @ (real_length @ S2)) @ (real_length @ T))))))).
% 2.85/1.56 thf(fact_190_view_Ohorizontal__chop__empty__right, axiom, (! [V2:(view_ext @ product_unit)]: ((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ V2) @ X_1)))))).
% 2.85/1.56 thf(fact_191_view_Ohorizontal__chop__empty__left, axiom, (! [V2:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit)]: ((((hchop @ V2) @ U2) @ V2)))))).
% 2.85/1.56 thf(fact_192_view_Ohorizontal__chop__assoc2, axiom, (! [V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((hchop @ V) @ V12) @ V23) & (((hchop @ V12) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((hchop @ V) @ V33) @ V4) & (((hchop @ V4) @ V42) @ V23)))))))).
% 2.85/1.56 thf(fact_193_view_Ohorizontal__chop__assoc1, axiom, (! [V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),V33:(view_ext @ product_unit),V42:(view_ext @ product_unit)]: ((((((hchop @ V) @ V12) @ V23) & (((hchop @ V23) @ V33) @ V42)) => (? [V4:(view_ext @ product_unit)]: (((((hchop @ V) @ V4) @ V42) & (((hchop @ V4) @ V12) @ V33)))))))).
% 2.85/1.56 thf(fact_194_view_Ohorizontal__chop1, axiom, (! [V:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit),X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ U2) @ X_1)))))).
% 2.85/1.56 thf(fact_195_view_Ohorizontal__chop__split__add, axiom, (! [X2:real,Y2:real,V:(view_ext @ product_unit)]: ((((((ord_less_eq @ real) @ (zero_zero @ real)) @ X2) & (((ord_less_eq @ real) @ (zero_zero @ real)) @ Y2)) => (((real_length @ ((ext @ product_unit) @ V)) = (((plus_plus @ real) @ X2) @ Y2)) => (? [U2:(view_ext @ product_unit),W3:(view_ext @ product_unit)]: (((((hchop @ V) @ U2) @ W3) & (((real_length @ ((ext @ product_unit) @ U2)) = X2) & ((real_length @ ((ext @ product_unit) @ W3)) = Y2)))))))))).
% 2.85/1.56 thf(fact_196_sensors_Olen__hchop__add, axiom, (! [Sensors:(cars > (traffic > (cars > real))),V:(view_ext @ product_unit),V12:(view_ext @ product_unit),V23:(view_ext @ product_unit),Ts:traffic,C2:cars]: (((sensors @ Sensors) => ((((hchop @ V) @ V12) @ V23) => ((real_length @ ((((len @ Sensors) @ V) @ Ts) @ C2)) = (((plus_plus @ real) @ (real_length @ ((((len @ Sensors) @ V12) @ Ts) @ C2))) @ (real_length @ ((((len @ Sensors) @ V23) @ Ts) @ C2))))))))).
% 2.85/1.56 thf(fact_197_sensors_Oright__space, axiom, (! [Sensors:(cars > (traffic > (cars > real))),Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((sensors @ Sensors) => ((right @ ((((space @ Sensors) @ Ts) @ V) @ C2)) = (((plus_plus @ real) @ ((pos @ Ts) @ C2)) @ (((Sensors @ ((own @ product_unit) @ V)) @ Ts) @ C2))))))).
% 2.85/1.56 thf(fact_198_view_Ohorizontal__chop__own__trans, axiom, (! [V:(view_ext @ product_unit),U4:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V) @ U4) @ W2) => (((own @ product_unit) @ U4) = ((own @ product_unit) @ W2)))))).
% 2.85/1.56 thf(fact_199_view_Ohorizontal__chop__leq2, axiom, (! [V:(view_ext @ product_unit),U4:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V) @ U4) @ W2) => (((ord_less_eq @ (view_ext @ product_unit)) @ W2) @ V))))).
% 2.85/1.56 thf(fact_200_view_Ohorizontal__chop__leq1, axiom, (! [V:(view_ext @ product_unit),U4:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V) @ U4) @ W2) => (((ord_less_eq @ (view_ext @ product_unit)) @ U4) @ V))))).
% 2.85/1.56 thf(fact_201_zero__less__two, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A))))))).
% 2.85/1.56 thf(fact_202_discrete, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => ((ord_less @ A) = (^ [A4:A]: (((ord_less_eq @ A) @ (((plus_plus @ A) @ A4) @ (one_one @ A)))))))))).
% 2.85/1.56 thf(fact_203_field__le__epsilon, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X2:A,Y2:A]: (((! [E4:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ E4) => (((ord_less_eq @ A) @ X2) @ (((plus_plus @ A) @ Y2) @ E4))))) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 2.85/1.56 thf(fact_204_add__mono1, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ (one_one @ A))) @ (((plus_plus @ A) @ B2) @ (one_one @ A)))))))))).
% 2.85/1.56 thf(fact_205_less__add__one, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 2.85/1.56 thf(fact_206_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y2:A]: (((X2 != Y2) => ((~ ((((ord_less @ A) @ X2) @ Y2))) => (((ord_less @ A) @ Y2) @ X2))))))))).
% 2.85/1.56 thf(fact_207_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 2.85/1.56 thf(fact_208_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X))))))))).
% 2.85/1.56 thf(fact_209_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.85/1.56 thf(fact_210_zero__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.85/1.56 thf(fact_211_not__one__le__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.85/1.56 thf(fact_212_not__one__less__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.85/1.56 thf(fact_213_zero__less__one, axiom, (! [A:$tType]: (((zero_less_one @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.85/1.56 thf(fact_214_add__less__zeroD, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ X2) @ Y2)) @ (zero_zero @ A)) => ((((ord_less @ A) @ X2) @ (zero_zero @ A)) | (((ord_less @ A) @ Y2) @ (zero_zero @ A)))))))))).
% 2.85/1.56 thf(fact_215_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.85/1.56 thf(fact_216_space__c, axiom, (((((space @ regular_regular) @ ts) @ v2) @ c) = (real_Abs_real_int @ ((((product_Pair @ real) @ real) @ (zero_zero @ real)) @ (one_one @ real))))).
% 2.85/1.56 thf(fact_217_hmlsl_Ospace__def, axiom, (! [Ts:traffic,V:(view_ext @ product_unit),C2:cars]: ((((((space @ regular_regular) @ Ts) @ V) @ C2) = (real_Abs_real_int @ ((((product_Pair @ real) @ real) @ ((pos @ Ts) @ C2)) @ (((plus_plus @ real) @ ((pos @ Ts) @ C2)) @ (((regular_regular @ ((own @ product_unit) @ V)) @ Ts) @ C2)))))))).
% 2.85/1.56 thf(fact_218_len__c, axiom, (((((len @ regular_regular) @ v2) @ ts) @ c) = (real_Abs_real_int @ ((((product_Pair @ real) @ real) @ (zero_zero @ real)) @ (one_one @ real))))).
% 2.85/1.56 thf(fact_219_sensors_Ospace__def, axiom, (! [Sensors:(cars > (traffic > (cars > real))),Ts:traffic,V:(view_ext @ product_unit),C2:cars]: (((sensors @ Sensors) => (((((space @ Sensors) @ Ts) @ V) @ C2) = (real_Abs_real_int @ ((((product_Pair @ real) @ real) @ ((pos @ Ts) @ C2)) @ (((plus_plus @ real) @ ((pos @ Ts) @ C2)) @ (((Sensors @ ((own @ product_unit) @ V)) @ Ts) @ C2))))))))).
% 2.85/1.56 thf(fact_220_is__num__normalize_I1_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.85/1.56 thf(fact_221_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.85/1.56 thf(fact_222_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.85/1.56 thf(fact_223_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.85/1.56 thf(fact_224_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.85/1.56 thf(fact_225_divides__aux__eq, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => (! [Q:A,R:A]: ((((unique455577585es_aux @ A) @ ((((product_Pair @ A) @ A) @ Q) @ R)) = (R = (zero_zero @ A))))))))).
% 2.85/1.56 thf(fact_226_real__int__class_Oshift__def, axiom, (real_shift = (^ [R2:real_int,X4:real]: ((real_Abs_real_int @ ((((product_Pair @ real) @ real) @ (((plus_plus @ real) @ (left @ R2)) @ X4)) @ (((plus_plus @ real) @ (right @ R2)) @ X4))))))).
% 2.85/1.56 thf(fact_227_shift__additivity, axiom, (! [R:real_int,X2:real,Y2:real]: ((((real_shift @ R) @ (((plus_plus @ real) @ X2) @ Y2)) = ((real_shift @ ((real_shift @ R) @ X2)) @ Y2))))).
% 2.85/1.56 thf(fact_228_shift__keeps__length, axiom, (! [X2:real]: ((real_length = (^ [R2:real_int]: ((real_length @ ((real_shift @ R2) @ X2)))))))).
% 2.85/1.56 thf(fact_229_shift__zero, axiom, (! [R:real_int]: ((((real_shift @ R) @ (zero_zero @ real)) = R)))).
% 2.85/1.56 thf(fact_230_shift__left__eq__right, axiom, (! [R:real_int,X2:real]: ((((ord_less_eq @ real) @ (left @ ((real_shift @ R) @ X2))) @ (right @ ((real_shift @ R) @ X2)))))).
% 2.85/1.56 thf(fact_231_ts__rep__def, axiom, (ts_rep = ((((product_Pair @ (cars > real)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real)))))) @ po) @ ((((product_Pair @ (cars > nat_int)) @ ((product_prod @ (cars > nat_int)) @ ((product_prod @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real))))) @ re) @ ((((product_Pair @ (cars > nat_int)) @ ((product_prod @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real)))) @ cl) @ ((((product_Pair @ (cars > (real > real))) @ ((product_prod @ (cars > real)) @ (cars > real))) @ dy) @ ((((product_Pair @ (cars > real)) @ (cars > real)) @ ps) @ sd))))))).
% 2.85/1.56 thf(fact_232_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 2.85/1.56 thf(fact_233_clm__def, axiom, (! [C:cars]: (((cl @ C) = (bot_bot @ nat_int))))).
% 2.85/1.56 thf(fact_234_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.85/1.56 thf(fact_235_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A4:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A4) & (((ord_less_eq @ A) @ A4) @ B4))))))))).
% 2.85/1.56 thf(fact_236_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.85/1.56 thf(fact_237_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A2) @ B2))))))))).
% 2.85/1.56 thf(fact_238_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.85/1.56 thf(fact_239_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less_eq @ A) @ X2) @ Z3))))))))).
% 2.85/1.56 thf(fact_240_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.85/1.56 thf(fact_241_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.56 thf(fact_242_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.56 thf(fact_243_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) & (((ord_less_eq @ A) @ B4) @ A4))))))))).
% 2.85/1.56 thf(fact_244_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 2.85/1.56 thf(fact_245_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z3:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z3)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z3)))) => (((((ord_less_eq @ A) @ X2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y2)))) => (((((ord_less_eq @ A) @ Z3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 2.85/1.56 thf(fact_246_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.85/1.56 thf(fact_247_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 2.85/1.56 thf(fact_248_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 2.85/1.56 thf(fact_249_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 2.85/1.56 thf(fact_250_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 2.85/1.56 thf(fact_251_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [X4:A,Y:A]: (((((ord_less_eq @ A) @ X4) @ Y) & (((ord_less_eq @ A) @ Y) @ X4))))))))).
% 2.85/1.56 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A6:$tType,A7:$tType]: (((preorder @ A7) => (preorder @ (A6 > A7)))))).
% 2.85/1.56 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: (((order @ A7) => (order @ (A6 > A7)))))).
% 2.85/1.56 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.85/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_1, axiom, (preorder @ $o)).
% 2.85/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.85/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, (order @ $o)).
% 2.85/1.56 thf(tcon_HOL_Obool___Orderings_Oord_3, axiom, (ord @ $o)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, (ordere516151231imp_le @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (strict2144017051up_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add, axiom, (ordere223160158up_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add, axiom, (strict797366125id_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add, axiom, (ordere1818651114id_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add, axiom, (ordere216010020id_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__semidom, axiom, (linordered_semidom @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Fields_Olinordered__field, axiom, (linordered_field @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__idom, axiom, (linordered_idom @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Osemigroup__add, axiom, (semigroup_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Rings_Ozero__less__one, axiom, (zero_less_one @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Rings_Ozero__neq__one, axiom, (zero_neq_one @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Orderings_Opreorder_4, axiom, (preorder @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Orderings_Olinorder_5, axiom, (linorder @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Omonoid__add, axiom, (monoid_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, (group_add @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Orderings_Oorder_6, axiom, (order @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, (neg_numeral @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Orderings_Oord_7, axiom, (ord @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Ozero, axiom, (zero @ real)).
% 2.85/1.56 thf(tcon_Real_Oreal___Groups_Oone, axiom, (one @ real)).
% 2.85/1.56 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_8, axiom, (preorder @ nat_int)).
% 2.85/1.56 thf(tcon_NatInt_Onat__int___Orderings_Oorder_9, axiom, (order @ nat_int)).
% 2.85/1.56 thf(tcon_NatInt_Onat__int___Orderings_Oord_10, axiom, (ord @ nat_int)).
% 2.85/1.56 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_11, axiom, (preorder @ real_int)).
% 2.85/1.56 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_12, axiom, (order @ real_int)).
% 2.85/1.56 thf(tcon_RealInt_Oreal__int___Orderings_Oord_13, axiom, (ord @ real_int)).
% 2.85/1.56 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_14, axiom, (preorder @ product_unit)).
% 2.85/1.56 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_15, axiom, (linorder @ product_unit)).
% 2.85/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oorder_16, axiom, (order @ product_unit)).
% 2.85/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oord_17, axiom, (ord @ product_unit)).
% 2.85/1.56 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_18, axiom, (! [A6:$tType]: (((order @ A6) => (preorder @ (view_ext @ A6)))))).
% 2.85/1.56 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_19, axiom, (! [A6:$tType]: (((order @ A6) => (order @ (view_ext @ A6)))))).
% 2.85/1.56 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_20, axiom, (! [A6:$tType]: (((order @ A6) => (ord @ (view_ext @ A6)))))).
% 2.85/1.56 thf(conj_0, conjecture, ((((ord_less @ real) @ (left @ ((((space @ regular_regular) @ ts) @ v) @ d))) @ (right @ ((ext @ product_unit) @ v))) & (((ord_less @ real) @ (left @ ((ext @ product_unit) @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ d))))).
% 2.85/1.56 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2DTF15185.p
% 2.85/1.56 ------------------------
% 2.85/1.59 ---- Cleaned THF ---
% 2.85/1.59 thf(ty_t_Views_Oview_Oview__ext,type,
% 2.85/1.59 view_ext: $tType > $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_Product__Type_Ounit,type,
% 2.85/1.59 product_unit: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_Product__Type_Oprod,type,
% 2.85/1.59 product_prod: $tType > $tType > $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_RealInt_Oreal__int,type,
% 2.85/1.59 real_int: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_Traffic_Otraffic,type,
% 2.85/1.59 traffic: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_NatInt_Onat__int,type,
% 2.85/1.59 nat_int: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_Real_Oreal,type,
% 2.85/1.59 real: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(ty_t_Cars_Ocars,type,
% 2.85/1.59 cars: $tType ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_HOL_Otype,type,
% 2.85/1.59 type:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oone,type,
% 2.85/1.59 one:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ozero,type,
% 2.85/1.59 zero:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Orderings_Oord,type,
% 2.85/1.59 ord:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Num_Oneg__numeral,type,
% 2.85/1.59 neg_numeral:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Orderings_Oorder,type,
% 2.85/1.59 order:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ogroup__add,type,
% 2.85/1.59 group_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Omonoid__add,type,
% 2.85/1.59 monoid_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Orderings_Olinorder,type,
% 2.85/1.59 linorder:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Orderings_Opreorder,type,
% 2.85/1.59 preorder:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.85/1.59 zero_neq_one:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Rings_Ozero__less__one,type,
% 2.85/1.59 zero_less_one:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.85/1.59 semigroup_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.85/1.59 linordered_idom:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.85/1.59 comm_monoid_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Fields_Olinordered__field,type,
% 2.85/1.59 linordered_field:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.85/1.59 ab_semigroup_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.85/1.59 linordered_semidom:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.85/1.59 cancel_semigroup_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.85/1.59 cancel1352612707id_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.85/1.59 linord219039673up_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.85/1.59 ordere216010020id_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.85/1.59 ordere779506340up_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.85/1.59 linord1659791738miring:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.85/1.59 canoni770627133id_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 2.85/1.59 ordere1818651114id_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 2.85/1.59 strict797366125id_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.85/1.59 ordere236663937imp_le:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.85/1.59 ordere223160158up_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.85/1.59 strict2144017051up_add:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 2.85/1.59 unique1598680935umeral:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.85/1.59 ordere516151231imp_le:
% 2.85/1.59 !>[A: $tType] : $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 2.85/1.59 unique455577585es_aux:
% 2.85/1.59 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.85/1.59 one_one:
% 2.85/1.59 !>[A: $tType] : A ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.85/1.59 plus_plus:
% 2.85/1.59 !>[A: $tType] : ( A > A > A ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.85/1.59 zero_zero:
% 2.85/1.59 !>[A: $tType] : A ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Length_Osensors_Olen,type,
% 2.85/1.59 len: ( cars > traffic > cars > real ) > ( view_ext @ product_unit ) > traffic > cars > real_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.85/1.59 bot_bot:
% 2.85/1.59 !>[A: $tType] : A ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.85/1.59 ord_less:
% 2.85/1.59 !>[A: $tType] : ( A > A > $o ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.85/1.59 ord_less_eq:
% 2.85/1.59 !>[A: $tType] : ( A > A > $o ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Product__Type_OPair,type,
% 2.85/1.59 product_Pair:
% 2.85/1.59 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_RealInt_Oleft,type,
% 2.85/1.59 left: real_int > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_RealInt_Oreal__int_OAbs__real__int,type,
% 2.85/1.59 real_Abs_real_int: ( product_prod @ real @ real ) > real_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 2.85/1.59 real_length: real_int > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 2.85/1.59 real_shift: real_int > real > real_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_RealInt_Oright,type,
% 2.85/1.59 right: real_int > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Regular__Sensors_Oregular,type,
% 2.85/1.59 regular_regular: cars > traffic > cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Sensors_Osensors,type,
% 2.85/1.59 sensors: ( cars > traffic > cars > real ) > $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Sensors_Osensors_Ospace,type,
% 2.85/1.59 space: ( cars > traffic > cars > real ) > traffic > ( view_ext @ product_unit ) > cars > real_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Traffic_Otraffic_OAbs__traffic,type,
% 2.85/1.59 abs_traffic: ( product_prod @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) ) > traffic ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 2.85/1.59 physical_size: traffic > cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Traffic_Otraffic_Opos,type,
% 2.85/1.59 pos: traffic > cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Views_Oview_Oext,type,
% 2.85/1.59 ext:
% 2.85/1.59 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Views_Oview_Ohchop,type,
% 2.85/1.59 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 2.85/1.59
% 2.85/1.59 thf(sy_c_Views_Oview_Oown,type,
% 2.85/1.59 own:
% 2.85/1.59 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_c____,type,
% 2.85/1.59 c: cars ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_cl____,type,
% 2.85/1.59 cl: cars > nat_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_d____,type,
% 2.85/1.59 d: cars ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_dy____,type,
% 2.85/1.59 dy: cars > real > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_po____,type,
% 2.85/1.59 po: cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_ps____,type,
% 2.85/1.59 ps: cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_re____,type,
% 2.85/1.59 re: cars > nat_int ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_sd____,type,
% 2.85/1.59 sd: cars > real ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_ts____,type,
% 2.85/1.59 ts: traffic ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_ts__rep____,type,
% 2.85/1.59 ts_rep: product_prod @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_v_H____,type,
% 2.85/1.59 v: view_ext @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(sy_v_v____,type,
% 2.85/1.59 v2: view_ext @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(fact_0__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062dy_O_A_092_060forall_062c_Ax_O_Ady_Ac_Ax_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.85/1.59 ~ ! [Dy: cars > real > real] :
% 2.85/1.59 ~ ! [C: cars,X: real] :
% 2.85/1.59 ( ( Dy @ C @ X )
% 2.85/1.59 = ( zero_zero @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_1_dyn__def,axiom,
% 2.85/1.59 ! [C: cars,X: real] :
% 2.85/1.59 ( ( dy @ C @ X )
% 2.85/1.59 = ( zero_zero @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_2_local_Ohmlsl_Osensors__ge,axiom,
% 2.85/1.59 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ E @ Ts @ C2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_3_hmlsl_Olen__non__empty__inside,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 2.85/1.59 => ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_4_v_H__d,axiom,
% 2.85/1.59 ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ v @ ts @ d ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_5_hmlsl_Ospace__nonempty,axiom,
% 2.85/1.59 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] : ( ord_less @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_6_ts__def,axiom,
% 2.85/1.59 ( ts
% 2.85/1.59 = ( abs_traffic @ ts_rep ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_7_assumption,axiom,
% 2.85/1.59 d != c ).
% 2.85/1.59
% 2.85/1.59 thf(fact_8_local_Ohmlsl_Olength__geq__zero,axiom,
% 2.85/1.59 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 | ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_9_v_H__rel__c,axiom,
% 2.85/1.59 ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext @ product_unit @ v ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_10_hmlsl_Oleft__space,axiom,
% 2.85/1.59 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 2.85/1.59 = ( pos @ Ts @ C2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_11_len__eq,axiom,
% 2.85/1.59 ( ( len @ regular_regular @ v @ ts @ c )
% 2.85/1.59 = ( len @ regular_regular @ v @ ts @ d ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_12_hmlsl_Olen__space__left,axiom,
% 2.85/1.59 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( ord_less_eq @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 2.85/1.59 => ( ord_less_eq @ real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_13_hmlsl_Olen__space__right,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) )
% 2.85/1.59 => ( ord_less_eq @ real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_14_regular__sensors_Osensors__le,axiom,
% 2.85/1.59 ! [E: cars,C2: cars,Ts: traffic] :
% 2.85/1.59 ( ( E != C2 )
% 2.85/1.59 => ( ord_less @ real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_15_ps__ge__zero,axiom,
% 2.85/1.59 ! [C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( ps @ C ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_16_sd__ge__zero,axiom,
% 2.85/1.59 ! [C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( sd @ C ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_17_hmlsl_Olen__left,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_18_hmlsl_Olen__right,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_19_v_H__c,axiom,
% 2.85/1.59 ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_20_hmlsl_Osensors__axioms,axiom,
% 2.85/1.59 sensors @ regular_regular ).
% 2.85/1.59
% 2.85/1.59 thf(fact_21_dyn__geq__zero,axiom,
% 2.85/1.59 ! [C: cars,X: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( dy @ C @ X ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_22_ps__def,axiom,
% 2.85/1.59 ! [C: cars] :
% 2.85/1.59 ( ( ps @ C )
% 2.85/1.59 = ( one_one @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_23_regular__sensors_Osensors__leq,axiom,
% 2.85/1.59 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_eq @ real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_24_sensors_Olen__non__empty__inside,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 2.85/1.59 => ( ( ord_less @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_25_other__len__zero,axiom,
% 2.85/1.59 ! [E2: cars] :
% 2.85/1.59 ( ( ( E2 != c )
% 2.85/1.59 & ( E2 != d ) )
% 2.85/1.59 => ( ( real_length @ ( len @ regular_regular @ v2 @ ts @ E2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_26_sensors_Olen__space__right,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) )
% 2.85/1.59 => ( ord_less_eq @ real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_27_sensors_Olen__space__left,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ord_less_eq @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) )
% 2.85/1.59 => ( ord_less_eq @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_28_lc,axiom,
% 2.85/1.59 ( ( left @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_29_sensors_Ospace__nonempty,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ord_less @ real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_30_sensors_Olen__right,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ord_less_eq @ real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_31_sensors_Olen__left,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_32_not__gr__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [N: A] :
% 2.85/1.59 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.85/1.59 = ( N
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_33_le__zero__eq,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [N: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.85/1.59 = ( N
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_34__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.85/1.59 ~ ! [Ps: cars > real] :
% 2.85/1.59 ~ ! [C: cars] :
% 2.85/1.59 ( ( Ps @ C )
% 2.85/1.59 = ( one_one @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_35_hmlsl_Olen__sub__int,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( ext @ product_unit @ V ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_36_hmlsl_Olen__empty__subview,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V3: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V ) )
% 2.85/1.59 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_37_lv,axiom,
% 2.85/1.59 ( ( left @ ( ext @ product_unit @ v2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_38_rc,axiom,
% 2.85/1.59 ( ( right @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 2.85/1.59 = ( one_one @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_39_one__reorient,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( one @ A )
% 2.85/1.59 => ! [X2: A] :
% 2.85/1.59 ( ( ( one_one @ A )
% 2.85/1.59 = X2 )
% 2.85/1.59 = ( X2
% 2.85/1.59 = ( one_one @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_40_sensors_Olen__sub__int,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ord_less_eq @ real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( ext @ product_unit @ V ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_41_sensors_Olen__empty__subview,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V3: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V3 @ V ) )
% 2.85/1.59 => ( ( real_length @ ( len @ Sensors @ V3 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_42_ext,axiom,
% 2.85/1.59 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.85/1.59 ( ! [X3: A] :
% 2.85/1.59 ( ( F @ X3 )
% 2.85/1.59 = ( G @ X3 ) )
% 2.85/1.59 => ( F = G ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_43_zero__reorient,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( zero @ A )
% 2.85/1.59 => ! [X2: A] :
% 2.85/1.59 ( ( ( zero_zero @ A )
% 2.85/1.59 = X2 )
% 2.85/1.59 = ( X2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_44_sensors_Olen_Ocong,axiom,
% 2.85/1.59 len = len ).
% 2.85/1.59
% 2.85/1.59 thf(fact_45_sensors_Ospace_Ocong,axiom,
% 2.85/1.59 space = space ).
% 2.85/1.59
% 2.85/1.59 thf(fact_46_zero__le,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_47_gr__zeroI,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [N: A] :
% 2.85/1.59 ( ( N
% 2.85/1.59 != ( zero_zero @ A ) )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_48_not__less__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [N: A] :
% 2.85/1.59 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_49_gr__implies__not__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [M: A,N: A] :
% 2.85/1.59 ( ( ord_less @ A @ M @ N )
% 2.85/1.59 => ( N
% 2.85/1.59 != ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_50_zero__less__iff__neq__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [N: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.85/1.59 = ( N
% 2.85/1.59 != ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_51_sensors__def,axiom,
% 2.85/1.59 ( sensors
% 2.85/1.59 = ( ^ [Sensors2: cars > traffic > cars > real] :
% 2.85/1.59 ! [E3: cars,Ts3: traffic,C3: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors2 @ E3 @ Ts3 @ C3 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_52_sensors_Ointro,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real] :
% 2.85/1.59 ( ! [E4: cars,Ts4: traffic,C4: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors @ E4 @ Ts4 @ C4 ) )
% 2.85/1.59 => ( sensors @ Sensors ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_53_sensors_Osensors__ge,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,E: cars,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ord_less @ real @ ( zero_zero @ real ) @ ( Sensors @ E @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_54_sensors_Oleft__space,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( left @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 2.85/1.59 = ( pos @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_55_size,axiom,
% 2.85/1.59 ! [C: cars] :
% 2.85/1.59 ( ( physical_size @ ts @ C )
% 2.85/1.59 = ( one_one @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_56_sensors__c,axiom,
% 2.85/1.59 ( ( regular_regular @ ( own @ product_unit @ v2 ) @ ts @ c )
% 2.85/1.59 = ( one_one @ real ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_57_hmlsl_Oview__leq__len__leq,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V ) @ ( ext @ product_unit @ V3 ) )
% 2.85/1.59 & ( ( own @ product_unit @ V )
% 2.85/1.59 = ( own @ product_unit @ V3 ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) )
% 2.85/1.59 => ( ord_less_eq @ real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_58_length__zero__iff__borders__eq,axiom,
% 2.85/1.59 ! [R: real_int] :
% 2.85/1.59 ( ( ( real_length @ R )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 = ( ( left @ R )
% 2.85/1.59 = ( right @ R ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_59_hmlsl_Olen__fills__subview,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 2.85/1.59 => ? [V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ V1 @ V22 )
% 2.85/1.59 & ( hchop @ V22 @ V4 @ V32 )
% 2.85/1.59 & ( ( len @ regular_regular @ V4 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V4 ) )
% 2.85/1.59 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C2 ) )
% 2.85/1.59 = ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_60_less__real__int__def,axiom,
% 2.85/1.59 ( ( ord_less @ real_int )
% 2.85/1.59 = ( ^ [R2: real_int,S: real_int] :
% 2.85/1.59 ( ( ord_less_eq @ real @ ( left @ S ) @ ( left @ R2 ) )
% 2.85/1.59 & ( ord_less_eq @ real @ ( right @ R2 ) @ ( right @ S ) )
% 2.85/1.59 & ~ ( ( ord_less_eq @ real @ ( left @ R2 ) @ ( left @ S ) )
% 2.85/1.59 & ( ord_less_eq @ real @ ( right @ S ) @ ( right @ R2 ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_61_less__eq__real__int__def,axiom,
% 2.85/1.59 ( ( ord_less_eq @ real_int )
% 2.85/1.59 = ( ^ [R2: real_int,S: real_int] :
% 2.85/1.59 ( ( ord_less_eq @ real @ ( left @ S ) @ ( left @ R2 ) )
% 2.85/1.59 & ( ord_less_eq @ real @ ( right @ R2 ) @ ( right @ S ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_62_left__leq__right,axiom,
% 2.85/1.59 ! [R: real_int] : ( ord_less_eq @ real @ ( left @ R ) @ ( right @ R ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_63_length__ge__zero,axiom,
% 2.85/1.59 ! [R: real_int] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( real_length @ R ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_64_local_Ohmlsl_Ohchop__assoc,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Phi @ Ts2 @ W )
% 2.85/1.59 & ? [X4: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ U @ X4 @ Y )
% 2.85/1.59 & ( Psi @ Ts2 @ X4 )
% 2.85/1.59 & ( Chi @ Ts2 @ Y ) ) ) )
% 2.85/1.59 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ? [X4: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ W @ X4 @ Y )
% 2.85/1.59 & ( Phi @ Ts2 @ X4 )
% 2.85/1.59 & ( Psi @ Ts2 @ Y ) )
% 2.85/1.59 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_65_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Phi @ Ts2 @ W )
% 2.85/1.59 & ( ( Psi @ Ts2 @ U )
% 2.85/1.59 | ( Chi @ Ts2 @ U ) ) ) )
% 2.85/1.59 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Phi @ Ts2 @ W )
% 2.85/1.59 & ( Psi @ Ts2 @ U ) )
% 2.85/1.59 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Phi @ Ts2 @ W )
% 2.85/1.59 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_66_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 2.85/1.59 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( ( Psi @ Ts2 @ W )
% 2.85/1.59 | ( Chi @ Ts2 @ W ) )
% 2.85/1.59 & ( Phi @ Ts2 @ U ) ) )
% 2.85/1.59 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Psi @ Ts2 @ W )
% 2.85/1.59 & ( Phi @ Ts2 @ U ) )
% 2.85/1.59 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( Chi @ Ts2 @ W )
% 2.85/1.59 & ( Phi @ Ts2 @ U ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_67_local_Ohmlsl_Ohchop__neg1,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ~ ? [Va: view_ext @ product_unit] :
% 2.85/1.59 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 2.85/1.59 & ( Phi @ Ts2 @ Va ) )
% 2.85/1.59 => ? [Va: view_ext @ product_unit] :
% 2.85/1.59 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 2.85/1.59 & ~ ( Phi @ Ts2 @ Va ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_68_local_Ohmlsl_Ohchop__neg2,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ~ ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ( Phi @ Ts2 @ U2 ) )
% 2.85/1.59 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_69_local_Ohmlsl_Ohchop__weaken,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( Phi @ Ts2 @ V2 )
% 2.85/1.59 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ? [Vb: view_ext @ product_unit] :
% 2.85/1.59 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 2.85/1.59 & ( Phi @ Ts2 @ Vb ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_70_local_Ohmlsl_Ohchop__weaken1,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( Phi @ Ts2 @ V2 )
% 2.85/1.59 => ? [Va: view_ext @ product_unit] :
% 2.85/1.59 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ Va @ X_1 )
% 2.85/1.59 & ( Phi @ Ts2 @ Va ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_71_local_Ohmlsl_Ohchop__weaken2,axiom,
% 2.85/1.59 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( Phi @ Ts2 @ V2 )
% 2.85/1.59 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_72_hmlsl_Olen__view__hchop__right,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V23 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_73_hmlsl_Olen__view__hchop__left,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V12 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_74_hmlsl_Olen__compose__hchop,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 & ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V12 ) )
% 2.85/1.59 & ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V23 ) ) )
% 2.85/1.59 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_75_hmlsl_Oext__eq__len__eq,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ( ( ext @ product_unit @ V )
% 2.85/1.59 = ( ext @ product_unit @ V3 ) )
% 2.85/1.59 & ( ( own @ product_unit @ V )
% 2.85/1.59 = ( own @ product_unit @ V3 ) ) )
% 2.85/1.59 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_76_local_Ohmlsl_Olength__split,axiom,
% 2.85/1.59 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.85/1.59 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_77_local_Ohmlsl_Olength__meld,axiom,
% 2.85/1.59 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ? [Va2: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va2 @ U3 )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ Va2 ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U3 ) ) ) )
% 2.85/1.59 => ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_78_local_Ohmlsl_Olength__dense,axiom,
% 2.85/1.59 ! [Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V2 ) ) )
% 2.85/1.59 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_79_hmlsl_Olen__empty__on__subview2,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_80_hmlsl_Olen__empty__on__subview1,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_81_hmlsl_Olen__hchop__right__right__border,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( right @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( right @ ( ext @ product_unit @ V23 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_82_hmlsl_Olen__hchop__right__left__border,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( left @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( left @ ( ext @ product_unit @ V23 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_83_hmlsl_Olen__hchop__left__right__border,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( right @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( right @ ( ext @ product_unit @ V12 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_84_hmlsl_Olen__hchop__left__left__border,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( left @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( left @ ( ext @ product_unit @ V12 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_85_regular__sensors_Ospace__eq,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( ( own @ product_unit @ V )
% 2.85/1.59 = ( own @ product_unit @ V3 ) )
% 2.85/1.59 => ( ( space @ regular_regular @ Ts @ V @ C2 )
% 2.85/1.59 = ( space @ regular_regular @ Ts @ V3 @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_86_sensors_Olen__compose__hchop,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 & ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V12 ) )
% 2.85/1.59 & ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V23 ) ) )
% 2.85/1.59 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_87_sensors_Olen__view__hchop__left,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V12 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_88_sensors_Olen__view__hchop__right,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V23 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_89_sensors_Oext__eq__len__eq,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( ext @ product_unit @ V )
% 2.85/1.59 = ( ext @ product_unit @ V3 ) )
% 2.85/1.59 & ( ( own @ product_unit @ V )
% 2.85/1.59 = ( own @ product_unit @ V3 ) ) )
% 2.85/1.59 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_90_sensors_Olen__empty__on__subview1,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_91_sensors_Olen__empty__on__subview2,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( zero_zero @ real ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_92_sensors_Olen__hchop__right__right__border,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( right @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( right @ ( ext @ product_unit @ V23 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_93_sensors_Olen__hchop__right__left__border,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( left @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 2.85/1.59 = ( left @ ( ext @ product_unit @ V23 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_94_sensors_Olen__hchop__left__right__border,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( right @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( right @ ( ext @ product_unit @ V12 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_95_sensors_Olen__hchop__left__left__border,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars,V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V ) )
% 2.85/1.59 & ( hchop @ V @ V12 @ V23 ) )
% 2.85/1.59 => ( ( left @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 2.85/1.59 = ( left @ ( ext @ product_unit @ V12 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_96_sensors_Olen__fills__subview,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 2.85/1.59 => ? [V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ V1 @ V22 )
% 2.85/1.59 & ( hchop @ V22 @ V4 @ V32 )
% 2.85/1.59 & ( ( len @ Sensors @ V4 @ Ts @ C2 )
% 2.85/1.59 = ( ext @ product_unit @ V4 ) )
% 2.85/1.59 & ( ( real_length @ ( len @ Sensors @ V4 @ Ts @ C2 ) )
% 2.85/1.59 = ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_97_sensors_Oview__leq__len__leq,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V3: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ V ) @ ( ext @ product_unit @ V3 ) )
% 2.85/1.59 & ( ( own @ product_unit @ V )
% 2.85/1.59 = ( own @ product_unit @ V3 ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) )
% 2.85/1.59 => ( ord_less_eq @ real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_98_view_Oh__chop__middle2,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U4 @ W2 )
% 2.85/1.59 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ W2 ) ) @ ( right @ ( ext @ product_unit @ V ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_99_view_Oh__chop__middle1,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U4 @ W2 )
% 2.85/1.59 => ( ord_less_eq @ real @ ( left @ ( ext @ product_unit @ V ) ) @ ( right @ ( ext @ product_unit @ U4 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_100_view_Ohorizontal__chop__non__empty,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit] :
% 2.85/1.59 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ V ) ) )
% 2.85/1.59 => ? [U2: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U2 @ W3 )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ U2 ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ W3 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_101_hmlsl_Oright__space,axiom,
% 2.85/1.59 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 2.85/1.59 = ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_102_local_Ohmlsl_Olength__add,axiom,
% 2.85/1.59 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 2.85/1.59 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 2.85/1.59 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.85/1.59 = ( plus_plus @ real @ X2 @ Y2 ) )
% 2.85/1.59 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ W @ U )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ W ) )
% 2.85/1.59 = X2 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ U ) )
% 2.85/1.59 = Y2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_103_local_Ohmlsl_Olength__add2,axiom,
% 2.85/1.59 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 2.85/1.59 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 2.85/1.59 => ( ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.85/1.59 = ( plus_plus @ real @ X2 @ Y2 ) )
% 2.85/1.59 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va @ U2 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ Va ) )
% 2.85/1.59 = X2 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ U2 ) )
% 2.85/1.59 = Y2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_104_traffic_OpsGeZero,axiom,
% 2.85/1.59 ! [Ts: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( physical_size @ Ts @ C ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_105_local_Ohmlsl_Olength__add1,axiom,
% 2.85/1.59 ! [X2: real,Y2: real,Ts2: traffic,V2: view_ext @ product_unit] :
% 2.85/1.59 ( ? [Va2: view_ext @ product_unit,U3: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V2 @ Va2 @ U3 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ Va2 ) )
% 2.85/1.59 = X2 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ U3 ) )
% 2.85/1.59 = Y2 ) )
% 2.85/1.59 => ( ( real_length @ ( ext @ product_unit @ V2 ) )
% 2.85/1.59 = ( plus_plus @ real @ X2 @ Y2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_106_add__left__cancel,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel_semigroup_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.85/1.59 = ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_107_add__right__cancel,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel_semigroup_add @ A )
% 2.85/1.59 => ! [B2: A,A2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.85/1.59 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.85/1.59 = ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_108_hmlsl_Olen__hchop__add,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 => ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( plus_plus @ real @ ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_109_add__le__cancel__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [A2: A,C2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.85/1.59 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_110_add__le__cancel__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [C2: A,A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.85/1.59 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_111_zero__eq__add__iff__both__eq__0,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ( zero_zero @ A )
% 2.85/1.59 = ( plus_plus @ A @ X2 @ Y2 ) )
% 2.85/1.59 = ( ( X2
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 & ( Y2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_112_add__eq__0__iff__both__eq__0,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ X2 @ Y2 )
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 = ( ( X2
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 & ( Y2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_113_add__cancel__right__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel1352612707id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( A2
% 2.85/1.59 = ( plus_plus @ A @ A2 @ B2 ) )
% 2.85/1.59 = ( B2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_114_add__cancel__right__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel1352612707id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( A2
% 2.85/1.59 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.85/1.59 = ( B2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_115_add__cancel__left__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel1352612707id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.85/1.59 = A2 )
% 2.85/1.59 = ( B2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_116_add__cancel__left__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel1352612707id_add @ A )
% 2.85/1.59 => ! [B2: A,A2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.85/1.59 = A2 )
% 2.85/1.59 = ( B2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_117_double__zero__sym,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ( zero_zero @ A )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.85/1.59 = ( A2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_118_double__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 = ( A2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_119_add_Oright__neutral,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( monoid_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 = A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_120_add_Oleft__neutral,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( monoid_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 = A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_121_add__less__cancel__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [C2: A,A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.85/1.59 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_122_add__less__cancel__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [A2: A,C2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.85/1.59 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_123_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.85/1.59 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_124_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.85/1.59 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_125_le__add__same__cancel2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.85/1.59 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_126_le__add__same__cancel1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.85/1.59 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_127_add__le__same__cancel2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.85/1.59 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_128_add__le__same__cancel1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [B2: A,A2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.85/1.59 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_129_add__less__same__cancel1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [B2: A,A2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.85/1.59 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_130_add__less__same__cancel2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.85/1.59 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_131_less__add__same__cancel1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.85/1.59 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_132_less__add__same__cancel2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere516151231imp_le @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.85/1.59 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_133_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.85/1.59 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_134_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord219039673up_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.85/1.59 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_135_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ab_semigroup_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_136_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( I = J )
% 2.85/1.59 & ( K = L ) )
% 2.85/1.59 => ( ( plus_plus @ A @ I @ K )
% 2.85/1.59 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_137_group__cancel_Oadd1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( comm_monoid_add @ A )
% 2.85/1.59 => ! [A3: A,K: A,A2: A,B2: A] :
% 2.85/1.59 ( ( A3
% 2.85/1.59 = ( plus_plus @ A @ K @ A2 ) )
% 2.85/1.59 => ( ( plus_plus @ A @ A3 @ B2 )
% 2.85/1.59 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_138_group__cancel_Oadd2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( comm_monoid_add @ A )
% 2.85/1.59 => ! [B3: A,K: A,B2: A,A2: A] :
% 2.85/1.59 ( ( B3
% 2.85/1.59 = ( plus_plus @ A @ K @ B2 ) )
% 2.85/1.59 => ( ( plus_plus @ A @ A2 @ B3 )
% 2.85/1.59 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_139_add_Oassoc,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( semigroup_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_140_add_Oleft__cancel,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( group_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.85/1.59 = ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_141_add_Oright__cancel,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( group_add @ A )
% 2.85/1.59 => ! [B2: A,A2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.85/1.59 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.85/1.59 = ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_142_add_Ocommute,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ab_semigroup_add @ A )
% 2.85/1.59 => ( ( plus_plus @ A )
% 2.85/1.59 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_143_add_Oleft__commute,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ab_semigroup_add @ A )
% 2.85/1.59 => ! [B2: A,A2: A,C2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_144_add__left__imp__eq,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel_semigroup_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.85/1.59 => ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_145_add__right__imp__eq,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( cancel_semigroup_add @ A )
% 2.85/1.59 => ! [B2: A,A2: A,C2: A] :
% 2.85/1.59 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.85/1.59 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.85/1.59 => ( B2 = C2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_146_add__le__imp__le__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [A2: A,C2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.85/1.59 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_147_add__le__imp__le__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [C2: A,A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.85/1.59 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_148_le__iff__add,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ( ( ord_less_eq @ A )
% 2.85/1.59 = ( ^ [A4: A,B4: A] :
% 2.85/1.59 ? [C3: A] :
% 2.85/1.59 ( B4
% 2.85/1.59 = ( plus_plus @ A @ A4 @ C3 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_149_add__right__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_150_less__eqE,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ~ ! [C4: A] :
% 2.85/1.59 ( B2
% 2.85/1.59 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_151_add__left__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_152_add__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ C2 @ D )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_153_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less_eq @ A @ I @ J )
% 2.85/1.59 & ( ord_less_eq @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_154_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( I = J )
% 2.85/1.59 & ( ord_less_eq @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_155_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere779506340up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less_eq @ A @ I @ J )
% 2.85/1.59 & ( K = L ) )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_156_add_Ogroup__left__neutral,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( group_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 = A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_157_add_Ocomm__neutral,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( comm_monoid_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 = A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_158_comm__monoid__add__class_Oadd__0,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( comm_monoid_add @ A )
% 2.85/1.59 => ! [A2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 = A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_159_add__mono__thms__linordered__field_I5_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less @ A @ I @ J )
% 2.85/1.59 & ( ord_less @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_160_add__mono__thms__linordered__field_I2_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( I = J )
% 2.85/1.59 & ( ord_less @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_161_add__mono__thms__linordered__field_I1_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less @ A @ I @ J )
% 2.85/1.59 & ( K = L ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_162_add__strict__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( strict2144017051up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less @ A @ C2 @ D )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_163_add__strict__left__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_164_add__strict__right__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_165_add__less__imp__less__left,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [C2: A,A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.85/1.59 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_166_add__less__imp__less__right,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere236663937imp_le @ A )
% 2.85/1.59 => ! [A2: A,C2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.85/1.59 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_167_add__nonpos__eq__0__iff,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ X2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less_eq @ A @ Y2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ( plus_plus @ A @ X2 @ Y2 )
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 = ( ( X2
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 & ( Y2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_168_add__nonneg__eq__0__iff,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y2 )
% 2.85/1.59 => ( ( ( plus_plus @ A @ X2 @ Y2 )
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 = ( ( X2
% 2.85/1.59 = ( zero_zero @ A ) )
% 2.85/1.59 & ( Y2
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_169_add__nonpos__nonpos,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_170_add__nonneg__nonneg,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_171_add__increasing2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [C2: A,B2: A,A2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.85/1.59 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_172_add__decreasing2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [C2: A,A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_173_add__increasing,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_174_add__decreasing,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,C2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_175_add__less__le__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ C2 @ D )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_176_add__le__less__mono,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A,D: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less @ A @ C2 @ D )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_177_add__mono__thms__linordered__field_I3_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less @ A @ I @ J )
% 2.85/1.59 & ( ord_less_eq @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_178_add__mono__thms__linordered__field_I4_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere223160158up_add @ A )
% 2.85/1.59 => ! [I: A,J: A,K: A,L: A] :
% 2.85/1.59 ( ( ( ord_less_eq @ A @ I @ J )
% 2.85/1.59 & ( ord_less @ A @ K @ L ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_179_add__neg__neg,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_180_add__pos__pos,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_181_canonically__ordered__monoid__add__class_OlessE,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( canoni770627133id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ~ ! [C4: A] :
% 2.85/1.59 ( ( B2
% 2.85/1.59 = ( plus_plus @ A @ A2 @ C4 ) )
% 2.85/1.59 => ( C4
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_182_pos__add__strict,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( strict797366125id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_183_add__strict__increasing2,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere1818651114id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_184_add__strict__increasing,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere1818651114id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_185_add__pos__nonneg,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_186_add__nonpos__neg,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_187_add__nonneg__pos,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.85/1.59 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_188_add__neg__nonpos,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ordere216010020id_add @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_189_consec__add,axiom,
% 2.85/1.59 ! [R: real_int,S2: real_int,T: real_int] :
% 2.85/1.59 ( ( ( ( left @ R )
% 2.85/1.59 = ( left @ S2 ) )
% 2.85/1.59 & ( ( right @ R )
% 2.85/1.59 = ( right @ T ) )
% 2.85/1.59 & ( ( right @ S2 )
% 2.85/1.59 = ( left @ T ) ) )
% 2.85/1.59 => ( ( real_length @ R )
% 2.85/1.59 = ( plus_plus @ real @ ( real_length @ S2 ) @ ( real_length @ T ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_190_view_Ohorizontal__chop__empty__right,axiom,
% 2.85/1.59 ! [V2: view_ext @ product_unit] :
% 2.85/1.59 ? [X_1: view_ext @ product_unit] : ( hchop @ V2 @ V2 @ X_1 ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_191_view_Ohorizontal__chop__empty__left,axiom,
% 2.85/1.59 ! [V2: view_ext @ product_unit] :
% 2.85/1.59 ? [U2: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ V2 ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_192_view_Ohorizontal__chop__assoc2,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 & ( hchop @ V12 @ V33 @ V42 ) )
% 2.85/1.59 => ? [V4: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ V33 @ V4 )
% 2.85/1.59 & ( hchop @ V4 @ V42 @ V23 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_193_view_Ohorizontal__chop__assoc1,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,V33: view_ext @ product_unit,V42: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 & ( hchop @ V23 @ V33 @ V42 ) )
% 2.85/1.59 => ? [V4: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ V4 @ V42 )
% 2.85/1.59 & ( hchop @ V4 @ V12 @ V33 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_194_view_Ohorizontal__chop1,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit] :
% 2.85/1.59 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V @ U2 @ X_1 ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_195_view_Ohorizontal__chop__split__add,axiom,
% 2.85/1.59 ! [X2: real,Y2: real,V: view_ext @ product_unit] :
% 2.85/1.59 ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X2 )
% 2.85/1.59 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Y2 ) )
% 2.85/1.59 => ( ( ( real_length @ ( ext @ product_unit @ V ) )
% 2.85/1.59 = ( plus_plus @ real @ X2 @ Y2 ) )
% 2.85/1.59 => ? [U2: view_ext @ product_unit,W3: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U2 @ W3 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ U2 ) )
% 2.85/1.59 = X2 )
% 2.85/1.59 & ( ( real_length @ ( ext @ product_unit @ W3 ) )
% 2.85/1.59 = Y2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_196_sensors_Olen__hchop__add,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,V: view_ext @ product_unit,V12: view_ext @ product_unit,V23: view_ext @ product_unit,Ts: traffic,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( hchop @ V @ V12 @ V23 )
% 2.85/1.59 => ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 2.85/1.59 = ( plus_plus @ real @ ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_197_sensors_Oright__space,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( right @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 2.85/1.59 = ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_198_view_Ohorizontal__chop__own__trans,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U4 @ W2 )
% 2.85/1.59 => ( ( own @ product_unit @ U4 )
% 2.85/1.59 = ( own @ product_unit @ W2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_199_view_Ohorizontal__chop__leq2,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U4 @ W2 )
% 2.85/1.59 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W2 @ V ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_200_view_Ohorizontal__chop__leq1,axiom,
% 2.85/1.59 ! [V: view_ext @ product_unit,U4: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.85/1.59 ( ( hchop @ V @ U4 @ W2 )
% 2.85/1.59 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U4 @ V ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_201_zero__less__two,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_202_discrete,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( unique1598680935umeral @ A )
% 2.85/1.59 => ( ( ord_less @ A )
% 2.85/1.59 = ( ^ [A4: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_203_field__le__epsilon,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_field @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ! [E4: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( zero_zero @ A ) @ E4 )
% 2.85/1.59 => ( ord_less_eq @ A @ X2 @ ( plus_plus @ A @ Y2 @ E4 ) ) )
% 2.85/1.59 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_204_add__mono1,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less @ A @ A2 @ B2 )
% 2.85/1.59 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) @ ( plus_plus @ A @ B2 @ ( one_one @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_205_less__add__one,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_semidom @ A )
% 2.85/1.59 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_206_linorder__neqE__linordered__idom,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_idom @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( X2 != Y2 )
% 2.85/1.59 => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 2.85/1.59 => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_207_linordered__field__no__ub,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_field @ A )
% 2.85/1.59 => ! [X: A] :
% 2.85/1.59 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_208_linordered__field__no__lb,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_field @ A )
% 2.85/1.59 => ! [X: A] :
% 2.85/1.59 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_209_zero__neq__one,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( zero_neq_one @ A )
% 2.85/1.59 => ( ( zero_zero @ A )
% 2.85/1.59 != ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_210_zero__le__one,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_211_not__one__le__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_212_not__one__less__zero,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_213_zero__less__one,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( zero_less_one @ A )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_214_add__less__zeroD,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linordered_idom @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ord_less @ A @ ( plus_plus @ A @ X2 @ Y2 ) @ ( zero_zero @ A ) )
% 2.85/1.59 => ( ( ord_less @ A @ X2 @ ( zero_zero @ A ) )
% 2.85/1.59 | ( ord_less @ A @ Y2 @ ( zero_zero @ A ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_215_less__numeral__extra_I1_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_216_space__c,axiom,
% 2.85/1.59 ( ( space @ regular_regular @ ts @ v2 @ c )
% 2.85/1.59 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( zero_zero @ real ) @ ( one_one @ real ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_217_hmlsl_Ospace__def,axiom,
% 2.85/1.59 ! [Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( space @ regular_regular @ Ts @ V @ C2 )
% 2.85/1.59 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( pos @ Ts @ C2 ) @ ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_218_len__c,axiom,
% 2.85/1.59 ( ( len @ regular_regular @ v2 @ ts @ c )
% 2.85/1.59 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( zero_zero @ real ) @ ( one_one @ real ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_219_sensors_Ospace__def,axiom,
% 2.85/1.59 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_ext @ product_unit,C2: cars] :
% 2.85/1.59 ( ( sensors @ Sensors )
% 2.85/1.59 => ( ( space @ Sensors @ Ts @ V @ C2 )
% 2.85/1.59 = ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( pos @ Ts @ C2 ) @ ( plus_plus @ real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own @ product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_220_is__num__normalize_I1_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( neg_numeral @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.85/1.59 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_221_le__numeral__extra_I3_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_222_less__numeral__extra_I3_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_223_le__numeral__extra_I4_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_224_less__numeral__extra_I4_J,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linord1659791738miring @ A )
% 2.85/1.59 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_225_divides__aux__eq,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( unique1598680935umeral @ A )
% 2.85/1.59 => ! [Q: A,R: A] :
% 2.85/1.59 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q @ R ) )
% 2.85/1.59 = ( R
% 2.85/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_226_real__int__class_Oshift__def,axiom,
% 2.85/1.59 ( real_shift
% 2.85/1.59 = ( ^ [R2: real_int,X4: real] : ( real_Abs_real_int @ ( product_Pair @ real @ real @ ( plus_plus @ real @ ( left @ R2 ) @ X4 ) @ ( plus_plus @ real @ ( right @ R2 ) @ X4 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_227_shift__additivity,axiom,
% 2.85/1.59 ! [R: real_int,X2: real,Y2: real] :
% 2.85/1.59 ( ( real_shift @ R @ ( plus_plus @ real @ X2 @ Y2 ) )
% 2.85/1.59 = ( real_shift @ ( real_shift @ R @ X2 ) @ Y2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_228_shift__keeps__length,axiom,
% 2.85/1.59 ! [X2: real] :
% 2.85/1.59 ( real_length
% 2.85/1.59 = ( ^ [R2: real_int] : ( real_length @ ( real_shift @ R2 @ X2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_229_shift__zero,axiom,
% 2.85/1.59 ! [R: real_int] :
% 2.85/1.59 ( ( real_shift @ R @ ( zero_zero @ real ) )
% 2.85/1.59 = R ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_230_shift__left__eq__right,axiom,
% 2.85/1.59 ! [R: real_int,X2: real] : ( ord_less_eq @ real @ ( left @ ( real_shift @ R @ X2 ) ) @ ( right @ ( real_shift @ R @ X2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_231_ts__rep__def,axiom,
% 2.85/1.59 ( ts_rep
% 2.85/1.59 = ( product_Pair @ ( cars > real ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) ) @ po @ ( product_Pair @ ( cars > nat_int ) @ ( product_prod @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) ) @ re @ ( product_Pair @ ( cars > nat_int ) @ ( product_prod @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) ) @ cl @ ( product_Pair @ ( cars > real > real ) @ ( product_prod @ ( cars > real ) @ ( cars > real ) ) @ dy @ ( product_Pair @ ( cars > real ) @ ( cars > real ) @ ps @ sd ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_232_order__refl,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( preorder @ A )
% 2.85/1.59 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_233_clm__def,axiom,
% 2.85/1.59 ! [C: cars] :
% 2.85/1.59 ( ( cl @ C )
% 2.85/1.59 = ( bot_bot @ nat_int ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_234_dual__order_Oantisym,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [B2: A,A2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( A2 = B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_235_dual__order_Oeq__iff,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 2.85/1.59 = ( ^ [A4: A,B4: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ B4 @ A4 )
% 2.85/1.59 & ( ord_less_eq @ A @ A4 @ B4 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_236_dual__order_Otrans,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [B2: A,A2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.85/1.59 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_237_linorder__wlog,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linorder @ A )
% 2.85/1.59 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.85/1.59 ( ! [A5: A,B5: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.85/1.59 => ( P @ A5 @ B5 ) )
% 2.85/1.59 => ( ! [A5: A,B5: A] :
% 2.85/1.59 ( ( P @ B5 @ A5 )
% 2.85/1.59 => ( P @ A5 @ B5 ) )
% 2.85/1.59 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_238_dual__order_Orefl,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_239_order__trans,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( preorder @ A )
% 2.85/1.59 => ! [X2: A,Y2: A,Z3: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 2.85/1.59 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_240_order__class_Oorder_Oantisym,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [A2: A,B2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.85/1.59 => ( A2 = B2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_241_ord__le__eq__trans,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ord @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( B2 = C2 )
% 2.85/1.59 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_242_ord__eq__le__trans,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( ord @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( A2 = B2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_243_order__class_Oorder_Oeq__iff,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 2.85/1.59 = ( ^ [A4: A,B4: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A4 @ B4 )
% 2.85/1.59 & ( ord_less_eq @ A @ B4 @ A4 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_244_antisym__conv,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [Y2: A,X2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 = ( X2 = Y2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_245_le__cases3,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linorder @ A )
% 2.85/1.59 => ! [X2: A,Y2: A,Z3: A] :
% 2.85/1.59 ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 2.85/1.59 => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 2.85/1.59 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 2.85/1.59 => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 2.85/1.59 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 2.85/1.59 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 2.85/1.59 => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_246_order_Otrans,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [A2: A,B2: A,C2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.85/1.59 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_247_le__cases,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linorder @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_248_eq__refl,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( preorder @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( X2 = Y2 )
% 2.85/1.59 => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_249_linear,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( linorder @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_250_antisym,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ! [X2: A,Y2: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ X2 @ Y2 )
% 2.85/1.59 => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 2.85/1.59 => ( X2 = Y2 ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(fact_251_eq__iff,axiom,
% 2.85/1.59 ! [A: $tType] :
% 2.85/1.59 ( ( order @ A )
% 2.85/1.59 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 2.85/1.59 = ( ^ [X4: A,Y: A] :
% 2.85/1.59 ( ( ord_less_eq @ A @ X4 @ Y )
% 2.85/1.59 & ( ord_less_eq @ A @ Y @ X4 ) ) ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.85/1.59 ! [A6: $tType,A7: $tType] :
% 2.85/1.59 ( ( preorder @ A7 )
% 2.85/1.59 => ( preorder @ ( A6 > A7 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.85/1.59 ! [A6: $tType,A7: $tType] :
% 2.85/1.59 ( ( order @ A7 )
% 2.85/1.59 => ( order @ ( A6 > A7 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_fun___Orderings_Oord,axiom,
% 2.85/1.59 ! [A6: $tType,A7: $tType] :
% 2.85/1.59 ( ( ord @ A7 )
% 2.85/1.59 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_HOL_Obool___Orderings_Opreorder_1,axiom,
% 2.85/1.59 preorder @ $o ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.85/1.59 linorder @ $o ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 2.85/1.59 order @ $o ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_HOL_Obool___Orderings_Oord_3,axiom,
% 2.85/1.59 ord @ $o ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.85/1.59 ordere516151231imp_le @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.85/1.59 strict2144017051up_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.85/1.59 ordere223160158up_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.85/1.59 ordere236663937imp_le @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 2.85/1.59 strict797366125id_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 2.85/1.59 ordere1818651114id_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring,axiom,
% 2.85/1.59 linord1659791738miring @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add,axiom,
% 2.85/1.59 ordere779506340up_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add,axiom,
% 2.85/1.59 ordere216010020id_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 2.85/1.59 linord219039673up_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add,axiom,
% 2.85/1.59 cancel1352612707id_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add,axiom,
% 2.85/1.59 cancel_semigroup_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Rings_Olinordered__semidom,axiom,
% 2.85/1.59 linordered_semidom @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add,axiom,
% 2.85/1.59 ab_semigroup_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 2.85/1.59 linordered_field @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add,axiom,
% 2.85/1.59 comm_monoid_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 2.85/1.59 linordered_idom @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Osemigroup__add,axiom,
% 2.85/1.59 semigroup_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Rings_Ozero__less__one,axiom,
% 2.85/1.59 zero_less_one @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Rings_Ozero__neq__one,axiom,
% 2.85/1.59 zero_neq_one @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Orderings_Opreorder_4,axiom,
% 2.85/1.59 preorder @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Orderings_Olinorder_5,axiom,
% 2.85/1.59 linorder @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Omonoid__add,axiom,
% 2.85/1.59 monoid_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 2.85/1.59 group_add @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Orderings_Oorder_6,axiom,
% 2.85/1.59 order @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 2.85/1.59 neg_numeral @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Orderings_Oord_7,axiom,
% 2.85/1.59 ord @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Ozero,axiom,
% 2.85/1.59 zero @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Real_Oreal___Groups_Oone,axiom,
% 2.85/1.59 one @ real ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_8,axiom,
% 2.85/1.59 preorder @ nat_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_NatInt_Onat__int___Orderings_Oorder_9,axiom,
% 2.85/1.59 order @ nat_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_NatInt_Onat__int___Orderings_Oord_10,axiom,
% 2.85/1.59 ord @ nat_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_11,axiom,
% 2.85/1.59 preorder @ real_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_12,axiom,
% 2.85/1.59 order @ real_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_RealInt_Oreal__int___Orderings_Oord_13,axiom,
% 2.85/1.59 ord @ real_int ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_14,axiom,
% 2.85/1.59 preorder @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_15,axiom,
% 2.85/1.59 linorder @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Product__Type_Ounit___Orderings_Oorder_16,axiom,
% 2.85/1.59 order @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Product__Type_Ounit___Orderings_Oord_17,axiom,
% 2.85/1.59 ord @ product_unit ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_18,axiom,
% 2.85/1.59 ! [A6: $tType] :
% 2.85/1.59 ( ( order @ A6 )
% 2.85/1.59 => ( preorder @ ( view_ext @ A6 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_19,axiom,
% 2.85/1.59 ! [A6: $tType] :
% 2.85/1.59 ( ( order @ A6 )
% 2.85/1.59 => ( order @ ( view_ext @ A6 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_20,axiom,
% 2.85/1.59 ! [A6: $tType] :
% 2.85/1.59 ( ( order @ A6 )
% 2.85/1.59 => ( ord @ ( view_ext @ A6 ) ) ) ).
% 2.85/1.59
% 2.85/1.59 thf(conj_0,conjecture,
% 2.85/1.59 ( ( ord_less @ real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext @ product_unit @ v ) ) )
% 2.85/1.59 & ( ord_less @ real @ ( left @ ( ext @ product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) ) ) ).
% 2.85/1.59 ------------------------
% 3.05/1.62 % (15386)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_15185 for (2999ds/2Mi)
% 3.05/1.62 % (15384)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_15185 for (2999ds/27Mi)
% 3.05/1.62 % (15383)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_15185 for (2999ds/4Mi)
% 3.05/1.62 % (15386)Instruction limit reached!
% 3.05/1.62 % (15386)------------------------------
% 3.05/1.62 % (15386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (15386)Termination reason: Unknown
% 3.05/1.62 % (15385)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/2Mi)
% 3.05/1.62 % (15386)Termination phase: shuffling
% 3.05/1.62 % (15382)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/183Mi)
% 3.05/1.62
% 3.05/1.62 % (15386)Memory used [KB]: 1279
% 3.05/1.62 % (15386)Time elapsed: 0.002 s
% 3.05/1.62 % (15386)Instructions burned: 2 (million)
% 3.05/1.62 % (15386)------------------------------
% 3.05/1.62 % (15386)------------------------------
% 3.05/1.62 % (15388)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/18Mi)
% 3.05/1.62 % (15387)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_15185 for (2999ds/275Mi)
% 3.05/1.62 % (15383)Instruction limit reached!
% 3.05/1.62 % (15383)------------------------------
% 3.05/1.62 % (15383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (15383)Termination reason: Unknown
% 3.05/1.62 % (15383)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (15383)Memory used [KB]: 1407
% 3.05/1.62 % (15383)Time elapsed: 0.003 s
% 3.05/1.62 % (15383)Instructions burned: 5 (million)
% 3.05/1.62 % (15383)------------------------------
% 3.05/1.62 % (15383)------------------------------
% 3.05/1.62 % (15385)Instruction limit reached!
% 3.05/1.62 % (15385)------------------------------
% 3.05/1.62 % (15385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (15385)Termination reason: Unknown
% 3.05/1.62 % (15385)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (15385)Memory used [KB]: 1279
% 3.05/1.62 % (15385)Time elapsed: 0.002 s
% 3.05/1.62 % (15385)Instructions burned: 3 (million)
% 3.05/1.62 % (15385)------------------------------
% 3.05/1.62 % (15385)------------------------------
% 3.05/1.62 % (15388)Instruction limit reached!
% 3.05/1.62 % (15388)------------------------------
% 3.05/1.62 % (15388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (15388)Termination reason: Unknown
% 3.05/1.62 % (15388)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (15388)Memory used [KB]: 1663
% 3.05/1.62 % (15388)Time elapsed: 0.008 s
% 3.05/1.62 % (15388)Instructions burned: 20 (million)
% 3.05/1.62 % (15388)------------------------------
% 3.05/1.62 % (15388)------------------------------
% 3.05/1.63 % (15384)Instruction limit reached!
% 3.05/1.63 % (15384)------------------------------
% 3.05/1.63 % (15384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.63 % (15384)Termination reason: Unknown
% 3.05/1.63 % (15384)Termination phase: Property scanning
% 3.05/1.63
% 3.05/1.63 % (15384)Memory used [KB]: 1663
% 3.05/1.63 % (15384)Time elapsed: 0.011 s
% 3.05/1.63 % (15384)Instructions burned: 30 (million)
% 3.05/1.63 % (15384)------------------------------
% 3.05/1.63 % (15384)------------------------------
% 3.05/1.63 % (15389)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/3Mi)
% 3.05/1.63 % (15390)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_15185 for (2999ds/37Mi)
% 3.05/1.63 % (15391)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_15185 for (2999ds/15Mi)
% 3.05/1.63 % (15389)Instruction limit reached!
% 3.05/1.63 % (15389)------------------------------
% 3.05/1.63 % (15389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.63 % (15389)Termination reason: Unknown
% 3.05/1.63 % (15389)Termination phase: shuffling
% 3.05/1.63
% 3.05/1.63 % (15389)Memory used [KB]: 1407
% 3.05/1.63 % (15389)Time elapsed: 0.002 s
% 3.05/1.63 % (15389)Instructions burned: 3 (million)
% 3.05/1.63 % (15389)------------------------------
% 3.05/1.63 % (15389)------------------------------
% 3.05/1.63 % (15391)Instruction limit reached!
% 3.05/1.63 % (15391)------------------------------
% 3.05/1.63 % (15391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.63 % (15391)Termination reason: Unknown
% 3.05/1.63 % (15391)Termination phase: shuffling
% 3.05/1.63
% 3.05/1.63 % (15391)Memory used [KB]: 1535
% 3.05/1.63 % (15391)Time elapsed: 0.007 s
% 3.05/1.63 % (15391)Instructions burned: 15 (million)
% 3.05/1.63 % (15391)------------------------------
% 3.05/1.63 % (15391)------------------------------
% 3.05/1.63 % (15392)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_15185 for (2999ds/3Mi)
% 3.05/1.64 % (15393)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_15185 for (2999ds/1041Mi)
% 3.05/1.64 % (15392)Instruction limit reached!
% 3.05/1.64 % (15392)------------------------------
% 3.05/1.64 % (15392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (15392)Termination reason: Unknown
% 3.05/1.64 % (15392)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (15392)Memory used [KB]: 1407
% 3.05/1.64 % (15392)Time elapsed: 0.004 s
% 3.05/1.64 % (15392)Instructions burned: 4 (million)
% 3.05/1.64 % (15392)------------------------------
% 3.05/1.64 % (15392)------------------------------
% 3.05/1.64 % (15395)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/7Mi)
% 3.05/1.64 % (15390)Instruction limit reached!
% 3.05/1.64 % (15390)------------------------------
% 3.05/1.64 % (15390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (15390)Termination reason: Unknown
% 3.05/1.64 % (15390)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (15390)Memory used [KB]: 2046
% 3.05/1.64 % (15390)Time elapsed: 0.013 s
% 3.05/1.64 % (15390)Instructions burned: 37 (million)
% 3.05/1.64 % (15390)------------------------------
% 3.05/1.64 % (15390)------------------------------
% 3.05/1.64 % (15395)Instruction limit reached!
% 3.05/1.64 % (15395)------------------------------
% 3.05/1.64 % (15395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (15395)Termination reason: Unknown
% 3.05/1.64 % (15395)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (15395)Memory used [KB]: 1407
% 3.05/1.64 % (15395)Time elapsed: 0.004 s
% 3.05/1.64 % (15395)Instructions burned: 9 (million)
% 3.05/1.64 % (15395)------------------------------
% 3.05/1.64 % (15395)------------------------------
% 3.05/1.64 % (15397)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/16Mi)
% 3.05/1.65 % (15399)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_15185 for (2999ds/3Mi)
% 3.05/1.65 % (15399)Instruction limit reached!
% 3.05/1.65 % (15399)------------------------------
% 3.05/1.65 % (15399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (15399)Termination reason: Unknown
% 3.05/1.65 % (15399)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (15399)Memory used [KB]: 1407
% 3.05/1.65 % (15399)Time elapsed: 0.004 s
% 3.05/1.65 % (15399)Instructions burned: 4 (million)
% 3.05/1.65 % (15399)------------------------------
% 3.05/1.65 % (15399)------------------------------
% 3.05/1.65 % (15397)Instruction limit reached!
% 3.05/1.65 % (15397)------------------------------
% 3.05/1.65 % (15397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (15397)Termination reason: Unknown
% 3.05/1.65 % (15397)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (15397)Memory used [KB]: 1535
% 3.05/1.65 % (15397)Time elapsed: 0.009 s
% 3.05/1.65 % (15397)Instructions burned: 18 (million)
% 3.05/1.65 % (15397)------------------------------
% 3.05/1.65 % (15397)------------------------------
% 3.05/1.65 % (15400)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/7Mi)
% 3.05/1.65 % (15398)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_15185 for (2999ds/3Mi)
% 3.05/1.65 % (15398)Instruction limit reached!
% 3.05/1.65 % (15398)------------------------------
% 3.05/1.65 % (15398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (15398)Termination reason: Unknown
% 3.05/1.65 % (15398)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (15398)Memory used [KB]: 1279
% 3.05/1.65 % (15398)Time elapsed: 0.003 s
% 3.05/1.66 % (15398)Instructions burned: 3 (million)
% 3.05/1.66 % (15398)------------------------------
% 3.05/1.66 % (15398)------------------------------
% 3.05/1.66 % (15400)Instruction limit reached!
% 3.05/1.66 % (15400)------------------------------
% 3.05/1.66 % (15400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (15400)Termination reason: Unknown
% 3.05/1.66 % (15400)Termination phase: shuffling
% 3.05/1.66
% 3.05/1.66 % (15400)Memory used [KB]: 1407
% 3.05/1.66 % (15400)Time elapsed: 0.006 s
% 3.05/1.66 % (15400)Instructions burned: 8 (million)
% 3.05/1.66 % (15400)------------------------------
% 3.05/1.66 % (15400)------------------------------
% 3.05/1.66 % (15408)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/3Mi)
% 3.05/1.66 % (15408)Instruction limit reached!
% 3.05/1.66 % (15408)------------------------------
% 3.05/1.66 % (15408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (15408)Termination reason: Unknown
% 3.05/1.66 % (15408)Termination phase: shuffling
% 3.05/1.66
% 3.05/1.66 % (15408)Memory used [KB]: 1407
% 3.05/1.66 % (15408)Time elapsed: 0.002 s
% 3.05/1.66 % (15408)Instructions burned: 3 (million)
% 3.05/1.66 % (15408)------------------------------
% 3.05/1.66 % (15408)------------------------------
% 3.05/1.67 % (15409)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/4Mi)
% 3.05/1.67 % (15409)Instruction limit reached!
% 3.05/1.67 % (15409)------------------------------
% 3.05/1.67 % (15409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (15409)Termination reason: Unknown
% 3.05/1.67 % (15409)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (15409)Memory used [KB]: 1407
% 3.05/1.67 % (15409)Time elapsed: 0.004 s
% 3.05/1.67 % (15409)Instructions burned: 5 (million)
% 3.05/1.67 % (15409)------------------------------
% 3.05/1.67 % (15409)------------------------------
% 3.05/1.67 % (15411)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/710Mi)
% 3.05/1.67 % (15410)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/18Mi)
% 3.05/1.67 % (15412)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15185 for (2999ds/6Mi)
% 3.05/1.68 % (15412)Instruction limit reached!
% 3.05/1.68 % (15412)------------------------------
% 3.05/1.68 % (15412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (15412)Termination reason: Unknown
% 3.05/1.68 % (15412)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (15412)Memory used [KB]: 1407
% 3.05/1.68 % (15412)Time elapsed: 0.004 s
% 3.05/1.68 % (15412)Instructions burned: 6 (million)
% 3.05/1.68 % (15412)------------------------------
% 3.05/1.68 % (15412)------------------------------
% 3.05/1.68 % (15387)First to succeed.
% 3.05/1.68 % (15387)Refutation found. Thanks to Tanya!
% 3.05/1.68 % SZS status Theorem for DTF2THF_15185
% 3.05/1.68 % SZS output start Proof for DTF2THF_15185
% 3.05/1.68 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 3.05/1.68 thf(type_def_7, type, cars: $tType).
% 3.05/1.68 thf(type_def_8, type, traffic: $tType).
% 3.05/1.68 thf(type_def_9, type, real: $tType).
% 3.05/1.68 thf(type_def_10, type, product_unit: $tType).
% 3.05/1.68 thf(type_def_11, type, view_ext: ($tType) > $tType).
% 3.05/1.68 thf(type_def_12, type, real_int: $tType).
% 3.05/1.68 thf(type_def_13, type, nat_int: $tType).
% 3.05/1.68 thf(func_def_0, type, view_ext: ($tType) > $tType).
% 3.05/1.68 thf(func_def_1, type, product_unit: $tType).
% 3.05/1.68 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 3.05/1.68 thf(func_def_3, type, real_int: $tType).
% 3.05/1.68 thf(func_def_4, type, traffic: $tType).
% 3.05/1.68 thf(func_def_5, type, nat_int: $tType).
% 3.05/1.68 thf(func_def_6, type, real: $tType).
% 3.05/1.68 thf(func_def_7, type, cars: $tType).
% 3.05/1.68 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_9, type, one: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_10, type, zero: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_12, type, neg_numeral: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_14, type, group_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_15, type, monoid_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_18, type, zero_neq_one: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_19, type, zero_less_one: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_20, type, semigroup_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_21, type, linordered_idom: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_22, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_23, type, linordered_field: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_24, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_25, type, linordered_semidom: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_26, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_27, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_28, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_29, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_30, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_31, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_32, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_33, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_34, type, strict797366125id_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_35, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_36, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_37, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_38, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_39, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 3.05/1.68 thf(func_def_40, type, unique455577585es_aux: !>[X0: $tType]:(product_prod @ X0 @ X0 > $o)).
% 3.05/1.68 thf(func_def_41, type, one_one: !>[X0: $tType]:(X0)).
% 3.05/1.68 thf(func_def_42, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.05/1.68 thf(func_def_43, type, zero_zero: !>[X0: $tType]:(X0)).
% 3.05/1.68 thf(func_def_44, type, len: (cars > traffic > cars > real) > view_ext @ product_unit > traffic > cars > real_int).
% 3.05/1.68 thf(func_def_45, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.05/1.68 thf(func_def_46, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.05/1.68 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.05/1.68 thf(func_def_48, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.05/1.68 thf(func_def_49, type, left: real_int > real).
% 3.05/1.68 thf(func_def_50, type, real_Abs_real_int: product_prod @ real @ real > real_int).
% 3.05/1.68 thf(func_def_51, type, real_length: real_int > real).
% 3.05/1.68 thf(func_def_52, type, real_shift: real_int > real > real_int).
% 3.05/1.68 thf(func_def_53, type, right: real_int > real).
% 3.05/1.68 thf(func_def_54, type, regular_regular: cars > traffic > cars > real).
% 3.05/1.68 thf(func_def_55, type, sensors: (cars > traffic > cars > real) > $o).
% 3.05/1.68 thf(func_def_56, type, space: (cars > traffic > cars > real) > traffic > view_ext @ product_unit > cars > real_int).
% 3.05/1.68 thf(func_def_57, type, abs_traffic: product_prod @ (cars > real) @ product_prod @ (cars > nat_int) @ product_prod @ (cars > nat_int) @ product_prod @ (cars > real > real) @ product_prod @ (cars > real) @ (cars > real) > traffic).
% 3.05/1.68 thf(func_def_58, type, physical_size: traffic > cars > real).
% 3.05/1.68 thf(func_def_59, type, pos: traffic > cars > real).
% 3.05/1.68 thf(func_def_60, type, ext: !>[X0: $tType]:(view_ext @ X0 > real_int)).
% 3.05/1.68 thf(func_def_61, type, hchop: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > $o).
% 3.05/1.68 thf(func_def_62, type, own: !>[X0: $tType]:(view_ext @ X0 > cars)).
% 3.05/1.68 thf(func_def_63, type, c: cars).
% 3.05/1.68 thf(func_def_64, type, cl: cars > nat_int).
% 3.05/1.68 thf(func_def_65, type, d: cars).
% 3.05/1.68 thf(func_def_66, type, dy: cars > real > real).
% 3.05/1.68 thf(func_def_67, type, po: cars > real).
% 3.05/1.68 thf(func_def_68, type, ps: cars > real).
% 3.05/1.68 thf(func_def_69, type, re: cars > nat_int).
% 3.05/1.68 thf(func_def_70, type, sd: cars > real).
% 3.05/1.68 thf(func_def_71, type, ts: traffic).
% 3.05/1.68 thf(func_def_72, type, ts_rep: product_prod @ (cars > real) @ product_prod @ (cars > nat_int) @ product_prod @ (cars > nat_int) @ product_prod @ (cars > real > real) @ product_prod @ (cars > real) @ (cars > real)).
% 3.05/1.68 thf(func_def_73, type, v: view_ext @ product_unit).
% 3.05/1.68 thf(func_def_74, type, v2: view_ext @ product_unit).
% 3.05/1.68 thf(func_def_88, type, sP0: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 3.05/1.68 thf(func_def_89, type, sP1: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > $o).
% 3.05/1.68 thf(func_def_90, type, sP2: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > $o).
% 3.05/1.68 thf(func_def_91, type, sP3: (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > $o).
% 3.05/1.68 thf(func_def_92, type, sK4: (cars > traffic > cars > real) > cars).
% 3.05/1.68 thf(func_def_93, type, sK5: (cars > traffic > cars > real) > traffic).
% 3.05/1.68 thf(func_def_94, type, sK6: (cars > traffic > cars > real) > cars).
% 3.05/1.68 thf(func_def_95, type, sK7: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_96, type, sK8: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_97, type, sK9: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_98, type, sK10: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_99, type, sK11: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_100, type, sK12: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_101, type, sK13: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_102, type, sK14: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_103, type, sK15: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_104, type, sK16: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_105, type, sK17: cars > traffic > view_ext @ product_unit > (cars > traffic > cars > real) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_106, type, sK18: cars > traffic > view_ext @ product_unit > (cars > traffic > cars > real) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_107, type, sK19: cars > traffic > view_ext @ product_unit > (cars > traffic > cars > real) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_108, type, sK20: cars > traffic > view_ext @ product_unit > (cars > traffic > cars > real) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_109, type, sK21: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_110, type, sK22: cars > real > real).
% 3.05/1.68 thf(func_def_111, type, sK23: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_112, type, sK24: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_113, type, sK25: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_114, type, sK26: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_115, type, sK27: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_116, type, sK28: view_ext @ product_unit > real > real > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_117, type, sK29: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_118, type, sK30: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_119, type, sK31: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_120, type, sK32: cars > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_121, type, sK33: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.05/1.68 thf(func_def_122, type, sK34: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_123, type, sK35: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_124, type, sK36: 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).
% 3.05/1.68 thf(func_def_125, type, sK37: 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).
% 3.05/1.68 thf(func_def_126, type, sK38: 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).
% 3.05/1.68 thf(func_def_127, type, sK39: 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).
% 3.05/1.68 thf(func_def_128, type, sK40: 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).
% 3.05/1.68 thf(func_def_129, 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).
% 3.05/1.68 thf(func_def_130, 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).
% 3.05/1.68 thf(func_def_131, 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).
% 3.05/1.68 thf(func_def_132, type, sK44: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_133, type, sK45: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_134, type, sK46: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_135, type, sK47: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_136, type, sK48: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_137, type, sK49: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_138, type, sK50: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_139, type, sK51: 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).
% 3.05/1.68 thf(func_def_140, type, sK52: 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).
% 3.05/1.68 thf(func_def_141, type, sK53: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_142, type, sK54: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_143, type, sK55: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_144, type, sK56: view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_145, type, sK57: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_146, type, sK58: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_147, type, sK59: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_148, type, sK60: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_149, type, sK61: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_150, type, sK62: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_151, type, sK63: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_152, type, sK64: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_153, type, sK65: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_154, type, sK66: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_155, type, sK67: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_156, type, sK68: (traffic > view_ext @ product_unit > $o) > (traffic > view_ext @ product_unit > $o) > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 3.05/1.68 thf(func_def_157, type, sK69: 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).
% 3.05/1.68 thf(func_def_158, type, sK70: 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).
% 3.05/1.68 thf(func_def_160, type, ph72: !>[X0: $tType]:(X0)).
% 3.05/1.68 thf(f1265,plain,(
% 3.05/1.68 $false),
% 3.05/1.68 inference(avatar_sat_refutation,[status(thm)],[f1224,f1243,f1264])).
% 3.05/1.68 thf(f1264,plain,(
% 3.05/1.68 spl71_2),
% 3.05/1.68 inference(avatar_contradiction_clause,[status(thm)],[f1263])).
% 3.05/1.68 thf(f1263,plain,(
% 3.05/1.68 $false | spl71_2),
% 3.05/1.68 inference(subsumption_resolution,[status(thm)],[f1262,f1103])).
% 3.05/1.68 thf(f1103,plain,(
% 3.05/1.68 ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) = $true)),
% 3.05/1.68 inference(cnf_transformation,[status(thm)],[f626])).
% 3.05/1.68 thf(f626,plain,(
% 3.05/1.68 ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) = $true)),
% 3.05/1.68 inference(fool_elimination,[status(thm)],[f625])).
% 3.05/1.68 thf(f625,plain,(
% 3.05/1.68 (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d)))),
% 3.05/1.68 inference(rectify,[status(thm)],[f5])).
% 3.05/1.68 thf(f5,axiom,(
% 3.05/1.68 (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d)))),
% 3.05/1.68 file('/export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2THF_15185.p',fact_4_v_H__d)).
% 3.05/1.68 thf(f1262,plain,(
% 3.05/1.68 ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) != $true) | spl71_2),
% 3.05/1.68 inference(subsumption_resolution,[status(thm)],[f1249,f1061])).
% 3.05/1.68 thf(f1061,plain,(
% 3.05/1.68 ((sensors @ regular_regular) = $true)),
% 3.05/1.68 inference(cnf_transformation,[status(thm)],[f630])).
% 3.05/1.68 thf(f630,plain,(
% 3.05/1.68 ((sensors @ regular_regular) = $true)),
% 3.05/1.68 inference(fool_elimination,[status(thm)],[f629])).
% 3.05/1.68 thf(f629,plain,(
% 3.05/1.68 (sensors @ regular_regular)),
% 3.05/1.68 inference(rectify,[status(thm)],[f21])).
% 3.05/1.68 thf(f21,axiom,(
% 3.05/1.68 (sensors @ regular_regular)),
% 3.05/1.68 file('/export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2THF_15185.p',fact_20_hmlsl_Osensors__axioms)).
% 3.05/1.68 thf(f1249,plain,(
% 3.05/1.68 ((sensors @ regular_regular) != $true) | ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) != $true) | spl71_2),
% 3.05/1.68 inference(trivial_inequality_removal,[status(thm)],[f1248])).
% 3.05/1.68 thf(f1248,plain,(
% 3.05/1.68 ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) != $true) | ((sensors @ regular_regular) != $true) | ($true != $true) | spl71_2),
% 3.05/1.68 inference(superposition,[status(thm)],[f1223,f1130])).
% 3.05/1.68 thf(f1130,plain,(
% 3.05/1.68 ( ! [X2 : traffic,X3 : cars,X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit] : (($true = (ord_less @ real @ (left @ (ext @ product_unit @ X1)) @ (right @ (space @ X0 @ X2 @ X1 @ X3)))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3)))) | ($true != (sensors @ X0))) )),
% 3.05/1.68 inference(cnf_transformation,[status(thm)],[f892])).
% 3.05/1.68 thf(f892,plain,(
% 3.05/1.68 ! [X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit,X2 : traffic,X3 : cars] : (($true != (sensors @ X0)) | (($true = (ord_less @ real @ (left @ (space @ X0 @ X2 @ X1 @ X3)) @ (right @ (ext @ product_unit @ X1)))) & ($true = (ord_less @ real @ (left @ (ext @ product_unit @ X1)) @ (right @ (space @ X0 @ X2 @ X1 @ X3))))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3)))))),
% 3.05/1.68 inference(flattening,[status(thm)],[f891])).
% 3.05/1.68 thf(f891,plain,(
% 3.05/1.68 ! [X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit,X2 : traffic,X3 : cars] : (((($true = (ord_less @ real @ (left @ (space @ X0 @ X2 @ X1 @ X3)) @ (right @ (ext @ product_unit @ X1)))) & ($true = (ord_less @ real @ (left @ (ext @ product_unit @ X1)) @ (right @ (space @ X0 @ X2 @ X1 @ X3))))) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3))))) | ($true != (sensors @ X0)))),
% 3.05/1.68 inference(ennf_transformation,[status(thm)],[f772])).
% 3.05/1.68 thf(f772,plain,(
% 3.05/1.68 ! [X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit,X2 : traffic,X3 : cars] : (($true = (sensors @ X0)) => (($true = (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3)))) => (($true = (ord_less @ real @ (left @ (space @ X0 @ X2 @ X1 @ X3)) @ (right @ (ext @ product_unit @ X1)))) & ($true = (ord_less @ real @ (left @ (ext @ product_unit @ X1)) @ (right @ (space @ X0 @ X2 @ X1 @ X3)))))))),
% 3.05/1.68 inference(fool_elimination,[status(thm)],[f771])).
% 3.05/1.68 thf(f771,plain,(
% 3.05/1.68 ! [X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit,X2 : traffic,X3 : cars] : ((sensors @ X0) => ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3))) => ((ord_less @ real @ (left @ (space @ X0 @ X2 @ X1 @ X3)) @ (right @ (ext @ product_unit @ X1))) & (ord_less @ real @ (left @ (ext @ product_unit @ X1)) @ (right @ (space @ X0 @ X2 @ X1 @ X3))))))),
% 3.05/1.68 inference(rectify,[status(thm)],[f25])).
% 3.05/1.68 thf(f25,axiom,(
% 3.05/1.68 ! [X12 : cars > traffic > cars > real,X9 : view_ext @ product_unit,X7 : traffic,X8 : cars] : ((sensors @ X12) => ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X12 @ X9 @ X7 @ X8))) => ((ord_less @ real @ (left @ (space @ X12 @ X7 @ X9 @ X8)) @ (right @ (ext @ product_unit @ X9))) & (ord_less @ real @ (left @ (ext @ product_unit @ X9)) @ (right @ (space @ X12 @ X7 @ X9 @ X8))))))),
% 3.05/1.68 file('/export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2THF_15185.p',fact_24_sensors_Olen__non__empty__inside)).
% 3.05/1.68 thf(f1223,plain,(
% 3.05/1.68 ((ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) != $true) | spl71_2),
% 3.05/1.68 inference(avatar_component_clause,[status(thm)],[f1221])).
% 3.05/1.68 thf(f1221,definition,(
% 3.05/1.68 spl71_2 <=> ((ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) = $true)),
% 3.05/1.68 introduced(definition,[new_symbols(naming,[spl71_2])],[avatar_definition])).
% 3.05/1.68 thf(f1243,plain,(
% 3.05/1.68 spl71_1),
% 3.05/1.68 inference(avatar_contradiction_clause,[status(thm)],[f1242])).
% 3.05/1.68 thf(f1242,plain,(
% 3.05/1.68 $false | spl71_1),
% 3.05/1.68 inference(subsumption_resolution,[status(thm)],[f1241,f1061])).
% 3.05/1.68 thf(f1241,plain,(
% 3.05/1.68 ((sensors @ regular_regular) != $true) | spl71_1),
% 3.05/1.68 inference(subsumption_resolution,[status(thm)],[f1228,f1103])).
% 3.05/1.68 thf(f1228,plain,(
% 3.05/1.68 ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) != $true) | ((sensors @ regular_regular) != $true) | spl71_1),
% 3.05/1.68 inference(trivial_inequality_removal,[status(thm)],[f1226])).
% 3.05/1.68 thf(f1226,plain,(
% 3.05/1.68 ((sensors @ regular_regular) != $true) | ((ord_less @ real @ zero_zero @ real @ (real_length @ (len @ regular_regular @ v @ ts @ d))) != $true) | ($true != $true) | spl71_1),
% 3.05/1.68 inference(superposition,[status(thm)],[f1219,f1131])).
% 3.05/1.68 thf(f1131,plain,(
% 3.05/1.68 ( ! [X2 : traffic,X3 : cars,X0 : cars > traffic > cars > real,X1 : view_ext @ product_unit] : (($true = (ord_less @ real @ (left @ (space @ X0 @ X2 @ X1 @ X3)) @ (right @ (ext @ product_unit @ X1)))) | ($true != (sensors @ X0)) | ($true != (ord_less @ real @ zero_zero @ real @ (real_length @ (len @ X0 @ X1 @ X2 @ X3))))) )),
% 3.05/1.68 inference(cnf_transformation,[status(thm)],[f892])).
% 3.05/1.68 thf(f1219,plain,(
% 3.05/1.68 ((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) != $true) | spl71_1),
% 3.05/1.68 inference(avatar_component_clause,[status(thm)],[f1217])).
% 3.05/1.68 thf(f1217,definition,(
% 3.05/1.68 spl71_1 <=> ((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) = $true)),
% 3.05/1.68 introduced(definition,[new_symbols(naming,[spl71_1])],[avatar_definition])).
% 3.05/1.68 thf(f1224,plain,(
% 3.05/1.68 ~spl71_1 | ~spl71_2),
% 3.05/1.68 inference(avatar_split_clause,[status(thm)],[f1082,f1221,f1217])).
% 3.05/1.68 thf(f1082,plain,(
% 3.05/1.68 ((ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) != $true) | ((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) != $true)),
% 3.05/1.68 inference(cnf_transformation,[status(thm)],[f902])).
% 3.05/1.68 thf(f902,plain,(
% 3.05/1.68 ((ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) != $true) | ((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) != $true)),
% 3.05/1.68 inference(ennf_transformation,[status(thm)],[f634])).
% 3.05/1.68 thf(f634,plain,(
% 3.05/1.68 ~(((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) = $true) & ((ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) = $true))),
% 3.05/1.68 inference(fool_elimination,[status(thm)],[f633])).
% 3.05/1.68 thf(f633,plain,(
% 3.05/1.68 ~((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) & (ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))))),
% 3.05/1.68 inference(rectify,[status(thm)],[f303])).
% 3.05/1.68 thf(f303,negated_conjecture,(
% 3.05/1.68 ~((ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) & (ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))))),
% 3.05/1.68 inference(negated_conjecture,[status(cth)],[f302])).
% 3.05/1.68 thf(f302,conjecture,(
% 3.05/1.68 (ord_less @ real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext @ product_unit @ v))) & (ord_less @ real @ (left @ (ext @ product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d)))),
% 3.05/1.68 file('/export/starexec/sandbox/tmp/tmp.RCeqlw0Dl5/DTF2THF_15185.p',conj_0)).
% 3.05/1.68 % SZS output end Proof for DTF2THF_15185
% 3.05/1.68 % (15387)------------------------------
% 3.05/1.68 % (15387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (15387)Termination reason: Refutation
% 3.05/1.68
% 3.05/1.68 % (15387)Memory used [KB]: 7036
% 3.05/1.68 % (15387)Time elapsed: 0.063 s
% 3.05/1.68 % (15387)Instructions burned: 104 (million)
% 3.05/1.68 % (15387)------------------------------
% 3.05/1.68 % (15387)------------------------------
% 3.05/1.68 % (15376)Success in time 0.067 s
%------------------------------------------------------------------------------