%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP170^1 : 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 : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:07 AM UTC 2026
% Result : Theorem 2.11s 1.34s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 107 ( 29 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 399 ( 15 ~; 10 |; 8 &; 361 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 13 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
real: $tType ).
thf(type_def_7,type,
cars: $tType ).
thf(type_def_8,type,
traffic: $tType ).
thf(type_def_9,type,
view_e774982825t_unit: $tType ).
thf(type_def_10,type,
real_int: $tType ).
thf(type_def_11,type,
nat_int: $tType ).
thf(type_def_12,type,
produc427086159s_real: $tType ).
thf(type_def_13,type,
produc1622321602s_real: $tType ).
thf(type_def_14,type,
produc28608506s_real: $tType ).
thf(type_def_15,type,
produc1603581272s_real: $tType ).
thf(type_def_16,type,
produc458204144s_real: $tType ).
thf(type_def_17,type,
produc957004601l_real: $tType ).
thf(func_def_0,type,
produc458204144s_real: $tType ).
thf(func_def_1,type,
produc1603581272s_real: $tType ).
thf(func_def_2,type,
produc28608506s_real: $tType ).
thf(func_def_3,type,
produc1622321602s_real: $tType ).
thf(func_def_4,type,
produc427086159s_real: $tType ).
thf(func_def_5,type,
produc957004601l_real: $tType ).
thf(func_def_6,type,
view_e774982825t_unit: $tType ).
thf(func_def_7,type,
real_int: $tType ).
thf(func_def_8,type,
nat_int: $tType ).
thf(func_def_9,type,
traffic: $tType ).
thf(func_def_10,type,
real: $tType ).
thf(func_def_11,type,
cars: $tType ).
thf(func_def_12,type,
one_one_real: real ).
thf(func_def_13,type,
plus_plus_real: real > real > real ).
thf(func_def_14,type,
zero_zero_real: real ).
thf(func_def_15,type,
len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
thf(func_def_16,type,
bot_bot_nat_int: nat_int ).
thf(func_def_17,type,
ord_less_real_int: real_int > real_int > $o ).
thf(func_def_18,type,
ord_less_real: real > real > $o ).
thf(func_def_19,type,
ord_less_eq_real_int: real_int > real_int > $o ).
thf(func_def_20,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_21,type,
ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(func_def_22,type,
produc795767668s_real: ( cars > real > real ) > produc427086159s_real > produc1622321602s_real ).
thf(func_def_23,type,
produc1348924850s_real: ( cars > nat_int ) > produc1622321602s_real > produc28608506s_real ).
thf(func_def_24,type,
produc1230243850s_real: ( cars > nat_int ) > produc28608506s_real > produc1603581272s_real ).
thf(func_def_25,type,
produc1439932679s_real: ( cars > real ) > ( cars > real ) > produc427086159s_real ).
thf(func_def_26,type,
produc1876576040s_real: ( cars > real ) > produc1603581272s_real > produc458204144s_real ).
thf(func_def_27,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(func_def_28,type,
left: real_int > real ).
thf(func_def_29,type,
real_Abs_real_int: produc957004601l_real > real_int ).
thf(func_def_30,type,
real_length: real_int > real ).
thf(func_def_31,type,
real_shift: real_int > real > real_int ).
thf(func_def_32,type,
right: real_int > real ).
thf(func_def_33,type,
regular_regular: cars > traffic > cars > real ).
thf(func_def_34,type,
sensors: ( cars > traffic > cars > real ) > $o ).
thf(func_def_35,type,
space: ( cars > traffic > cars > real ) > traffic > view_e774982825t_unit > cars > real_int ).
thf(func_def_36,type,
abs_traffic: produc458204144s_real > traffic ).
thf(func_def_37,type,
physical_size: traffic > cars > real ).
thf(func_def_38,type,
pos: traffic > cars > real ).
thf(func_def_39,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(func_def_40,type,
hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(func_def_41,type,
own_Product_unit: view_e774982825t_unit > cars ).
thf(func_def_42,type,
c: cars ).
thf(func_def_43,type,
cl: cars > nat_int ).
thf(func_def_44,type,
d: cars ).
thf(func_def_45,type,
dy: cars > real > real ).
thf(func_def_46,type,
po: cars > real ).
thf(func_def_47,type,
ps: cars > real ).
thf(func_def_48,type,
re: cars > nat_int ).
thf(func_def_49,type,
sd: cars > real ).
thf(func_def_50,type,
ts: traffic ).
thf(func_def_51,type,
ts_rep: produc458204144s_real ).
thf(func_def_52,type,
v: view_e774982825t_unit ).
thf(func_def_53,type,
v2: view_e774982825t_unit ).
thf(func_def_66,type,
sK0: real > real ).
thf(func_def_67,type,
sK1: real > real ).
thf(func_def_68,type,
sK2: real > real > real ).
thf(func_def_69,type,
sK3: cars > real > real ).
thf(func_def_71,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f1793,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f897,f1750,f1792]) ).
thf(f1792,plain,
spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f1791]) ).
thf(f1791,plain,
( $false
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f1790,f892]) ).
thf(f892,plain,
( ( ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) )
!= $true )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f890]) ).
thf(f890,definition,
( spl4_1
<=> ( ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f1790,plain,
( ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f1781,f828]) ).
thf(f828,plain,
( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f466]) ).
thf(f466,plain,
( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f465]) ).
thf(f465,plain,
ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ),
file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_19_v_H__c) ).
thf(f1781,plain,
( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) )
!= $true )
| ( ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f806,f804]) ).
thf(f804,plain,
( ( len @ regular_regular @ v @ ts @ d )
= ( len @ regular_regular @ v @ ts @ c ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,axiom,
( ( len @ regular_regular @ v @ ts @ d )
= ( len @ regular_regular @ v @ ts @ c ) ),
file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_11_len__eq) ).
thf(f806,plain,
! [X2: traffic,X0: view_e774982825t_unit,X1: cars] :
( ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X0 @ X2 @ X1 ) ) ) )
| ( ( ord_less_real @ ( left @ ( ext_Product_unit @ X0 ) ) @ ( right @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f767]) ).
thf(f767,plain,
! [X0: view_e774982825t_unit,X1: cars,X2: traffic] :
( ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X0 @ X2 @ X1 ) ) ) )
| ( ( ( ord_less_real @ ( left @ ( ext_Product_unit @ X0 ) ) @ ( right @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) )
= $true )
& ( ( ord_less_real @ ( left @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) @ ( right @ ( ext_Product_unit @ X0 ) ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f504]) ).
thf(f504,plain,
! [X0: view_e774982825t_unit,X1: cars,X2: traffic] :
( ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X0 @ X2 @ X1 ) ) ) )
=> ( ( ( ord_less_real @ ( left @ ( ext_Product_unit @ X0 ) ) @ ( right @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) )
= $true )
& ( ( ord_less_real @ ( left @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) @ ( right @ ( ext_Product_unit @ X0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f503]) ).
thf(f503,plain,
! [X0: view_e774982825t_unit,X1: cars,X2: traffic] :
( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X0 @ X2 @ X1 ) ) )
=> ( ( ord_less_real @ ( left @ ( ext_Product_unit @ X0 ) ) @ ( right @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) )
& ( ord_less_real @ ( left @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) @ ( right @ ( ext_Product_unit @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X6: view_e774982825t_unit,X5: cars,X4: traffic] :
( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X6 @ X4 @ X5 ) ) )
=> ( ( ord_less_real @ ( left @ ( ext_Product_unit @ X6 ) ) @ ( right @ ( space @ regular_regular @ X4 @ X6 @ X5 ) ) )
& ( ord_less_real @ ( left @ ( space @ regular_regular @ X4 @ X6 @ X5 ) ) @ ( right @ ( ext_Product_unit @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_3_hmlsl_Olen__non__empty__inside) ).
thf(f1750,plain,
spl4_2,
inference(avatar_split_clause,[status(thm)],[f1749,f894]) ).
thf(f894,definition,
( spl4_2
<=> ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f1749,plain,
( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f1740,f828]) ).
thf(f1740,plain,
( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) )
!= $true )
| ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f805,f804]) ).
thf(f805,plain,
! [X2: traffic,X0: view_e774982825t_unit,X1: cars] :
( ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X0 @ X2 @ X1 ) ) ) )
| ( ( ord_less_real @ ( left @ ( space @ regular_regular @ X2 @ X0 @ X1 ) ) @ ( right @ ( ext_Product_unit @ X0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f767]) ).
thf(f897,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f837,f894,f890]) ).
thf(f837,plain,
( ( ( 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 ) ),
inference(cnf_transformation,[status(thm)],[f732]) ).
thf(f732,plain,
( ( ( 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 ) ),
inference(ennf_transformation,[status(thm)],[f616]) ).
thf(f616,plain,
~ ( ( ( 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 ) ),
inference(fool_elimination,[status(thm)],[f615]) ).
thf(f615,plain,
~ ( ( 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 ) ) ) ),
inference(rectify,[status(thm)],[f269]) ).
thf(f269,negated_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 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f268]) ).
thf(f268,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 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP170^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 03:28:25 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : ITP170^1 : TPTP v9.2.1. Released v7.5.0.
% 0.08/0.31 % Domain : Interactive Theorem Proving
% 0.08/0.31 % Problem : Sledgehammer Safety_Regular problem prob_415__3354378_1
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.08/0.31 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.08/0.31 % Source : [Des21]
% 0.08/0.31 % Names : Safety_Regular/prob_415__3354378_1 [Des21]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.08/0.31 % Syntax : Number of formulae : 322 ( 122 unt; 54 typ; 0 def)
% 0.08/0.31 % Number of atoms : 683 ( 248 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 12 ( 2 avg)
% 0.08/0.31 % Number of connectives : 2476 ( 28 ~; 7 |; 116 &;2101 @)
% 0.08/0.31 % ( 0 <=>; 224 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 16 ( 7 avg)
% 0.08/0.31 % Number of types : 13 ( 12 usr)
% 0.08/0.31 % Number of type conns : 189 ( 189 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 43 ( 42 usr; 9 con; 0-4 aty)
% 0.08/0.31 % Number of variables : 775 ( 46 ^; 661 !; 68 ?; 775 :)
% 0.08/0.31 % SPC : TH0_THM_EQU_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:16.446
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % Could-be-implicit typings (12)
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J_J,type,
% 0.08/0.31 produc458204144s_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J,type,
% 0.08/0.31 produc1603581272s_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J,type,
% 0.08/0.31 produc28608506s_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J,type,
% 0.08/0.31 produc1622321602s_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J,type,
% 0.08/0.31 produc427086159s_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.08/0.31 produc957004601l_real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 0.08/0.31 view_e774982825t_unit: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__RealInt__Oreal____int,type,
% 0.08/0.31 real_int: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__NatInt__Onat____int,type,
% 0.08/0.31 nat_int: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Traffic__Otraffic,type,
% 0.08/0.31 traffic: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Real__Oreal,type,
% 0.08/0.31 real: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(ty_n_t__Cars__Ocars,type,
% 0.08/0.31 cars: $tType ).
% 0.08/0.31
% 0.08/0.31 % Explicit typings (42)
% 0.08/0.31 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 0.08/0.31 one_one_real: real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.08/0.31 plus_plus_real: real > real > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.08/0.31 zero_zero_real: real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Length_Osensors_Olen,type,
% 0.08/0.31 len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Obot__class_Obot_001t__NatInt__Onat____int,type,
% 0.08/0.31 bot_bot_nat_int: nat_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Oord__class_Oless_001t__RealInt__Oreal____int,type,
% 0.08/0.31 ord_less_real_int: real_int > real_int > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.08/0.31 ord_less_real: real > real > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__RealInt__Oreal____int,type,
% 0.08/0.31 ord_less_eq_real_int: real_int > real_int > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.08/0.31 ord_less_eq_real: real > real > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 0.08/0.31 ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J,type,
% 0.08/0.31 produc795767668s_real: ( cars > real > real ) > produc427086159s_real > produc1622321602s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J,type,
% 0.08/0.31 produc1348924850s_real: ( cars > nat_int ) > produc1622321602s_real > produc28608506s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J,type,
% 0.08/0.31 produc1230243850s_real: ( cars > nat_int ) > produc28608506s_real > produc1603581272s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__Real__Oreal_J_001_062_It__Cars__Ocars_Mt__Real__Oreal_J,type,
% 0.08/0.31 produc1439932679s_real: ( cars > real ) > ( cars > real ) > produc427086159s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J,type,
% 0.08/0.31 produc1876576040s_real: ( cars > real ) > produc1603581272s_real > produc458204144s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.08/0.31 produc705216881l_real: real > real > produc957004601l_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_RealInt_Oleft,type,
% 0.08/0.31 left: real_int > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_RealInt_Oreal__int_OAbs__real__int,type,
% 0.08/0.31 real_Abs_real_int: produc957004601l_real > real_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 0.08/0.31 real_length: real_int > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 0.08/0.31 real_shift: real_int > real > real_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_RealInt_Oright,type,
% 0.08/0.31 right: real_int > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Regular__Sensors_Oregular,type,
% 0.08/0.31 regular_regular: cars > traffic > cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Sensors_Osensors,type,
% 0.08/0.31 sensors: ( cars > traffic > cars > real ) > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Sensors_Osensors_Ospace,type,
% 0.08/0.31 space: ( cars > traffic > cars > real ) > traffic > view_e774982825t_unit > cars > real_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Traffic_Otraffic_OAbs__traffic,type,
% 0.08/0.31 abs_traffic: produc458204144s_real > traffic ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 0.08/0.31 physical_size: traffic > cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Traffic_Otraffic_Opos,type,
% 0.08/0.31 pos: traffic > cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Views_Oview_Oext_001t__Product____Type__Ounit,type,
% 0.08/0.31 ext_Product_unit: view_e774982825t_unit > real_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Views_Oview_Ohchop,type,
% 0.08/0.31 hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 0.08/0.31
% 0.08/0.31 thf(sy_c_Views_Oview_Oown_001t__Product____Type__Ounit,type,
% 0.08/0.31 own_Product_unit: view_e774982825t_unit > cars ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_c____,type,
% 0.08/0.31 c: cars ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_cl____,type,
% 0.08/0.31 cl: cars > nat_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_d____,type,
% 0.08/0.31 d: cars ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_dy____,type,
% 0.08/0.31 dy: cars > real > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_po____,type,
% 0.08/0.31 po: cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_ps____,type,
% 0.08/0.31 ps: cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_re____,type,
% 0.08/0.31 re: cars > nat_int ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_sd____,type,
% 0.08/0.31 sd: cars > real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_ts____,type,
% 0.08/0.31 ts: traffic ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_ts__rep____,type,
% 0.08/0.31 ts_rep: produc458204144s_real ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_v_H____,type,
% 0.08/0.31 v: view_e774982825t_unit ).
% 0.08/0.31
% 0.08/0.31 thf(sy_v_v____,type,
% 0.08/0.31 v2: view_e774982825t_unit ).
% 0.08/0.31
% 0.08/0.31 % Relevant facts (267)
% 0.08/0.31 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,
% 0.08/0.31 ~ ! [Dy: cars > real > real] :
% 0.08/0.31 ~ ! [C: cars,X: real] :
% 0.08/0.31 ( ( Dy @ C @ X )
% 0.08/0.31 = zero_zero_real ) ).
% 0.08/0.31
% 0.08/0.31 % \<open>\<And>thesis. (\<And>dy. \<forall>c x. dy c x = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.08/0.31 thf(fact_1_dyn__def,axiom,
% 0.08/0.31 ! [C: cars,X: real] :
% 0.08/0.31 ( ( dy @ C @ X )
% 0.08/0.31 = zero_zero_real ) ).
% 0.08/0.31
% 0.08/0.31 % dyn_def
% 0.08/0.31 thf(fact_2_local_Ohmlsl_Osensors__ge,axiom,
% 0.08/0.31 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_real @ zero_zero_real @ ( regular_regular @ E @ Ts @ C2 ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.sensors_ge
% 0.08/0.31 thf(fact_3_hmlsl_Olen__non__empty__inside,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 0.08/0.31 => ( ( ord_less_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 0.08/0.31 & ( ord_less_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_non_empty_inside
% 0.08/0.31 thf(fact_4_v_H__d,axiom,
% 0.08/0.31 ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ d ) ) ).
% 0.08/0.31
% 0.08/0.31 % v'_d
% 0.08/0.31 thf(fact_5_hmlsl_Ospace__nonempty,axiom,
% 0.08/0.31 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] : ( ord_less_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.space_nonempty
% 0.08/0.31 thf(fact_6_ts__def,axiom,
% 0.08/0.31 ( ts
% 0.08/0.31 = ( abs_traffic @ ts_rep ) ) ).
% 0.08/0.31
% 0.08/0.31 % ts_def
% 0.08/0.31 thf(fact_7_assumption,axiom,
% 0.08/0.31 d != c ).
% 0.08/0.31
% 0.08/0.31 % assumption
% 0.08/0.31 thf(fact_8_local_Ohmlsl_Olength__geq__zero,axiom,
% 0.08/0.31 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.08/0.31 = zero_zero_real )
% 0.08/0.31 | ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.length_geq_zero
% 0.08/0.31 thf(fact_9_v_H__rel__c,axiom,
% 0.08/0.31 ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
% 0.08/0.31 & ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % v'_rel_c
% 0.08/0.31 thf(fact_10_hmlsl_Oleft__space,axiom,
% 0.08/0.31 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.31 ( ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 0.08/0.31 = ( pos @ Ts @ C2 ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.left_space
% 0.08/0.31 thf(fact_11_len__eq,axiom,
% 0.08/0.31 ( ( len @ regular_regular @ v @ ts @ c )
% 0.08/0.31 = ( len @ regular_regular @ v @ ts @ d ) ) ).
% 0.08/0.31
% 0.08/0.31 % len_eq
% 0.08/0.31 thf(fact_12_hmlsl_Olen__space__left,axiom,
% 0.08/0.31 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.31 ( ( ord_less_eq_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 0.08/0.31 => ( ord_less_eq_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_space_left
% 0.08/0.31 thf(fact_13_hmlsl_Olen__space__right,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) )
% 0.08/0.31 => ( ord_less_eq_real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_space_right
% 0.08/0.31 thf(fact_14_regular__sensors_Osensors__le,axiom,
% 0.08/0.31 ! [E: cars,C2: cars,Ts: traffic] :
% 0.08/0.31 ( ( E != C2 )
% 0.08/0.31 => ( ord_less_real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % regular_sensors.sensors_le
% 0.08/0.31 thf(fact_15_ps__ge__zero,axiom,
% 0.08/0.31 ! [C: cars] : ( ord_less_real @ zero_zero_real @ ( ps @ C ) ) ).
% 0.08/0.31
% 0.08/0.31 % ps_ge_zero
% 0.08/0.31 thf(fact_16_sd__ge__zero,axiom,
% 0.08/0.31 ! [C: cars] : ( ord_less_real @ zero_zero_real @ ( sd @ C ) ) ).
% 0.08/0.31
% 0.08/0.31 % sd_ge_zero
% 0.08/0.31 thf(fact_17_hmlsl_Olen__left,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_left
% 0.08/0.31 thf(fact_18_hmlsl_Olen__right,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_right
% 0.08/0.31 thf(fact_19_v_H__c,axiom,
% 0.08/0.31 ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) ).
% 0.08/0.31
% 0.08/0.31 % v'_c
% 0.08/0.31 thf(fact_20_hmlsl_Osensors__axioms,axiom,
% 0.08/0.31 sensors @ regular_regular ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.sensors_axioms
% 0.08/0.31 thf(fact_21_dyn__geq__zero,axiom,
% 0.08/0.31 ! [C: cars,X: real] : ( ord_less_eq_real @ zero_zero_real @ ( dy @ C @ X ) ) ).
% 0.08/0.31
% 0.08/0.31 % dyn_geq_zero
% 0.08/0.31 thf(fact_22_ps__def,axiom,
% 0.08/0.31 ! [C: cars] :
% 0.08/0.31 ( ( ps @ C )
% 0.08/0.31 = one_one_real ) ).
% 0.08/0.31
% 0.08/0.31 % ps_def
% 0.08/0.31 thf(fact_23_regular__sensors_Osensors__leq,axiom,
% 0.08/0.31 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ).
% 0.08/0.31
% 0.08/0.31 % regular_sensors.sensors_leq
% 0.08/0.31 thf(fact_24_sensors_Olen__non__empty__inside,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 0.08/0.31 => ( ( ord_less_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 0.08/0.31 & ( ord_less_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_non_empty_inside
% 0.08/0.31 thf(fact_25_other__len__zero,axiom,
% 0.08/0.31 ! [E2: cars] :
% 0.08/0.31 ( ( ( E2 != c )
% 0.08/0.31 & ( E2 != d ) )
% 0.08/0.31 => ( ( real_length @ ( len @ regular_regular @ v2 @ ts @ E2 ) )
% 0.08/0.31 = zero_zero_real ) ) ).
% 0.08/0.31
% 0.08/0.31 % other_len_zero
% 0.08/0.31 thf(fact_26_sensors_Olen__space__right,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) )
% 0.08/0.31 => ( ord_less_eq_real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_space_right
% 0.08/0.31 thf(fact_27_sensors_Olen__space__left,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ( ord_less_eq_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 0.08/0.31 => ( ord_less_eq_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_space_left
% 0.08/0.31 thf(fact_28_lc,axiom,
% 0.08/0.31 ( ( left @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 0.08/0.31 = zero_zero_real ) ).
% 0.08/0.31
% 0.08/0.31 % lc
% 0.08/0.31 thf(fact_29_sensors_Ospace__nonempty,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ord_less_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.space_nonempty
% 0.08/0.31 thf(fact_30_sensors_Olen__right,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ord_less_eq_real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_right
% 0.08/0.31 thf(fact_31_sensors_Olen__left,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_left
% 0.08/0.31 thf(fact_32__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,
% 0.08/0.31 ~ ! [Ps: cars > real] :
% 0.08/0.31 ~ ! [C: cars] :
% 0.08/0.31 ( ( Ps @ C )
% 0.08/0.31 = one_one_real ) ).
% 0.08/0.31
% 0.08/0.31 % \<open>\<And>thesis. (\<And>ps. \<forall>c. ps c = 1 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.08/0.31 thf(fact_33_hmlsl_Olen__sub__int,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( ext_Product_unit @ V ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_sub_int
% 0.08/0.31 thf(fact_34_hmlsl_Olen__empty__subview,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V3: view_e774982825t_unit] :
% 0.08/0.31 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.08/0.31 = zero_zero_real )
% 0.08/0.31 & ( ord_le461438217t_unit @ V3 @ V ) )
% 0.08/0.31 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C2 ) )
% 0.08/0.31 = zero_zero_real ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_empty_subview
% 0.08/0.31 thf(fact_35_lv,axiom,
% 0.08/0.31 ( ( left @ ( ext_Product_unit @ v2 ) )
% 0.08/0.31 = zero_zero_real ) ).
% 0.08/0.31
% 0.08/0.31 % lv
% 0.08/0.31 thf(fact_36_rc,axiom,
% 0.08/0.31 ( ( right @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 0.08/0.31 = one_one_real ) ).
% 0.08/0.31
% 0.08/0.31 % rc
% 0.08/0.31 thf(fact_37_one__reorient,axiom,
% 0.08/0.31 ! [X2: real] :
% 0.08/0.31 ( ( one_one_real = X2 )
% 0.08/0.31 = ( X2 = one_one_real ) ) ).
% 0.08/0.31
% 0.08/0.31 % one_reorient
% 0.08/0.31 thf(fact_38_sensors_Olen__sub__int,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ord_less_eq_real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( ext_Product_unit @ V ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_sub_int
% 0.08/0.31 thf(fact_39_sensors_Olen__empty__subview,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V3: view_e774982825t_unit] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.08/0.31 = zero_zero_real )
% 0.08/0.31 & ( ord_le461438217t_unit @ V3 @ V ) )
% 0.08/0.31 => ( ( real_length @ ( len @ Sensors @ V3 @ Ts @ C2 ) )
% 0.08/0.31 = zero_zero_real ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.len_empty_subview
% 0.08/0.31 thf(fact_40_zero__reorient,axiom,
% 0.08/0.31 ! [X2: real] :
% 0.08/0.31 ( ( zero_zero_real = X2 )
% 0.08/0.31 = ( X2 = zero_zero_real ) ) ).
% 0.08/0.31
% 0.08/0.31 % zero_reorient
% 0.08/0.31 thf(fact_41_sensors_Olen_Ocong,axiom,
% 0.08/0.31 len = len ).
% 0.08/0.31
% 0.08/0.31 % sensors.len.cong
% 0.08/0.31 thf(fact_42_sensors_Ospace_Ocong,axiom,
% 0.08/0.31 space = space ).
% 0.08/0.31
% 0.08/0.31 % sensors.space.cong
% 0.08/0.31 thf(fact_43_sensors__def,axiom,
% 0.08/0.31 ( sensors
% 0.08/0.31 = ( ^ [Sensors2: cars > traffic > cars > real] :
% 0.08/0.31 ! [E3: cars,Ts3: traffic,C3: cars] : ( ord_less_real @ zero_zero_real @ ( Sensors2 @ E3 @ Ts3 @ C3 ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors_def
% 0.08/0.31 thf(fact_44_sensors_Ointro,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real] :
% 0.08/0.31 ( ! [E4: cars,Ts4: traffic,C4: cars] : ( ord_less_real @ zero_zero_real @ ( Sensors @ E4 @ Ts4 @ C4 ) )
% 0.08/0.31 => ( sensors @ Sensors ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.intro
% 0.08/0.31 thf(fact_45_sensors_Osensors__ge,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,E: cars,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ord_less_real @ zero_zero_real @ ( Sensors @ E @ Ts @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.sensors_ge
% 0.08/0.31 thf(fact_46_sensors_Oleft__space,axiom,
% 0.08/0.31 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.31 ( ( sensors @ Sensors )
% 0.08/0.31 => ( ( left @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 0.08/0.31 = ( pos @ Ts @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % sensors.left_space
% 0.08/0.31 thf(fact_47_size,axiom,
% 0.08/0.31 ! [C: cars] :
% 0.08/0.31 ( ( physical_size @ ts @ C )
% 0.08/0.31 = one_one_real ) ).
% 0.08/0.31
% 0.08/0.31 % size
% 0.08/0.31 thf(fact_48_sensors__c,axiom,
% 0.08/0.31 ( ( regular_regular @ ( own_Product_unit @ v2 ) @ ts @ c )
% 0.08/0.31 = one_one_real ) ).
% 0.08/0.31
% 0.08/0.31 % sensors_c
% 0.08/0.31 thf(fact_49_hmlsl_Oview__leq__len__leq,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V ) @ ( ext_Product_unit @ V3 ) )
% 0.08/0.31 & ( ( own_Product_unit @ V )
% 0.08/0.31 = ( own_Product_unit @ V3 ) )
% 0.08/0.31 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) )
% 0.08/0.31 => ( ord_less_eq_real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.view_leq_len_leq
% 0.08/0.31 thf(fact_50_length__zero__iff__borders__eq,axiom,
% 0.08/0.31 ! [R: real_int] :
% 0.08/0.31 ( ( ( real_length @ R )
% 0.08/0.31 = zero_zero_real )
% 0.08/0.31 = ( ( left @ R )
% 0.08/0.31 = ( right @ R ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % length_zero_iff_borders_eq
% 0.08/0.31 thf(fact_51_hmlsl_Olen__fills__subview,axiom,
% 0.08/0.31 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.31 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 0.08/0.31 => ? [V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V @ V1 @ V22 )
% 0.08/0.31 & ( hchop @ V22 @ V4 @ V32 )
% 0.08/0.31 & ( ( len @ regular_regular @ V4 @ Ts @ C2 )
% 0.08/0.31 = ( ext_Product_unit @ V4 ) )
% 0.08/0.31 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C2 ) )
% 0.08/0.31 = ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % hmlsl.len_fills_subview
% 0.08/0.31 thf(fact_52_less__real__int__def,axiom,
% 0.08/0.31 ( ord_less_real_int
% 0.08/0.31 = ( ^ [R2: real_int,S: real_int] :
% 0.08/0.31 ( ( ord_less_eq_real @ ( left @ S ) @ ( left @ R2 ) )
% 0.08/0.31 & ( ord_less_eq_real @ ( right @ R2 ) @ ( right @ S ) )
% 0.08/0.31 & ~ ( ( ord_less_eq_real @ ( left @ R2 ) @ ( left @ S ) )
% 0.08/0.31 & ( ord_less_eq_real @ ( right @ S ) @ ( right @ R2 ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % less_real_int_def
% 0.08/0.31 thf(fact_53_less__eq__real__int__def,axiom,
% 0.08/0.31 ( ord_less_eq_real_int
% 0.08/0.31 = ( ^ [R2: real_int,S: real_int] :
% 0.08/0.31 ( ( ord_less_eq_real @ ( left @ S ) @ ( left @ R2 ) )
% 0.08/0.31 & ( ord_less_eq_real @ ( right @ R2 ) @ ( right @ S ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % less_eq_real_int_def
% 0.08/0.31 thf(fact_54_left__leq__right,axiom,
% 0.08/0.31 ! [R: real_int] : ( ord_less_eq_real @ ( left @ R ) @ ( right @ R ) ) ).
% 0.08/0.31
% 0.08/0.31 % left_leq_right
% 0.08/0.31 thf(fact_55_length__ge__zero,axiom,
% 0.08/0.31 ! [R: real_int] : ( ord_less_eq_real @ zero_zero_real @ ( real_length @ R ) ) ).
% 0.08/0.31
% 0.08/0.31 % length_ge_zero
% 0.08/0.31 thf(fact_56_local_Ohmlsl_Ohchop__assoc,axiom,
% 0.08/0.31 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Phi @ Ts2 @ W )
% 0.08/0.31 & ? [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ U @ X3 @ Y )
% 0.08/0.31 & ( Psi @ Ts2 @ X3 )
% 0.08/0.31 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.08/0.31 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ? [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ W @ X3 @ Y )
% 0.08/0.31 & ( Phi @ Ts2 @ X3 )
% 0.08/0.31 & ( Psi @ Ts2 @ Y ) )
% 0.08/0.31 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_assoc
% 0.08/0.31 thf(fact_57_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 0.08/0.31 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Phi @ Ts2 @ W )
% 0.08/0.31 & ( ( Psi @ Ts2 @ U )
% 0.08/0.31 | ( Chi @ Ts2 @ U ) ) ) )
% 0.08/0.31 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Phi @ Ts2 @ W )
% 0.08/0.31 & ( Psi @ Ts2 @ U ) )
% 0.08/0.31 | ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Phi @ Ts2 @ W )
% 0.08/0.31 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_disj_distr1
% 0.08/0.31 thf(fact_58_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 0.08/0.31 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( ( Psi @ Ts2 @ W )
% 0.08/0.31 | ( Chi @ Ts2 @ W ) )
% 0.08/0.31 & ( Phi @ Ts2 @ U ) ) )
% 0.08/0.31 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Psi @ Ts2 @ W )
% 0.08/0.31 & ( Phi @ Ts2 @ U ) )
% 0.08/0.31 | ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ W @ U )
% 0.08/0.31 & ( Chi @ Ts2 @ W )
% 0.08/0.31 & ( Phi @ Ts2 @ U ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_disj_distr2
% 0.08/0.31 thf(fact_59_local_Ohmlsl_Ohchop__neg1,axiom,
% 0.08/0.31 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ~ ? [Va: view_e774982825t_unit] :
% 0.08/0.31 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.08/0.31 & ( Phi @ Ts2 @ Va ) )
% 0.08/0.31 => ? [Va: view_e774982825t_unit] :
% 0.08/0.31 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.08/0.31 & ~ ( Phi @ Ts2 @ Va ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_neg1
% 0.08/0.31 thf(fact_60_local_Ohmlsl_Ohchop__neg2,axiom,
% 0.08/0.31 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ~ ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.31 & ( Phi @ Ts2 @ U2 ) )
% 0.08/0.31 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.31 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_neg2
% 0.08/0.31 thf(fact_61_local_Ohmlsl_Ohchop__weaken,axiom,
% 0.08/0.31 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.31 ( ( Phi @ Ts2 @ V2 )
% 0.08/0.31 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.31 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.31 & ? [Vb: view_e774982825t_unit] :
% 0.08/0.31 ( ? [X_1: view_e774982825t_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 0.08/0.31 & ( Phi @ Ts2 @ Vb ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 % local.hmlsl.hchop_weaken
% 0.08/0.31 thf(fact_62_local_Ohmlsl_Ohchop__weaken1,axiom,
% 0.08/0.32 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( Phi @ Ts2 @ V2 )
% 0.08/0.32 => ? [Va: view_e774982825t_unit] :
% 0.08/0.32 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 0.08/0.32 & ( Phi @ Ts2 @ Va ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.hchop_weaken1
% 0.08/0.32 thf(fact_63_local_Ohmlsl_Ohchop__weaken2,axiom,
% 0.08/0.32 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( Phi @ Ts2 @ V2 )
% 0.08/0.32 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.32 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.hchop_weaken2
% 0.08/0.32 thf(fact_64_hmlsl_Olen__view__hchop__right,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V23 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_view_hchop_right
% 0.08/0.32 thf(fact_65_hmlsl_Olen__view__hchop__left,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V12 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_view_hchop_left
% 0.08/0.32 thf(fact_66_hmlsl_Olen__compose__hchop,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 & ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V12 ) )
% 0.08/0.32 & ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V23 ) ) )
% 0.08/0.32 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_compose_hchop
% 0.08/0.32 thf(fact_67_hmlsl_Oext__eq__len__eq,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( ( ( ext_Product_unit @ V )
% 0.08/0.32 = ( ext_Product_unit @ V3 ) )
% 0.08/0.32 & ( ( own_Product_unit @ V )
% 0.08/0.32 = ( own_Product_unit @ V3 ) ) )
% 0.08/0.32 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.ext_eq_len_eq
% 0.08/0.32 thf(fact_68_local_Ohmlsl_Olength__split,axiom,
% 0.08/0.32 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.08/0.32 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_split
% 0.08/0.32 thf(fact_69_local_Ohmlsl_Olength__meld,axiom,
% 0.08/0.32 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ? [Va2: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ Va2 @ U3 )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) ) )
% 0.08/0.32 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_meld
% 0.08/0.32 thf(fact_70_local_Ohmlsl_Olength__dense,axiom,
% 0.08/0.32 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.08/0.32 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ W @ U )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_dense
% 0.08/0.32 thf(fact_71_hmlsl_Olen__empty__on__subview2,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_empty_on_subview2
% 0.08/0.32 thf(fact_72_hmlsl_Olen__empty__on__subview1,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_empty_on_subview1
% 0.08/0.32 thf(fact_73_hmlsl_Olen__hchop__right__right__border,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( right @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = ( right @ ( ext_Product_unit @ V23 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_hchop_right_right_border
% 0.08/0.32 thf(fact_74_hmlsl_Olen__hchop__right__left__border,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( left @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = ( left @ ( ext_Product_unit @ V23 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_hchop_right_left_border
% 0.08/0.32 thf(fact_75_hmlsl_Olen__hchop__left__right__border,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( right @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = ( right @ ( ext_Product_unit @ V12 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_hchop_left_right_border
% 0.08/0.32 thf(fact_76_hmlsl_Olen__hchop__left__left__border,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( left @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = ( left @ ( ext_Product_unit @ V12 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_hchop_left_left_border
% 0.08/0.32 thf(fact_77_regular__sensors_Ospace__eq,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( ( own_Product_unit @ V )
% 0.08/0.32 = ( own_Product_unit @ V3 ) )
% 0.08/0.32 => ( ( space @ regular_regular @ Ts @ V @ C2 )
% 0.08/0.32 = ( space @ regular_regular @ Ts @ V3 @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % regular_sensors.space_eq
% 0.08/0.32 thf(fact_78_sensors_Olen__compose__hchop,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 & ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V12 ) )
% 0.08/0.32 & ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V23 ) ) )
% 0.08/0.32 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_compose_hchop
% 0.08/0.32 thf(fact_79_sensors_Olen__view__hchop__left,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V12 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_view_hchop_left
% 0.08/0.32 thf(fact_80_sensors_Olen__view__hchop__right,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V23 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_view_hchop_right
% 0.08/0.32 thf(fact_81_sensors_Oext__eq__len__eq,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( ext_Product_unit @ V )
% 0.08/0.32 = ( ext_Product_unit @ V3 ) )
% 0.08/0.32 & ( ( own_Product_unit @ V )
% 0.08/0.32 = ( own_Product_unit @ V3 ) ) )
% 0.08/0.32 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.ext_eq_len_eq
% 0.08/0.32 thf(fact_82_sensors_Olen__empty__on__subview1,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_empty_on_subview1
% 0.08/0.32 thf(fact_83_sensors_Olen__empty__on__subview2,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_empty_on_subview2
% 0.08/0.32 thf(fact_84_sensors_Olen__hchop__right__right__border,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( right @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = ( right @ ( ext_Product_unit @ V23 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_hchop_right_right_border
% 0.08/0.32 thf(fact_85_sensors_Olen__hchop__right__left__border,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( left @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 0.08/0.32 = ( left @ ( ext_Product_unit @ V23 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_hchop_right_left_border
% 0.08/0.32 thf(fact_86_sensors_Olen__hchop__left__right__border,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( right @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = ( right @ ( ext_Product_unit @ V12 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_hchop_left_right_border
% 0.08/0.32 thf(fact_87_sensors_Olen__hchop__left__left__border,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V ) )
% 0.08/0.32 & ( hchop @ V @ V12 @ V23 ) )
% 0.08/0.32 => ( ( left @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 0.08/0.32 = ( left @ ( ext_Product_unit @ V12 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_hchop_left_left_border
% 0.08/0.32 thf(fact_88_sensors_Olen__fills__subview,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 0.08/0.32 => ? [V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ V1 @ V22 )
% 0.08/0.32 & ( hchop @ V22 @ V4 @ V32 )
% 0.08/0.32 & ( ( len @ Sensors @ V4 @ Ts @ C2 )
% 0.08/0.32 = ( ext_Product_unit @ V4 ) )
% 0.08/0.32 & ( ( real_length @ ( len @ Sensors @ V4 @ Ts @ C2 ) )
% 0.08/0.32 = ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_fills_subview
% 0.08/0.32 thf(fact_89_sensors_Oview__leq__len__leq,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V ) @ ( ext_Product_unit @ V3 ) )
% 0.08/0.32 & ( ( own_Product_unit @ V )
% 0.08/0.32 = ( own_Product_unit @ V3 ) )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) )
% 0.08/0.32 => ( ord_less_eq_real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.view_leq_len_leq
% 0.08/0.32 thf(fact_90_view_Oh__chop__middle2,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U4 @ W2 )
% 0.08/0.32 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ W2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.h_chop_middle2
% 0.08/0.32 thf(fact_91_view_Oh__chop__middle1,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U4 @ W2 )
% 0.08/0.32 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( ext_Product_unit @ U4 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.h_chop_middle1
% 0.08/0.32 thf(fact_92_view_Ohorizontal__chop__non__empty,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.08/0.32 => ? [U2: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U2 @ W3 )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 0.08/0.32 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W3 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_non_empty
% 0.08/0.32 thf(fact_93_hmlsl_Oright__space,axiom,
% 0.08/0.32 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.32 ( ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 0.08/0.32 = ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.right_space
% 0.08/0.32 thf(fact_94_local_Ohmlsl_Olength__add,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.08/0.32 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 0.08/0.32 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.08/0.32 = ( plus_plus_real @ X2 @ Y2 ) )
% 0.08/0.32 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ W @ U )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ W ) )
% 0.08/0.32 = X2 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ U ) )
% 0.08/0.32 = Y2 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_add
% 0.08/0.32 thf(fact_95_local_Ohmlsl_Olength__add2,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.08/0.32 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 0.08/0.32 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.08/0.32 = ( plus_plus_real @ X2 @ Y2 ) )
% 0.08/0.32 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ Va @ U2 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ Va ) )
% 0.08/0.32 = X2 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ U2 ) )
% 0.08/0.32 = Y2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_add2
% 0.08/0.32 thf(fact_96_traffic_OpsGeZero,axiom,
% 0.08/0.32 ! [Ts: traffic,C: cars] : ( ord_less_real @ zero_zero_real @ ( physical_size @ Ts @ C ) ) ).
% 0.08/0.32
% 0.08/0.32 % traffic.psGeZero
% 0.08/0.32 thf(fact_97_local_Ohmlsl_Olength__add1,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 0.08/0.32 ( ? [Va2: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V2 @ Va2 @ U3 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ Va2 ) )
% 0.08/0.32 = X2 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ U3 ) )
% 0.08/0.32 = Y2 ) )
% 0.08/0.32 => ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.08/0.32 = ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % local.hmlsl.length_add1
% 0.08/0.32 thf(fact_98_add__left__cancel,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ A @ B )
% 0.08/0.32 = ( plus_plus_real @ A @ C2 ) )
% 0.08/0.32 = ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_left_cancel
% 0.08/0.32 thf(fact_99_add__right__cancel,axiom,
% 0.08/0.32 ! [B: real,A: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ B @ A )
% 0.08/0.32 = ( plus_plus_real @ C2 @ A ) )
% 0.08/0.32 = ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_right_cancel
% 0.08/0.32 thf(fact_100_hmlsl_Olen__hchop__add,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 => ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 0.08/0.32 = ( plus_plus_real @ ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.len_hchop_add
% 0.08/0.32 thf(fact_101_add__le__cancel__right,axiom,
% 0.08/0.32 ! [A: real,C2: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.08/0.32 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_cancel_right
% 0.08/0.32 thf(fact_102_add__le__cancel__left,axiom,
% 0.08/0.32 ! [C2: real,A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.08/0.32 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_cancel_left
% 0.08/0.32 thf(fact_103_add__cancel__right__right,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( A
% 0.08/0.32 = ( plus_plus_real @ A @ B ) )
% 0.08/0.32 = ( B = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_cancel_right_right
% 0.08/0.32 thf(fact_104_add__cancel__right__left,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( A
% 0.08/0.32 = ( plus_plus_real @ B @ A ) )
% 0.08/0.32 = ( B = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_cancel_right_left
% 0.08/0.32 thf(fact_105_add__cancel__left__right,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ A @ B )
% 0.08/0.32 = A )
% 0.08/0.32 = ( B = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_cancel_left_right
% 0.08/0.32 thf(fact_106_add__cancel__left__left,axiom,
% 0.08/0.32 ! [B: real,A: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ B @ A )
% 0.08/0.32 = A )
% 0.08/0.32 = ( B = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_cancel_left_left
% 0.08/0.32 thf(fact_107_double__zero__sym,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( zero_zero_real
% 0.08/0.32 = ( plus_plus_real @ A @ A ) )
% 0.08/0.32 = ( A = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % double_zero_sym
% 0.08/0.32 thf(fact_108_double__zero,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ A @ A )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 = ( A = zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % double_zero
% 0.08/0.32 thf(fact_109_add_Oright__neutral,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.08/0.32 = A ) ).
% 0.08/0.32
% 0.08/0.32 % add.right_neutral
% 0.08/0.32 thf(fact_110_add_Oleft__neutral,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.08/0.32 = A ) ).
% 0.08/0.32
% 0.08/0.32 % add.left_neutral
% 0.08/0.32 thf(fact_111_add__less__cancel__left,axiom,
% 0.08/0.32 ! [C2: real,A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.08/0.32 = ( ord_less_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_cancel_left
% 0.08/0.32 thf(fact_112_add__less__cancel__right,axiom,
% 0.08/0.32 ! [A: real,C2: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.08/0.32 = ( ord_less_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_cancel_right
% 0.08/0.32 thf(fact_113_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.08/0.32 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.08/0.32
% 0.08/0.32 % zero_le_double_add_iff_zero_le_single_add
% 0.08/0.32 thf(fact_114_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.08/0.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % double_add_le_zero_iff_single_add_le_zero
% 0.08/0.32 thf(fact_115_le__add__same__cancel2,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.08/0.32 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % le_add_same_cancel2
% 0.08/0.32 thf(fact_116_le__add__same__cancel1,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.08/0.32 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % le_add_same_cancel1
% 0.08/0.32 thf(fact_117_add__le__same__cancel2,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.08/0.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_same_cancel2
% 0.08/0.32 thf(fact_118_add__le__same__cancel1,axiom,
% 0.08/0.32 ! [B: real,A: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.08/0.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_same_cancel1
% 0.08/0.32 thf(fact_119_add__less__same__cancel1,axiom,
% 0.08/0.32 ! [B: real,A: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.08/0.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_same_cancel1
% 0.08/0.32 thf(fact_120_add__less__same__cancel2,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.08/0.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_same_cancel2
% 0.08/0.32 thf(fact_121_less__add__same__cancel1,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.08/0.32 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % less_add_same_cancel1
% 0.08/0.32 thf(fact_122_less__add__same__cancel2,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.08/0.32 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % less_add_same_cancel2
% 0.08/0.32 thf(fact_123_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.08/0.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % double_add_less_zero_iff_single_add_less_zero
% 0.08/0.32 thf(fact_124_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.08/0.32 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.08/0.32
% 0.08/0.32 % zero_less_double_add_iff_zero_less_single_add
% 0.08/0.32 thf(fact_125_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.08/0.32 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ab_semigroup_add_class.add_ac(1)
% 0.08/0.32 thf(fact_126_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( I = J )
% 0.08/0.32 & ( K = L ) )
% 0.08/0.32 => ( ( plus_plus_real @ I @ K )
% 0.08/0.32 = ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_semiring(4)
% 0.08/0.32 thf(fact_127_group__cancel_Oadd1,axiom,
% 0.08/0.32 ! [A2: real,K: real,A: real,B: real] :
% 0.08/0.32 ( ( A2
% 0.08/0.32 = ( plus_plus_real @ K @ A ) )
% 0.08/0.32 => ( ( plus_plus_real @ A2 @ B )
% 0.08/0.32 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % group_cancel.add1
% 0.08/0.32 thf(fact_128_group__cancel_Oadd2,axiom,
% 0.08/0.32 ! [B2: real,K: real,B: real,A: real] :
% 0.08/0.32 ( ( B2
% 0.08/0.32 = ( plus_plus_real @ K @ B ) )
% 0.08/0.32 => ( ( plus_plus_real @ A @ B2 )
% 0.08/0.32 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % group_cancel.add2
% 0.08/0.32 thf(fact_129_add_Oassoc,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.08/0.32 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add.assoc
% 0.08/0.32 thf(fact_130_add_Oleft__cancel,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ A @ B )
% 0.08/0.32 = ( plus_plus_real @ A @ C2 ) )
% 0.08/0.32 = ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add.left_cancel
% 0.08/0.32 thf(fact_131_add_Oright__cancel,axiom,
% 0.08/0.32 ! [B: real,A: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ B @ A )
% 0.08/0.32 = ( plus_plus_real @ C2 @ A ) )
% 0.08/0.32 = ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add.right_cancel
% 0.08/0.32 thf(fact_132_add_Ocommute,axiom,
% 0.08/0.32 ( plus_plus_real
% 0.08/0.32 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add.commute
% 0.08/0.32 thf(fact_133_add_Oleft__commute,axiom,
% 0.08/0.32 ! [B: real,A: real,C2: real] :
% 0.08/0.32 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 0.08/0.32 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add.left_commute
% 0.08/0.32 thf(fact_134_add__left__imp__eq,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ A @ B )
% 0.08/0.32 = ( plus_plus_real @ A @ C2 ) )
% 0.08/0.32 => ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_left_imp_eq
% 0.08/0.32 thf(fact_135_add__right__imp__eq,axiom,
% 0.08/0.32 ! [B: real,A: real,C2: real] :
% 0.08/0.32 ( ( ( plus_plus_real @ B @ A )
% 0.08/0.32 = ( plus_plus_real @ C2 @ A ) )
% 0.08/0.32 => ( B = C2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_right_imp_eq
% 0.08/0.32 thf(fact_136_add__le__imp__le__right,axiom,
% 0.08/0.32 ! [A: real,C2: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.08/0.32 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_imp_le_right
% 0.08/0.32 thf(fact_137_add__le__imp__le__left,axiom,
% 0.08/0.32 ! [C2: real,A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.08/0.32 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_imp_le_left
% 0.08/0.32 thf(fact_138_add__right__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_right_mono
% 0.08/0.32 thf(fact_139_add__left__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_left_mono
% 0.08/0.32 thf(fact_140_add__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real,D: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real @ C2 @ D )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono
% 0.08/0.32 thf(fact_141_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ I @ J )
% 0.08/0.32 & ( ord_less_eq_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_semiring(1)
% 0.08/0.32 thf(fact_142_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( I = J )
% 0.08/0.32 & ( ord_less_eq_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_semiring(2)
% 0.08/0.32 thf(fact_143_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ I @ J )
% 0.08/0.32 & ( K = L ) )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_semiring(3)
% 0.08/0.32 thf(fact_144_add_Ogroup__left__neutral,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.08/0.32 = A ) ).
% 0.08/0.32
% 0.08/0.32 % add.group_left_neutral
% 0.08/0.32 thf(fact_145_add_Ocomm__neutral,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.08/0.32 = A ) ).
% 0.08/0.32
% 0.08/0.32 % add.comm_neutral
% 0.08/0.32 thf(fact_146_comm__monoid__add__class_Oadd__0,axiom,
% 0.08/0.32 ! [A: real] :
% 0.08/0.32 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.08/0.32 = A ) ).
% 0.08/0.32
% 0.08/0.32 % comm_monoid_add_class.add_0
% 0.08/0.32 thf(fact_147_add__mono__thms__linordered__field_I5_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_real @ I @ J )
% 0.08/0.32 & ( ord_less_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_field(5)
% 0.08/0.32 thf(fact_148_add__mono__thms__linordered__field_I2_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( I = J )
% 0.08/0.32 & ( ord_less_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_field(2)
% 0.08/0.32 thf(fact_149_add__mono__thms__linordered__field_I1_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_real @ I @ J )
% 0.08/0.32 & ( K = L ) )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_field(1)
% 0.08/0.32 thf(fact_150_add__strict__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real,D: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_real @ C2 @ D )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_strict_mono
% 0.08/0.32 thf(fact_151_add__strict__left__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ B )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_strict_left_mono
% 0.08/0.32 thf(fact_152_add__strict__right__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ B )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_strict_right_mono
% 0.08/0.32 thf(fact_153_add__less__imp__less__left,axiom,
% 0.08/0.32 ! [C2: real,A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.08/0.32 => ( ord_less_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_imp_less_left
% 0.08/0.32 thf(fact_154_add__less__imp__less__right,axiom,
% 0.08/0.32 ! [A: real,C2: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.08/0.32 => ( ord_less_real @ A @ B ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_imp_less_right
% 0.08/0.32 thf(fact_155_add__nonpos__eq__0__iff,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 0.08/0.32 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 = ( ( X2 = zero_zero_real )
% 0.08/0.32 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonpos_eq_0_iff
% 0.08/0.32 thf(fact_156_add__nonneg__eq__0__iff,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.08/0.32 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.08/0.32 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 0.08/0.32 = zero_zero_real )
% 0.08/0.32 = ( ( X2 = zero_zero_real )
% 0.08/0.32 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonneg_eq_0_iff
% 0.08/0.32 thf(fact_157_add__nonpos__nonpos,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonpos_nonpos
% 0.08/0.32 thf(fact_158_add__nonneg__nonneg,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.08/0.32 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonneg_nonneg
% 0.08/0.32 thf(fact_159_add__increasing2,axiom,
% 0.08/0.32 ! [C2: real,B: real,A: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ A )
% 0.08/0.32 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_increasing2
% 0.08/0.32 thf(fact_160_add__decreasing2,axiom,
% 0.08/0.32 ! [C2: real,A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_decreasing2
% 0.08/0.32 thf(fact_161_add__increasing,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_increasing
% 0.08/0.32 thf(fact_162_add__decreasing,axiom,
% 0.08/0.32 ! [A: real,C2: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_eq_real @ C2 @ B )
% 0.08/0.32 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_decreasing
% 0.08/0.32 thf(fact_163_add__less__le__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real,D: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real @ C2 @ D )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_le_mono
% 0.08/0.32 thf(fact_164_add__le__less__mono,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real,D: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_real @ C2 @ D )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_le_less_mono
% 0.08/0.32 thf(fact_165_add__mono__thms__linordered__field_I3_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_real @ I @ J )
% 0.08/0.32 & ( ord_less_eq_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_field(3)
% 0.08/0.32 thf(fact_166_add__mono__thms__linordered__field_I4_J,axiom,
% 0.08/0.32 ! [I: real,J: real,K: real,L: real] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ I @ J )
% 0.08/0.32 & ( ord_less_real @ K @ L ) )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono_thms_linordered_field(4)
% 0.08/0.32 thf(fact_167_add__neg__neg,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_neg_neg
% 0.08/0.32 thf(fact_168_add__pos__pos,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.08/0.32 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_pos_pos
% 0.08/0.32 thf(fact_169_pos__add__strict,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % pos_add_strict
% 0.08/0.32 thf(fact_170_add__strict__increasing2,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_strict_increasing2
% 0.08/0.32 thf(fact_171_add__strict__increasing,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_strict_increasing
% 0.08/0.32 thf(fact_172_add__pos__nonneg,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.08/0.32 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_pos_nonneg
% 0.08/0.32 thf(fact_173_add__nonpos__neg,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonpos_neg
% 0.08/0.32 thf(fact_174_add__nonneg__pos,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.08/0.32 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.08/0.32 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_nonneg_pos
% 0.08/0.32 thf(fact_175_add__neg__nonpos,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_neg_nonpos
% 0.08/0.32 thf(fact_176_consec__add,axiom,
% 0.08/0.32 ! [R: real_int,S2: real_int,T: real_int] :
% 0.08/0.32 ( ( ( ( left @ R )
% 0.08/0.32 = ( left @ S2 ) )
% 0.08/0.32 & ( ( right @ R )
% 0.08/0.32 = ( right @ T ) )
% 0.08/0.32 & ( ( right @ S2 )
% 0.08/0.32 = ( left @ T ) ) )
% 0.08/0.32 => ( ( real_length @ R )
% 0.08/0.32 = ( plus_plus_real @ ( real_length @ S2 ) @ ( real_length @ T ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % consec_add
% 0.08/0.32 thf(fact_177_view_Ohorizontal__chop__empty__right,axiom,
% 0.08/0.32 ! [V2: view_e774982825t_unit] :
% 0.08/0.32 ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ V2 @ X_1 ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_empty_right
% 0.08/0.32 thf(fact_178_view_Ohorizontal__chop__empty__left,axiom,
% 0.08/0.32 ! [V2: view_e774982825t_unit] :
% 0.08/0.32 ? [U2: view_e774982825t_unit] : ( hchop @ V2 @ U2 @ V2 ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_empty_left
% 0.08/0.32 thf(fact_179_view_Ohorizontal__chop__assoc2,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 & ( hchop @ V12 @ V33 @ V42 ) )
% 0.08/0.32 => ? [V4: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ V33 @ V4 )
% 0.08/0.32 & ( hchop @ V4 @ V42 @ V23 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_assoc2
% 0.08/0.32 thf(fact_180_view_Ohorizontal__chop__assoc1,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 & ( hchop @ V23 @ V33 @ V42 ) )
% 0.08/0.32 => ? [V4: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ V4 @ V42 )
% 0.08/0.32 & ( hchop @ V4 @ V12 @ V33 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_assoc1
% 0.08/0.32 thf(fact_181_view_Ohorizontal__chop1,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit] :
% 0.08/0.32 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( hchop @ V @ U2 @ X_1 ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop1
% 0.08/0.32 thf(fact_182_view_Ohorizontal__chop__split__add,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,V: view_e774982825t_unit] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 0.08/0.32 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 0.08/0.32 => ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 0.08/0.32 = ( plus_plus_real @ X2 @ Y2 ) )
% 0.08/0.32 => ? [U2: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U2 @ W3 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ U2 ) )
% 0.08/0.32 = X2 )
% 0.08/0.32 & ( ( real_length @ ( ext_Product_unit @ W3 ) )
% 0.08/0.32 = Y2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_split_add
% 0.08/0.32 thf(fact_183_sensors_Olen__hchop__add,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( hchop @ V @ V12 @ V23 )
% 0.08/0.32 => ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 0.08/0.32 = ( plus_plus_real @ ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.len_hchop_add
% 0.08/0.32 thf(fact_184_sensors_Oright__space,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( right @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 0.08/0.32 = ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.right_space
% 0.08/0.32 thf(fact_185_view_Ohorizontal__chop__own__trans,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U4 @ W2 )
% 0.08/0.32 => ( ( own_Product_unit @ U4 )
% 0.08/0.32 = ( own_Product_unit @ W2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_own_trans
% 0.08/0.32 thf(fact_186_view_Ohorizontal__chop__leq2,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U4 @ W2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ W2 @ V ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_leq2
% 0.08/0.32 thf(fact_187_view_Ohorizontal__chop__leq1,axiom,
% 0.08/0.32 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.08/0.32 ( ( hchop @ V @ U4 @ W2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ U4 @ V ) ) ).
% 0.08/0.32
% 0.08/0.32 % view.horizontal_chop_leq1
% 0.08/0.32 thf(fact_188_zero__less__two,axiom,
% 0.08/0.32 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.08/0.32
% 0.08/0.32 % zero_less_two
% 0.08/0.32 thf(fact_189_field__le__epsilon,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ! [E4: real] :
% 0.08/0.32 ( ( ord_less_real @ zero_zero_real @ E4 )
% 0.08/0.32 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y2 @ E4 ) ) )
% 0.08/0.32 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % field_le_epsilon
% 0.08/0.32 thf(fact_190_add__mono1,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_real @ A @ B )
% 0.08/0.32 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_mono1
% 0.08/0.32 thf(fact_191_less__add__one,axiom,
% 0.08/0.32 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.08/0.32
% 0.08/0.32 % less_add_one
% 0.08/0.32 thf(fact_192_linorder__neqE__linordered__idom,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( X2 != Y2 )
% 0.08/0.32 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.08/0.32 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % linorder_neqE_linordered_idom
% 0.08/0.32 thf(fact_193_linordered__field__no__ub,axiom,
% 0.08/0.32 ! [X: real] :
% 0.08/0.32 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 0.08/0.32
% 0.08/0.32 % linordered_field_no_ub
% 0.08/0.32 thf(fact_194_linordered__field__no__lb,axiom,
% 0.08/0.32 ! [X: real] :
% 0.08/0.32 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 0.08/0.32
% 0.08/0.32 % linordered_field_no_lb
% 0.08/0.32 thf(fact_195_zero__neq__one,axiom,
% 0.08/0.32 zero_zero_real != one_one_real ).
% 0.08/0.32
% 0.08/0.32 % zero_neq_one
% 0.08/0.32 thf(fact_196_zero__le__one,axiom,
% 0.08/0.32 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.08/0.32
% 0.08/0.32 % zero_le_one
% 0.08/0.32 thf(fact_197_not__one__le__zero,axiom,
% 0.08/0.32 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.08/0.32
% 0.08/0.32 % not_one_le_zero
% 0.08/0.32 thf(fact_198_not__one__less__zero,axiom,
% 0.08/0.32 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.08/0.32
% 0.08/0.32 % not_one_less_zero
% 0.08/0.32 thf(fact_199_zero__less__one,axiom,
% 0.08/0.32 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.08/0.32
% 0.08/0.32 % zero_less_one
% 0.08/0.32 thf(fact_200_add__less__zeroD,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 0.08/0.32 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 0.08/0.32 | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % add_less_zeroD
% 0.08/0.32 thf(fact_201_less__numeral__extra_I1_J,axiom,
% 0.08/0.32 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.08/0.32
% 0.08/0.32 % less_numeral_extra(1)
% 0.08/0.32 thf(fact_202_space__c,axiom,
% 0.08/0.32 ( ( space @ regular_regular @ ts @ v2 @ c )
% 0.08/0.32 = ( real_Abs_real_int @ ( produc705216881l_real @ zero_zero_real @ one_one_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % space_c
% 0.08/0.32 thf(fact_203_hmlsl_Ospace__def,axiom,
% 0.08/0.32 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.32 ( ( space @ regular_regular @ Ts @ V @ C2 )
% 0.08/0.32 = ( real_Abs_real_int @ ( produc705216881l_real @ ( pos @ Ts @ C2 ) @ ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % hmlsl.space_def
% 0.08/0.32 thf(fact_204_len__c,axiom,
% 0.08/0.32 ( ( len @ regular_regular @ v2 @ ts @ c )
% 0.08/0.32 = ( real_Abs_real_int @ ( produc705216881l_real @ zero_zero_real @ one_one_real ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % len_c
% 0.08/0.32 thf(fact_205_sensors_Ospace__def,axiom,
% 0.08/0.32 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 0.08/0.32 ( ( sensors @ Sensors )
% 0.08/0.32 => ( ( space @ Sensors @ Ts @ V @ C2 )
% 0.08/0.32 = ( real_Abs_real_int @ ( produc705216881l_real @ ( pos @ Ts @ C2 ) @ ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % sensors.space_def
% 0.08/0.32 thf(fact_206_is__num__normalize_I1_J,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.08/0.32 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % is_num_normalize(1)
% 0.08/0.32 thf(fact_207_le__numeral__extra_I3_J,axiom,
% 0.08/0.32 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.08/0.32
% 0.08/0.32 % le_numeral_extra(3)
% 0.08/0.32 thf(fact_208_less__numeral__extra_I3_J,axiom,
% 0.08/0.32 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.08/0.32
% 0.08/0.32 % less_numeral_extra(3)
% 0.08/0.32 thf(fact_209_le__numeral__extra_I4_J,axiom,
% 0.08/0.32 ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.08/0.32
% 0.08/0.32 % le_numeral_extra(4)
% 0.08/0.32 thf(fact_210_less__numeral__extra_I4_J,axiom,
% 0.08/0.32 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.08/0.32
% 0.08/0.32 % less_numeral_extra(4)
% 0.08/0.32 thf(fact_211_real__int__class_Oshift__def,axiom,
% 0.08/0.32 ( real_shift
% 0.08/0.32 = ( ^ [R2: real_int,X3: real] : ( real_Abs_real_int @ ( produc705216881l_real @ ( plus_plus_real @ ( left @ R2 ) @ X3 ) @ ( plus_plus_real @ ( right @ R2 ) @ X3 ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % real_int_class.shift_def
% 0.08/0.32 thf(fact_212_shift__additivity,axiom,
% 0.08/0.32 ! [R: real_int,X2: real,Y2: real] :
% 0.08/0.32 ( ( real_shift @ R @ ( plus_plus_real @ X2 @ Y2 ) )
% 0.08/0.32 = ( real_shift @ ( real_shift @ R @ X2 ) @ Y2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % shift_additivity
% 0.08/0.32 thf(fact_213_shift__keeps__length,axiom,
% 0.08/0.32 ! [X2: real] :
% 0.08/0.32 ( real_length
% 0.08/0.32 = ( ^ [R2: real_int] : ( real_length @ ( real_shift @ R2 @ X2 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % shift_keeps_length
% 0.08/0.32 thf(fact_214_shift__zero,axiom,
% 0.08/0.32 ! [R: real_int] :
% 0.08/0.32 ( ( real_shift @ R @ zero_zero_real )
% 0.08/0.32 = R ) ).
% 0.08/0.32
% 0.08/0.32 % shift_zero
% 0.08/0.32 thf(fact_215_shift__left__eq__right,axiom,
% 0.08/0.32 ! [R: real_int,X2: real] : ( ord_less_eq_real @ ( left @ ( real_shift @ R @ X2 ) ) @ ( right @ ( real_shift @ R @ X2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % shift_left_eq_right
% 0.08/0.32 thf(fact_216_ts__rep__def,axiom,
% 0.08/0.32 ( ts_rep
% 0.08/0.32 = ( produc1876576040s_real @ po @ ( produc1230243850s_real @ re @ ( produc1348924850s_real @ cl @ ( produc795767668s_real @ dy @ ( produc1439932679s_real @ ps @ sd ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ts_rep_def
% 0.08/0.32 thf(fact_217_order__refl,axiom,
% 0.08/0.32 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.08/0.32
% 0.08/0.32 % order_refl
% 0.08/0.32 thf(fact_218_order__refl,axiom,
% 0.08/0.32 ! [X2: real_int] : ( ord_less_eq_real_int @ X2 @ X2 ) ).
% 0.08/0.32
% 0.08/0.32 % order_refl
% 0.08/0.32 thf(fact_219_order__refl,axiom,
% 0.08/0.32 ! [X2: view_e774982825t_unit] : ( ord_le461438217t_unit @ X2 @ X2 ) ).
% 0.08/0.32
% 0.08/0.32 % order_refl
% 0.08/0.32 thf(fact_220_clm__def,axiom,
% 0.08/0.32 ! [C: cars] :
% 0.08/0.32 ( ( cl @ C )
% 0.08/0.32 = bot_bot_nat_int ) ).
% 0.08/0.32
% 0.08/0.32 % clm_def
% 0.08/0.32 thf(fact_221_dual__order_Oantisym,axiom,
% 0.08/0.32 ! [B: real,A: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ B @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.antisym
% 0.08/0.32 thf(fact_222_dual__order_Oantisym,axiom,
% 0.08/0.32 ! [B: real_int,A: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ B @ A )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ A @ B )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.antisym
% 0.08/0.32 thf(fact_223_dual__order_Oantisym,axiom,
% 0.08/0.32 ! [B: view_e774982825t_unit,A: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ B @ A )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ A @ B )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.antisym
% 0.08/0.32 thf(fact_224_dual__order_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: real,B3: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ B3 @ A3 )
% 0.08/0.32 & ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.eq_iff
% 0.08/0.32 thf(fact_225_dual__order_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: real_int,B3: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ B3 @ A3 )
% 0.08/0.32 & ( ord_less_eq_real_int @ A3 @ B3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.eq_iff
% 0.08/0.32 thf(fact_226_dual__order_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: view_e774982825t_unit,B3: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ B3 @ A3 )
% 0.08/0.32 & ( ord_le461438217t_unit @ A3 @ B3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.eq_iff
% 0.08/0.32 thf(fact_227_dual__order_Otrans,axiom,
% 0.08/0.32 ! [B: real,A: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ B @ A )
% 0.08/0.32 => ( ( ord_less_eq_real @ C2 @ B )
% 0.08/0.32 => ( ord_less_eq_real @ C2 @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.trans
% 0.08/0.32 thf(fact_228_dual__order_Otrans,axiom,
% 0.08/0.32 ! [B: real_int,A: real_int,C2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ B @ A )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ C2 @ B )
% 0.08/0.32 => ( ord_less_eq_real_int @ C2 @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.trans
% 0.08/0.32 thf(fact_229_dual__order_Otrans,axiom,
% 0.08/0.32 ! [B: view_e774982825t_unit,A: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ B @ A )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ C2 @ B )
% 0.08/0.32 => ( ord_le461438217t_unit @ C2 @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.trans
% 0.08/0.32 thf(fact_230_linorder__wlog,axiom,
% 0.08/0.32 ! [P: real > real > $o,A: real,B: real] :
% 0.08/0.32 ( ! [A4: real,B4: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A4 @ B4 )
% 0.08/0.32 => ( P @ A4 @ B4 ) )
% 0.08/0.32 => ( ! [A4: real,B4: real] :
% 0.08/0.32 ( ( P @ B4 @ A4 )
% 0.08/0.32 => ( P @ A4 @ B4 ) )
% 0.08/0.32 => ( P @ A @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % linorder_wlog
% 0.08/0.32 thf(fact_231_dual__order_Orefl,axiom,
% 0.08/0.32 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.refl
% 0.08/0.32 thf(fact_232_dual__order_Orefl,axiom,
% 0.08/0.32 ! [A: real_int] : ( ord_less_eq_real_int @ A @ A ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.refl
% 0.08/0.32 thf(fact_233_dual__order_Orefl,axiom,
% 0.08/0.32 ! [A: view_e774982825t_unit] : ( ord_le461438217t_unit @ A @ A ) ).
% 0.08/0.32
% 0.08/0.32 % dual_order.refl
% 0.08/0.32 thf(fact_234_order__trans,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,Z2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_less_eq_real @ Y2 @ Z2 )
% 0.08/0.32 => ( ord_less_eq_real @ X2 @ Z2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_trans
% 0.08/0.32 thf(fact_235_order__trans,axiom,
% 0.08/0.32 ! [X2: real_int,Y2: real_int,Z2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ Y2 @ Z2 )
% 0.08/0.32 => ( ord_less_eq_real_int @ X2 @ Z2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_trans
% 0.08/0.32 thf(fact_236_order__trans,axiom,
% 0.08/0.32 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit,Z2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ Y2 @ Z2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ X2 @ Z2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_trans
% 0.08/0.32 thf(fact_237_order__class_Oorder_Oantisym,axiom,
% 0.08/0.32 ! [A: real,B: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ A )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.antisym
% 0.08/0.32 thf(fact_238_order__class_Oorder_Oantisym,axiom,
% 0.08/0.32 ! [A: real_int,B: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ B @ A )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.antisym
% 0.08/0.32 thf(fact_239_order__class_Oorder_Oantisym,axiom,
% 0.08/0.32 ! [A: view_e774982825t_unit,B: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ A @ B )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ B @ A )
% 0.08/0.32 => ( A = B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.antisym
% 0.08/0.32 thf(fact_240_ord__le__eq__trans,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ( B = C2 )
% 0.08/0.32 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_le_eq_trans
% 0.08/0.32 thf(fact_241_ord__le__eq__trans,axiom,
% 0.08/0.32 ! [A: real_int,B: real_int,C2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ A @ B )
% 0.08/0.32 => ( ( B = C2 )
% 0.08/0.32 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_le_eq_trans
% 0.08/0.32 thf(fact_242_ord__le__eq__trans,axiom,
% 0.08/0.32 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ A @ B )
% 0.08/0.32 => ( ( B = C2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_le_eq_trans
% 0.08/0.32 thf(fact_243_ord__eq__le__trans,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_eq_le_trans
% 0.08/0.32 thf(fact_244_ord__eq__le__trans,axiom,
% 0.08/0.32 ! [A: real_int,B: real_int,C2: real_int] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ B @ C2 )
% 0.08/0.32 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_eq_le_trans
% 0.08/0.32 thf(fact_245_ord__eq__le__trans,axiom,
% 0.08/0.32 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ B @ C2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % ord_eq_le_trans
% 0.08/0.32 thf(fact_246_order__class_Oorder_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: real,B3: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A3 @ B3 )
% 0.08/0.32 & ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.eq_iff
% 0.08/0.32 thf(fact_247_order__class_Oorder_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: real_int,B3: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ A3 @ B3 )
% 0.08/0.32 & ( ord_less_eq_real_int @ B3 @ A3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.eq_iff
% 0.08/0.32 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [A3: view_e774982825t_unit,B3: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ A3 @ B3 )
% 0.08/0.32 & ( ord_le461438217t_unit @ B3 @ A3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order_class.order.eq_iff
% 0.08/0.32 thf(fact_249_antisym__conv,axiom,
% 0.08/0.32 ! [Y2: real,X2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.08/0.32 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 = ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym_conv
% 0.08/0.32 thf(fact_250_antisym__conv,axiom,
% 0.08/0.32 ! [Y2: real_int,X2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ Y2 @ X2 )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 0.08/0.32 = ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym_conv
% 0.08/0.32 thf(fact_251_antisym__conv,axiom,
% 0.08/0.32 ! [Y2: view_e774982825t_unit,X2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ Y2 @ X2 )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 0.08/0.32 = ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym_conv
% 0.08/0.32 thf(fact_252_le__cases3,axiom,
% 0.08/0.32 ! [X2: real,Y2: real,Z2: real] :
% 0.08/0.32 ( ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ Y2 @ Z2 ) )
% 0.08/0.32 => ( ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ X2 @ Z2 ) )
% 0.08/0.32 => ( ( ( ord_less_eq_real @ X2 @ Z2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ Z2 @ Y2 ) )
% 0.08/0.32 => ( ( ( ord_less_eq_real @ Z2 @ Y2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ Y2 @ X2 ) )
% 0.08/0.32 => ( ( ( ord_less_eq_real @ Y2 @ Z2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ Z2 @ X2 ) )
% 0.08/0.32 => ~ ( ( ord_less_eq_real @ Z2 @ X2 )
% 0.08/0.32 => ~ ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % le_cases3
% 0.08/0.32 thf(fact_253_order_Otrans,axiom,
% 0.08/0.32 ! [A: real,B: real,C2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real @ B @ C2 )
% 0.08/0.32 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order.trans
% 0.08/0.32 thf(fact_254_order_Otrans,axiom,
% 0.08/0.32 ! [A: real_int,B: real_int,C2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ A @ B )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ B @ C2 )
% 0.08/0.32 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order.trans
% 0.08/0.32 thf(fact_255_order_Otrans,axiom,
% 0.08/0.32 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ A @ B )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ B @ C2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % order.trans
% 0.08/0.32 thf(fact_256_le__cases,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ~ ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % le_cases
% 0.08/0.32 thf(fact_257_eq__refl,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( X2 = Y2 )
% 0.08/0.32 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_refl
% 0.08/0.32 thf(fact_258_eq__refl,axiom,
% 0.08/0.32 ! [X2: real_int,Y2: real_int] :
% 0.08/0.32 ( ( X2 = Y2 )
% 0.08/0.32 => ( ord_less_eq_real_int @ X2 @ Y2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_refl
% 0.08/0.32 thf(fact_259_eq__refl,axiom,
% 0.08/0.32 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
% 0.08/0.32 ( ( X2 = Y2 )
% 0.08/0.32 => ( ord_le461438217t_unit @ X2 @ Y2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_refl
% 0.08/0.32 thf(fact_260_linear,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 | ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.08/0.32
% 0.08/0.32 % linear
% 0.08/0.32 thf(fact_261_antisym,axiom,
% 0.08/0.32 ! [X2: real,Y2: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.08/0.32 => ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym
% 0.08/0.32 thf(fact_262_antisym,axiom,
% 0.08/0.32 ! [X2: real_int,Y2: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_less_eq_real_int @ Y2 @ X2 )
% 0.08/0.32 => ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym
% 0.08/0.32 thf(fact_263_antisym,axiom,
% 0.08/0.32 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 0.08/0.32 => ( ( ord_le461438217t_unit @ Y2 @ X2 )
% 0.08/0.32 => ( X2 = Y2 ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % antisym
% 0.08/0.32 thf(fact_264_eq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [X3: real,Y: real] :
% 0.08/0.32 ( ( ord_less_eq_real @ X3 @ Y )
% 0.08/0.32 & ( ord_less_eq_real @ Y @ X3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_iff
% 0.08/0.32 thf(fact_265_eq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [X3: real_int,Y: real_int] :
% 0.08/0.32 ( ( ord_less_eq_real_int @ X3 @ Y )
% 0.08/0.32 & ( ord_less_eq_real_int @ Y @ X3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_iff
% 0.08/0.32 thf(fact_266_eq__iff,axiom,
% 0.08/0.32 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 0.08/0.32 = ( ^ [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.08/0.32 ( ( ord_le461438217t_unit @ X3 @ Y )
% 0.08/0.32 & ( ord_le461438217t_unit @ Y @ X3 ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 % eq_iff
% 0.08/0.32
% 0.08/0.32 % Conjectures (1)
% 0.08/0.32 thf(conj_0,conjecture,
% 0.08/0.32 ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
% 0.08/0.32 & ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 ------------------------
% 1.83/1.10 ---- Embedded in THF ---
% 1.83/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.83/1.10 %%% Generated on Tue Feb 24 03:28:26 EST 2026
% 1.83/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.83/1.10 %%% Logic specification used:
% 1.83/1.10 %%% thf(spec, logic, $$dhol).
% 1.83/1.10
% 1.83/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2DTF9673.p
% See solution above
% 1.83/1.10 ------------------------
% 1.83/1.12 ---- Cleaned THF ---
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J_J,type,
% 1.83/1.12 produc458204144s_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J,type,
% 1.83/1.12 produc1603581272s_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J,type,
% 1.83/1.12 produc28608506s_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J,type,
% 1.83/1.12 produc1622321602s_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J,type,
% 1.83/1.12 produc427086159s_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 1.83/1.12 produc957004601l_real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 1.83/1.12 view_e774982825t_unit: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__RealInt__Oreal____int,type,
% 1.83/1.12 real_int: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__NatInt__Onat____int,type,
% 1.83/1.12 nat_int: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Traffic__Otraffic,type,
% 1.83/1.12 traffic: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Real__Oreal,type,
% 1.83/1.12 real: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(ty_n_t__Cars__Ocars,type,
% 1.83/1.12 cars: $tType ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 1.83/1.12 one_one_real: real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 1.83/1.12 plus_plus_real: real > real > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 1.83/1.12 zero_zero_real: real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Length_Osensors_Olen,type,
% 1.83/1.12 len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Obot__class_Obot_001t__NatInt__Onat____int,type,
% 1.83/1.12 bot_bot_nat_int: nat_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Oord__class_Oless_001t__RealInt__Oreal____int,type,
% 1.83/1.12 ord_less_real_int: real_int > real_int > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 1.83/1.12 ord_less_real: real > real > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__RealInt__Oreal____int,type,
% 1.83/1.12 ord_less_eq_real_int: real_int > real_int > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 1.83/1.12 ord_less_eq_real: real > real > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 1.83/1.12 ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J,type,
% 1.83/1.12 produc795767668s_real: ( cars > real > real ) > produc427086159s_real > produc1622321602s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J,type,
% 1.83/1.12 produc1348924850s_real: ( cars > nat_int ) > produc1622321602s_real > produc28608506s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J,type,
% 1.83/1.12 produc1230243850s_real: ( cars > nat_int ) > produc28608506s_real > produc1603581272s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__Real__Oreal_J_001_062_It__Cars__Ocars_Mt__Real__Oreal_J,type,
% 1.83/1.12 produc1439932679s_real: ( cars > real ) > ( cars > real ) > produc427086159s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001_062_It__Cars__Ocars_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__NatInt__Onat____int_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__Cars__Ocars_Mt__Real__Oreal_J_M_062_It__Cars__Ocars_Mt__Real__Oreal_J_J_J_J_J,type,
% 1.83/1.12 produc1876576040s_real: ( cars > real ) > produc1603581272s_real > produc458204144s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.83/1.12 produc705216881l_real: real > real > produc957004601l_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_RealInt_Oleft,type,
% 1.83/1.12 left: real_int > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_RealInt_Oreal__int_OAbs__real__int,type,
% 1.83/1.12 real_Abs_real_int: produc957004601l_real > real_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 1.83/1.12 real_length: real_int > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 1.83/1.12 real_shift: real_int > real > real_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_RealInt_Oright,type,
% 1.83/1.12 right: real_int > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Regular__Sensors_Oregular,type,
% 1.83/1.12 regular_regular: cars > traffic > cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Sensors_Osensors,type,
% 1.83/1.12 sensors: ( cars > traffic > cars > real ) > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Sensors_Osensors_Ospace,type,
% 1.83/1.12 space: ( cars > traffic > cars > real ) > traffic > view_e774982825t_unit > cars > real_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Traffic_Otraffic_OAbs__traffic,type,
% 1.83/1.12 abs_traffic: produc458204144s_real > traffic ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 1.83/1.12 physical_size: traffic > cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Traffic_Otraffic_Opos,type,
% 1.83/1.12 pos: traffic > cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Views_Oview_Oext_001t__Product____Type__Ounit,type,
% 1.83/1.12 ext_Product_unit: view_e774982825t_unit > real_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Views_Oview_Ohchop,type,
% 1.83/1.12 hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 1.83/1.12
% 1.83/1.12 thf(sy_c_Views_Oview_Oown_001t__Product____Type__Ounit,type,
% 1.83/1.12 own_Product_unit: view_e774982825t_unit > cars ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_c____,type,
% 1.83/1.12 c: cars ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_cl____,type,
% 1.83/1.12 cl: cars > nat_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_d____,type,
% 1.83/1.12 d: cars ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_dy____,type,
% 1.83/1.12 dy: cars > real > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_po____,type,
% 1.83/1.12 po: cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_ps____,type,
% 1.83/1.12 ps: cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_re____,type,
% 1.83/1.12 re: cars > nat_int ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_sd____,type,
% 1.83/1.12 sd: cars > real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_ts____,type,
% 1.83/1.12 ts: traffic ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_ts__rep____,type,
% 1.83/1.12 ts_rep: produc458204144s_real ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_v_H____,type,
% 1.83/1.12 v: view_e774982825t_unit ).
% 1.83/1.12
% 1.83/1.12 thf(sy_v_v____,type,
% 1.83/1.12 v2: view_e774982825t_unit ).
% 1.83/1.12
% 1.83/1.12 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,
% 1.83/1.12 ~ ! [Dy: cars > real > real] :
% 1.83/1.12 ~ ! [C: cars,X: real] :
% 1.83/1.12 ( ( Dy @ C @ X )
% 1.83/1.12 = zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_1_dyn__def,axiom,
% 1.83/1.12 ! [C: cars,X: real] :
% 1.83/1.12 ( ( dy @ C @ X )
% 1.83/1.12 = zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_2_local_Ohmlsl_Osensors__ge,axiom,
% 1.83/1.12 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_real @ zero_zero_real @ ( regular_regular @ E @ Ts @ C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_3_hmlsl_Olen__non__empty__inside,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 1.83/1.12 => ( ( ord_less_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 1.83/1.12 & ( ord_less_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_4_v_H__d,axiom,
% 1.83/1.12 ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ d ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_5_hmlsl_Ospace__nonempty,axiom,
% 1.83/1.12 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] : ( ord_less_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_6_ts__def,axiom,
% 1.83/1.12 ( ts
% 1.83/1.12 = ( abs_traffic @ ts_rep ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_7_assumption,axiom,
% 1.83/1.12 d != c ).
% 1.83/1.12
% 1.83/1.12 thf(fact_8_local_Ohmlsl_Olength__geq__zero,axiom,
% 1.83/1.12 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 | ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_9_v_H__rel__c,axiom,
% 1.83/1.12 ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
% 1.83/1.12 & ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_10_hmlsl_Oleft__space,axiom,
% 1.83/1.12 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 1.83/1.12 = ( pos @ Ts @ C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_11_len__eq,axiom,
% 1.83/1.12 ( ( len @ regular_regular @ v @ ts @ c )
% 1.83/1.12 = ( len @ regular_regular @ v @ ts @ d ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_12_hmlsl_Olen__space__left,axiom,
% 1.83/1.12 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( left @ ( space @ regular_regular @ Ts @ V @ C2 ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_13_hmlsl_Olen__space__right,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_14_regular__sensors_Osensors__le,axiom,
% 1.83/1.12 ! [E: cars,C2: cars,Ts: traffic] :
% 1.83/1.12 ( ( E != C2 )
% 1.83/1.12 => ( ord_less_real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_15_ps__ge__zero,axiom,
% 1.83/1.12 ! [C: cars] : ( ord_less_real @ zero_zero_real @ ( ps @ C ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_16_sd__ge__zero,axiom,
% 1.83/1.12 ! [C: cars] : ( ord_less_real @ zero_zero_real @ ( sd @ C ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_17_hmlsl_Olen__left,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( left @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_18_hmlsl_Olen__right,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( right @ ( len @ regular_regular @ V @ Ts @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_19_v_H__c,axiom,
% 1.83/1.12 ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ c ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_20_hmlsl_Osensors__axioms,axiom,
% 1.83/1.12 sensors @ regular_regular ).
% 1.83/1.12
% 1.83/1.12 thf(fact_21_dyn__geq__zero,axiom,
% 1.83/1.12 ! [C: cars,X: real] : ( ord_less_eq_real @ zero_zero_real @ ( dy @ C @ X ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_22_ps__def,axiom,
% 1.83/1.12 ! [C: cars] :
% 1.83/1.12 ( ( ps @ C )
% 1.83/1.12 = one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_23_regular__sensors_Osensors__leq,axiom,
% 1.83/1.12 ! [E: cars,Ts: traffic,C2: cars] : ( ord_less_eq_real @ ( regular_regular @ E @ Ts @ C2 ) @ ( regular_regular @ C2 @ Ts @ C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_24_sensors_Olen__non__empty__inside,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 1.83/1.12 => ( ( ord_less_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 1.83/1.12 & ( ord_less_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_25_other__len__zero,axiom,
% 1.83/1.12 ! [E2: cars] :
% 1.83/1.12 ( ( ( E2 != c )
% 1.83/1.12 & ( E2 != d ) )
% 1.83/1.12 => ( ( real_length @ ( len @ regular_regular @ v2 @ ts @ E2 ) )
% 1.83/1.12 = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_26_sensors_Olen__space__right,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_27_sensors_Olen__space__left,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ord_less_eq_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_28_lc,axiom,
% 1.83/1.12 ( ( left @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 1.83/1.12 = zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_29_sensors_Ospace__nonempty,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ord_less_real @ ( left @ ( space @ Sensors @ Ts @ V @ C2 ) ) @ ( right @ ( space @ Sensors @ Ts @ V @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_30_sensors_Olen__right,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ord_less_eq_real @ ( right @ ( len @ Sensors @ V @ Ts @ C2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_31_sensors_Olen__left,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( left @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_32__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,
% 1.83/1.12 ~ ! [Ps: cars > real] :
% 1.83/1.12 ~ ! [C: cars] :
% 1.83/1.12 ( ( Ps @ C )
% 1.83/1.12 = one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_33_hmlsl_Olen__sub__int,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] : ( ord_less_eq_real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( ext_Product_unit @ V ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_34_hmlsl_Olen__empty__subview,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V3: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( ord_le461438217t_unit @ V3 @ V ) )
% 1.83/1.12 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_35_lv,axiom,
% 1.83/1.12 ( ( left @ ( ext_Product_unit @ v2 ) )
% 1.83/1.12 = zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_36_rc,axiom,
% 1.83/1.12 ( ( right @ ( space @ regular_regular @ ts @ v2 @ c ) )
% 1.83/1.12 = one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_37_one__reorient,axiom,
% 1.83/1.12 ! [X2: real] :
% 1.83/1.12 ( ( one_one_real = X2 )
% 1.83/1.12 = ( X2 = one_one_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_38_sensors_Olen__sub__int,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ord_less_eq_real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( ext_Product_unit @ V ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_39_sensors_Olen__empty__subview,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V3: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( ord_le461438217t_unit @ V3 @ V ) )
% 1.83/1.12 => ( ( real_length @ ( len @ Sensors @ V3 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_40_zero__reorient,axiom,
% 1.83/1.12 ! [X2: real] :
% 1.83/1.12 ( ( zero_zero_real = X2 )
% 1.83/1.12 = ( X2 = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_41_sensors_Olen_Ocong,axiom,
% 1.83/1.12 len = len ).
% 1.83/1.12
% 1.83/1.12 thf(fact_42_sensors_Ospace_Ocong,axiom,
% 1.83/1.12 space = space ).
% 1.83/1.12
% 1.83/1.12 thf(fact_43_sensors__def,axiom,
% 1.83/1.12 ( sensors
% 1.83/1.12 = ( ^ [Sensors2: cars > traffic > cars > real] :
% 1.83/1.12 ! [E3: cars,Ts3: traffic,C3: cars] : ( ord_less_real @ zero_zero_real @ ( Sensors2 @ E3 @ Ts3 @ C3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_44_sensors_Ointro,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real] :
% 1.83/1.12 ( ! [E4: cars,Ts4: traffic,C4: cars] : ( ord_less_real @ zero_zero_real @ ( Sensors @ E4 @ Ts4 @ C4 ) )
% 1.83/1.12 => ( sensors @ Sensors ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_45_sensors_Osensors__ge,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,E: cars,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ord_less_real @ zero_zero_real @ ( Sensors @ E @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_46_sensors_Oleft__space,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( left @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 1.83/1.12 = ( pos @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_47_size,axiom,
% 1.83/1.12 ! [C: cars] :
% 1.83/1.12 ( ( physical_size @ ts @ C )
% 1.83/1.12 = one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_48_sensors__c,axiom,
% 1.83/1.12 ( ( regular_regular @ ( own_Product_unit @ v2 ) @ ts @ c )
% 1.83/1.12 = one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_49_hmlsl_Oview__leq__len__leq,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V ) @ ( ext_Product_unit @ V3 ) )
% 1.83/1.12 & ( ( own_Product_unit @ V )
% 1.83/1.12 = ( own_Product_unit @ V3 ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) )
% 1.83/1.12 => ( ord_less_eq_real_int @ ( len @ regular_regular @ V @ Ts @ C2 ) @ ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_50_length__zero__iff__borders__eq,axiom,
% 1.83/1.12 ! [R: real_int] :
% 1.83/1.12 ( ( ( real_length @ R )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 = ( ( left @ R )
% 1.83/1.12 = ( right @ R ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_51_hmlsl_Olen__fills__subview,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) )
% 1.83/1.12 => ? [V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ V1 @ V22 )
% 1.83/1.12 & ( hchop @ V22 @ V4 @ V32 )
% 1.83/1.12 & ( ( len @ regular_regular @ V4 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V4 ) )
% 1.83/1.12 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C2 ) )
% 1.83/1.12 = ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_52_less__real__int__def,axiom,
% 1.83/1.12 ( ord_less_real_int
% 1.83/1.12 = ( ^ [R2: real_int,S: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( left @ S ) @ ( left @ R2 ) )
% 1.83/1.12 & ( ord_less_eq_real @ ( right @ R2 ) @ ( right @ S ) )
% 1.83/1.12 & ~ ( ( ord_less_eq_real @ ( left @ R2 ) @ ( left @ S ) )
% 1.83/1.12 & ( ord_less_eq_real @ ( right @ S ) @ ( right @ R2 ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_53_less__eq__real__int__def,axiom,
% 1.83/1.12 ( ord_less_eq_real_int
% 1.83/1.12 = ( ^ [R2: real_int,S: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( left @ S ) @ ( left @ R2 ) )
% 1.83/1.12 & ( ord_less_eq_real @ ( right @ R2 ) @ ( right @ S ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_54_left__leq__right,axiom,
% 1.83/1.12 ! [R: real_int] : ( ord_less_eq_real @ ( left @ R ) @ ( right @ R ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_55_length__ge__zero,axiom,
% 1.83/1.12 ! [R: real_int] : ( ord_less_eq_real @ zero_zero_real @ ( real_length @ R ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_56_local_Ohmlsl_Ohchop__assoc,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Phi @ Ts2 @ W )
% 1.83/1.12 & ? [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ U @ X3 @ Y )
% 1.83/1.12 & ( Psi @ Ts2 @ X3 )
% 1.83/1.12 & ( Chi @ Ts2 @ Y ) ) ) )
% 1.83/1.12 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ? [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ W @ X3 @ Y )
% 1.83/1.12 & ( Phi @ Ts2 @ X3 )
% 1.83/1.12 & ( Psi @ Ts2 @ Y ) )
% 1.83/1.12 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_57_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Phi @ Ts2 @ W )
% 1.83/1.12 & ( ( Psi @ Ts2 @ U )
% 1.83/1.12 | ( Chi @ Ts2 @ U ) ) ) )
% 1.83/1.12 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Phi @ Ts2 @ W )
% 1.83/1.12 & ( Psi @ Ts2 @ U ) )
% 1.83/1.12 | ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Phi @ Ts2 @ W )
% 1.83/1.12 & ( Chi @ Ts2 @ U ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_58_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 1.83/1.12 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( ( Psi @ Ts2 @ W )
% 1.83/1.12 | ( Chi @ Ts2 @ W ) )
% 1.83/1.12 & ( Phi @ Ts2 @ U ) ) )
% 1.83/1.12 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Psi @ Ts2 @ W )
% 1.83/1.12 & ( Phi @ Ts2 @ U ) )
% 1.83/1.12 | ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( Chi @ Ts2 @ W )
% 1.83/1.12 & ( Phi @ Ts2 @ U ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_59_local_Ohmlsl_Ohchop__neg1,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ~ ? [Va: view_e774982825t_unit] :
% 1.83/1.12 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 1.83/1.12 & ( Phi @ Ts2 @ Va ) )
% 1.83/1.12 => ? [Va: view_e774982825t_unit] :
% 1.83/1.12 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 1.83/1.12 & ~ ( Phi @ Ts2 @ Va ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_60_local_Ohmlsl_Ohchop__neg2,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ~ ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ( Phi @ Ts2 @ U2 ) )
% 1.83/1.12 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_61_local_Ohmlsl_Ohchop__weaken,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( Phi @ Ts2 @ V2 )
% 1.83/1.12 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ? [Vb: view_e774982825t_unit] :
% 1.83/1.12 ( ? [X_1: view_e774982825t_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 1.83/1.12 & ( Phi @ Ts2 @ Vb ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_62_local_Ohmlsl_Ohchop__weaken1,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( Phi @ Ts2 @ V2 )
% 1.83/1.12 => ? [Va: view_e774982825t_unit] :
% 1.83/1.12 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ Va @ X_1 )
% 1.83/1.12 & ( Phi @ Ts2 @ Va ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_63_local_Ohmlsl_Ohchop__weaken2,axiom,
% 1.83/1.12 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( Phi @ Ts2 @ V2 )
% 1.83/1.12 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_64_hmlsl_Olen__view__hchop__right,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V23 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_65_hmlsl_Olen__view__hchop__left,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V12 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_66_hmlsl_Olen__compose__hchop,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 & ( ( len @ regular_regular @ V12 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V12 ) )
% 1.83/1.12 & ( ( len @ regular_regular @ V23 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V23 ) ) )
% 1.83/1.12 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_67_hmlsl_Oext__eq__len__eq,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ( ( ext_Product_unit @ V )
% 1.83/1.12 = ( ext_Product_unit @ V3 ) )
% 1.83/1.12 & ( ( own_Product_unit @ V )
% 1.83/1.12 = ( own_Product_unit @ V3 ) ) )
% 1.83/1.12 => ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( len @ regular_regular @ V3 @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_68_local_Ohmlsl_Olength__split,axiom,
% 1.83/1.12 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 1.83/1.12 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_69_local_Ohmlsl_Olength__meld,axiom,
% 1.83/1.12 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ? [Va2: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va2 @ U3 )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) ) )
% 1.83/1.12 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_70_local_Ohmlsl_Olength__dense,axiom,
% 1.83/1.12 ! [Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 1.83/1.12 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_71_hmlsl_Olen__empty__on__subview2,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_72_hmlsl_Olen__empty__on__subview1,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_73_hmlsl_Olen__hchop__right__right__border,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( right @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = ( right @ ( ext_Product_unit @ V23 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_74_hmlsl_Olen__hchop__right__left__border,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( left @ ( len @ regular_regular @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = ( left @ ( ext_Product_unit @ V23 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_75_hmlsl_Olen__hchop__left__right__border,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( right @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = ( right @ ( ext_Product_unit @ V12 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_76_hmlsl_Olen__hchop__left__left__border,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ( len @ regular_regular @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( left @ ( len @ regular_regular @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = ( left @ ( ext_Product_unit @ V12 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_77_regular__sensors_Ospace__eq,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( ( own_Product_unit @ V )
% 1.83/1.12 = ( own_Product_unit @ V3 ) )
% 1.83/1.12 => ( ( space @ regular_regular @ Ts @ V @ C2 )
% 1.83/1.12 = ( space @ regular_regular @ Ts @ V3 @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_78_sensors_Olen__compose__hchop,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 & ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V12 ) )
% 1.83/1.12 & ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V23 ) ) )
% 1.83/1.12 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_79_sensors_Olen__view__hchop__left,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( len @ Sensors @ V12 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V12 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_80_sensors_Olen__view__hchop__right,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( len @ Sensors @ V23 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V23 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_81_sensors_Oext__eq__len__eq,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( ext_Product_unit @ V )
% 1.83/1.12 = ( ext_Product_unit @ V3 ) )
% 1.83/1.12 & ( ( own_Product_unit @ V )
% 1.83/1.12 = ( own_Product_unit @ V3 ) ) )
% 1.83/1.12 => ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_82_sensors_Olen__empty__on__subview1,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_83_sensors_Olen__empty__on__subview2,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_84_sensors_Olen__hchop__right__right__border,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( right @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = ( right @ ( ext_Product_unit @ V23 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_85_sensors_Olen__hchop__right__left__border,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( left @ ( len @ Sensors @ V23 @ Ts @ C2 ) )
% 1.83/1.12 = ( left @ ( ext_Product_unit @ V23 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_86_sensors_Olen__hchop__left__right__border,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( right @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = ( right @ ( ext_Product_unit @ V12 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_87_sensors_Olen__hchop__left__left__border,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars,V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ( len @ Sensors @ V @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V ) )
% 1.83/1.12 & ( hchop @ V @ V12 @ V23 ) )
% 1.83/1.12 => ( ( left @ ( len @ Sensors @ V12 @ Ts @ C2 ) )
% 1.83/1.12 = ( left @ ( ext_Product_unit @ V12 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_88_sensors_Olen__fills__subview,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) )
% 1.83/1.12 => ? [V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ V1 @ V22 )
% 1.83/1.12 & ( hchop @ V22 @ V4 @ V32 )
% 1.83/1.12 & ( ( len @ Sensors @ V4 @ Ts @ C2 )
% 1.83/1.12 = ( ext_Product_unit @ V4 ) )
% 1.83/1.12 & ( ( real_length @ ( len @ Sensors @ V4 @ Ts @ C2 ) )
% 1.83/1.12 = ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_89_sensors_Oview__leq__len__leq,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V ) @ ( ext_Product_unit @ V3 ) )
% 1.83/1.12 & ( ( own_Product_unit @ V )
% 1.83/1.12 = ( own_Product_unit @ V3 ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) ) ) )
% 1.83/1.12 => ( ord_less_eq_real_int @ ( len @ Sensors @ V @ Ts @ C2 ) @ ( len @ Sensors @ V3 @ Ts @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_90_view_Oh__chop__middle2,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U4 @ W2 )
% 1.83/1.12 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ W2 ) ) @ ( right @ ( ext_Product_unit @ V ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_91_view_Oh__chop__middle1,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U4 @ W2 )
% 1.83/1.12 => ( ord_less_eq_real @ ( left @ ( ext_Product_unit @ V ) ) @ ( right @ ( ext_Product_unit @ U4 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_92_view_Ohorizontal__chop__non__empty,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 1.83/1.12 => ? [U2: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U2 @ W3 )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 1.83/1.12 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W3 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_93_hmlsl_Oright__space,axiom,
% 1.83/1.12 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( right @ ( space @ regular_regular @ Ts @ V @ C2 ) )
% 1.83/1.12 = ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_94_local_Ohmlsl_Olength__add,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 1.83/1.12 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 1.83/1.12 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 1.83/1.12 = ( plus_plus_real @ X2 @ Y2 ) )
% 1.83/1.12 = ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ W @ U )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ W ) )
% 1.83/1.12 = X2 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ U ) )
% 1.83/1.12 = Y2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_95_local_Ohmlsl_Olength__add2,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 1.83/1.12 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 1.83/1.12 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 1.83/1.12 = ( plus_plus_real @ X2 @ Y2 ) )
% 1.83/1.12 => ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va @ U2 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ Va ) )
% 1.83/1.12 = X2 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ U2 ) )
% 1.83/1.12 = Y2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_96_traffic_OpsGeZero,axiom,
% 1.83/1.12 ! [Ts: traffic,C: cars] : ( ord_less_real @ zero_zero_real @ ( physical_size @ Ts @ C ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_97_local_Ohmlsl_Olength__add1,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,Ts2: traffic,V2: view_e774982825t_unit] :
% 1.83/1.12 ( ? [Va2: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V2 @ Va2 @ U3 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ Va2 ) )
% 1.83/1.12 = X2 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ U3 ) )
% 1.83/1.12 = Y2 ) )
% 1.83/1.12 => ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 1.83/1.12 = ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_98_add__left__cancel,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ A @ B )
% 1.83/1.12 = ( plus_plus_real @ A @ C2 ) )
% 1.83/1.12 = ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_99_add__right__cancel,axiom,
% 1.83/1.12 ! [B: real,A: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ B @ A )
% 1.83/1.12 = ( plus_plus_real @ C2 @ A ) )
% 1.83/1.12 = ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_100_hmlsl_Olen__hchop__add,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 => ( ( real_length @ ( len @ regular_regular @ V @ Ts @ C2 ) )
% 1.83/1.12 = ( plus_plus_real @ ( real_length @ ( len @ regular_regular @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ regular_regular @ V23 @ Ts @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_101_add__le__cancel__right,axiom,
% 1.83/1.12 ! [A: real,C2: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 1.83/1.12 = ( ord_less_eq_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_102_add__le__cancel__left,axiom,
% 1.83/1.12 ! [C2: real,A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 1.83/1.12 = ( ord_less_eq_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_103_add__cancel__right__right,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( A
% 1.83/1.12 = ( plus_plus_real @ A @ B ) )
% 1.83/1.12 = ( B = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_104_add__cancel__right__left,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( A
% 1.83/1.12 = ( plus_plus_real @ B @ A ) )
% 1.83/1.12 = ( B = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_105_add__cancel__left__right,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ A @ B )
% 1.83/1.12 = A )
% 1.83/1.12 = ( B = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_106_add__cancel__left__left,axiom,
% 1.83/1.12 ! [B: real,A: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ B @ A )
% 1.83/1.12 = A )
% 1.83/1.12 = ( B = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_107_double__zero__sym,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( zero_zero_real
% 1.83/1.12 = ( plus_plus_real @ A @ A ) )
% 1.83/1.12 = ( A = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_108_double__zero,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ A @ A )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 = ( A = zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_109_add_Oright__neutral,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( plus_plus_real @ A @ zero_zero_real )
% 1.83/1.12 = A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_110_add_Oleft__neutral,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( plus_plus_real @ zero_zero_real @ A )
% 1.83/1.12 = A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_111_add__less__cancel__left,axiom,
% 1.83/1.12 ! [C2: real,A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 1.83/1.12 = ( ord_less_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_112_add__less__cancel__right,axiom,
% 1.83/1.12 ! [A: real,C2: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 1.83/1.12 = ( ord_less_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_113_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 1.83/1.12 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_114_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 1.83/1.12 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_115_le__add__same__cancel2,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 1.83/1.12 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_116_le__add__same__cancel1,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 1.83/1.12 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_117_add__le__same__cancel2,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 1.83/1.12 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_118_add__le__same__cancel1,axiom,
% 1.83/1.12 ! [B: real,A: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 1.83/1.12 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_119_add__less__same__cancel1,axiom,
% 1.83/1.12 ! [B: real,A: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 1.83/1.12 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_120_add__less__same__cancel2,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 1.83/1.12 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_121_less__add__same__cancel1,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 1.83/1.12 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_122_less__add__same__cancel2,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 1.83/1.12 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_123_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 1.83/1.12 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_124_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 1.83/1.12 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_125_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 1.83/1.12 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_126_add__mono__thms__linordered__semiring_I4_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( I = J )
% 1.83/1.12 & ( K = L ) )
% 1.83/1.12 => ( ( plus_plus_real @ I @ K )
% 1.83/1.12 = ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_127_group__cancel_Oadd1,axiom,
% 1.83/1.12 ! [A2: real,K: real,A: real,B: real] :
% 1.83/1.12 ( ( A2
% 1.83/1.12 = ( plus_plus_real @ K @ A ) )
% 1.83/1.12 => ( ( plus_plus_real @ A2 @ B )
% 1.83/1.12 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_128_group__cancel_Oadd2,axiom,
% 1.83/1.12 ! [B2: real,K: real,B: real,A: real] :
% 1.83/1.12 ( ( B2
% 1.83/1.12 = ( plus_plus_real @ K @ B ) )
% 1.83/1.12 => ( ( plus_plus_real @ A @ B2 )
% 1.83/1.12 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_129_add_Oassoc,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 1.83/1.12 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_130_add_Oleft__cancel,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ A @ B )
% 1.83/1.12 = ( plus_plus_real @ A @ C2 ) )
% 1.83/1.12 = ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_131_add_Oright__cancel,axiom,
% 1.83/1.12 ! [B: real,A: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ B @ A )
% 1.83/1.12 = ( plus_plus_real @ C2 @ A ) )
% 1.83/1.12 = ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_132_add_Ocommute,axiom,
% 1.83/1.12 ( plus_plus_real
% 1.83/1.12 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_133_add_Oleft__commute,axiom,
% 1.83/1.12 ! [B: real,A: real,C2: real] :
% 1.83/1.12 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 1.83/1.12 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_134_add__left__imp__eq,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ A @ B )
% 1.83/1.12 = ( plus_plus_real @ A @ C2 ) )
% 1.83/1.12 => ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_135_add__right__imp__eq,axiom,
% 1.83/1.12 ! [B: real,A: real,C2: real] :
% 1.83/1.12 ( ( ( plus_plus_real @ B @ A )
% 1.83/1.12 = ( plus_plus_real @ C2 @ A ) )
% 1.83/1.12 => ( B = C2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_136_add__le__imp__le__right,axiom,
% 1.83/1.12 ! [A: real,C2: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 1.83/1.12 => ( ord_less_eq_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_137_add__le__imp__le__left,axiom,
% 1.83/1.12 ! [C2: real,A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 1.83/1.12 => ( ord_less_eq_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_138_add__right__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_139_add__left__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_140_add__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real,D: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real @ C2 @ D )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_141_add__mono__thms__linordered__semiring_I1_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ I @ J )
% 1.83/1.12 & ( ord_less_eq_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_142_add__mono__thms__linordered__semiring_I2_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( I = J )
% 1.83/1.12 & ( ord_less_eq_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_143_add__mono__thms__linordered__semiring_I3_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ I @ J )
% 1.83/1.12 & ( K = L ) )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_144_add_Ogroup__left__neutral,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( plus_plus_real @ zero_zero_real @ A )
% 1.83/1.12 = A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_145_add_Ocomm__neutral,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( plus_plus_real @ A @ zero_zero_real )
% 1.83/1.12 = A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_146_comm__monoid__add__class_Oadd__0,axiom,
% 1.83/1.12 ! [A: real] :
% 1.83/1.12 ( ( plus_plus_real @ zero_zero_real @ A )
% 1.83/1.12 = A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_147_add__mono__thms__linordered__field_I5_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_real @ I @ J )
% 1.83/1.12 & ( ord_less_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_148_add__mono__thms__linordered__field_I2_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( I = J )
% 1.83/1.12 & ( ord_less_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_149_add__mono__thms__linordered__field_I1_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_real @ I @ J )
% 1.83/1.12 & ( K = L ) )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_150_add__strict__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real,D: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_real @ C2 @ D )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_151_add__strict__left__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ B )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_152_add__strict__right__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ B )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_153_add__less__imp__less__left,axiom,
% 1.83/1.12 ! [C2: real,A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 1.83/1.12 => ( ord_less_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_154_add__less__imp__less__right,axiom,
% 1.83/1.12 ! [A: real,C2: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 1.83/1.12 => ( ord_less_real @ A @ B ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_155_add__nonpos__eq__0__iff,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 1.83/1.12 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 = ( ( X2 = zero_zero_real )
% 1.83/1.12 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_156_add__nonneg__eq__0__iff,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 1.83/1.12 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.83/1.12 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 1.83/1.12 = zero_zero_real )
% 1.83/1.12 = ( ( X2 = zero_zero_real )
% 1.83/1.12 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_157_add__nonpos__nonpos,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_158_add__nonneg__nonneg,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 1.83/1.12 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_159_add__increasing2,axiom,
% 1.83/1.12 ! [C2: real,B: real,A: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ A )
% 1.83/1.12 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_160_add__decreasing2,axiom,
% 1.83/1.12 ! [C2: real,A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_161_add__increasing,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_162_add__decreasing,axiom,
% 1.83/1.12 ! [A: real,C2: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_eq_real @ C2 @ B )
% 1.83/1.12 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_163_add__less__le__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real,D: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real @ C2 @ D )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_164_add__le__less__mono,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real,D: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_real @ C2 @ D )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_165_add__mono__thms__linordered__field_I3_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_real @ I @ J )
% 1.83/1.12 & ( ord_less_eq_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_166_add__mono__thms__linordered__field_I4_J,axiom,
% 1.83/1.12 ! [I: real,J: real,K: real,L: real] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ I @ J )
% 1.83/1.12 & ( ord_less_real @ K @ L ) )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_167_add__neg__neg,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_168_add__pos__pos,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_real @ zero_zero_real @ B )
% 1.83/1.12 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_169_pos__add__strict,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_170_add__strict__increasing2,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_171_add__strict__increasing,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_172_add__pos__nonneg,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 1.83/1.12 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_173_add__nonpos__neg,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_174_add__nonneg__pos,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.83/1.12 => ( ( ord_less_real @ zero_zero_real @ B )
% 1.83/1.12 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_175_add__neg__nonpos,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_176_consec__add,axiom,
% 1.83/1.12 ! [R: real_int,S2: real_int,T: real_int] :
% 1.83/1.12 ( ( ( ( left @ R )
% 1.83/1.12 = ( left @ S2 ) )
% 1.83/1.12 & ( ( right @ R )
% 1.83/1.12 = ( right @ T ) )
% 1.83/1.12 & ( ( right @ S2 )
% 1.83/1.12 = ( left @ T ) ) )
% 1.83/1.12 => ( ( real_length @ R )
% 1.83/1.12 = ( plus_plus_real @ ( real_length @ S2 ) @ ( real_length @ T ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_177_view_Ohorizontal__chop__empty__right,axiom,
% 1.83/1.12 ! [V2: view_e774982825t_unit] :
% 1.83/1.12 ? [X_1: view_e774982825t_unit] : ( hchop @ V2 @ V2 @ X_1 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_178_view_Ohorizontal__chop__empty__left,axiom,
% 1.83/1.12 ! [V2: view_e774982825t_unit] :
% 1.83/1.12 ? [U2: view_e774982825t_unit] : ( hchop @ V2 @ U2 @ V2 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_179_view_Ohorizontal__chop__assoc2,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 & ( hchop @ V12 @ V33 @ V42 ) )
% 1.83/1.12 => ? [V4: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ V33 @ V4 )
% 1.83/1.12 & ( hchop @ V4 @ V42 @ V23 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_180_view_Ohorizontal__chop__assoc1,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 & ( hchop @ V23 @ V33 @ V42 ) )
% 1.83/1.12 => ? [V4: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ V4 @ V42 )
% 1.83/1.12 & ( hchop @ V4 @ V12 @ V33 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_181_view_Ohorizontal__chop1,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit] :
% 1.83/1.12 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( hchop @ V @ U2 @ X_1 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_182_view_Ohorizontal__chop__split__add,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,V: view_e774982825t_unit] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 1.83/1.12 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) )
% 1.83/1.12 => ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 1.83/1.12 = ( plus_plus_real @ X2 @ Y2 ) )
% 1.83/1.12 => ? [U2: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U2 @ W3 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ U2 ) )
% 1.83/1.12 = X2 )
% 1.83/1.12 & ( ( real_length @ ( ext_Product_unit @ W3 ) )
% 1.83/1.12 = Y2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_183_sensors_Olen__hchop__add,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,V: view_e774982825t_unit,V12: view_e774982825t_unit,V23: view_e774982825t_unit,Ts: traffic,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( hchop @ V @ V12 @ V23 )
% 1.83/1.12 => ( ( real_length @ ( len @ Sensors @ V @ Ts @ C2 ) )
% 1.83/1.12 = ( plus_plus_real @ ( real_length @ ( len @ Sensors @ V12 @ Ts @ C2 ) ) @ ( real_length @ ( len @ Sensors @ V23 @ Ts @ C2 ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_184_sensors_Oright__space,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( right @ ( space @ Sensors @ Ts @ V @ C2 ) )
% 1.83/1.12 = ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_185_view_Ohorizontal__chop__own__trans,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U4 @ W2 )
% 1.83/1.12 => ( ( own_Product_unit @ U4 )
% 1.83/1.12 = ( own_Product_unit @ W2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_186_view_Ohorizontal__chop__leq2,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U4 @ W2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ W2 @ V ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_187_view_Ohorizontal__chop__leq1,axiom,
% 1.83/1.12 ! [V: view_e774982825t_unit,U4: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 1.83/1.12 ( ( hchop @ V @ U4 @ W2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ U4 @ V ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_188_zero__less__two,axiom,
% 1.83/1.12 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_189_field__le__epsilon,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ! [E4: real] :
% 1.83/1.12 ( ( ord_less_real @ zero_zero_real @ E4 )
% 1.83/1.12 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y2 @ E4 ) ) )
% 1.83/1.12 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_190_add__mono1,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_real @ A @ B )
% 1.83/1.12 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_191_less__add__one,axiom,
% 1.83/1.12 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_192_linorder__neqE__linordered__idom,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( X2 != Y2 )
% 1.83/1.12 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 1.83/1.12 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_193_linordered__field__no__ub,axiom,
% 1.83/1.12 ! [X: real] :
% 1.83/1.12 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_194_linordered__field__no__lb,axiom,
% 1.83/1.12 ! [X: real] :
% 1.83/1.12 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_195_zero__neq__one,axiom,
% 1.83/1.12 zero_zero_real != one_one_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_196_zero__le__one,axiom,
% 1.83/1.12 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_197_not__one__le__zero,axiom,
% 1.83/1.12 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_198_not__one__less__zero,axiom,
% 1.83/1.12 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_199_zero__less__one,axiom,
% 1.83/1.12 ord_less_real @ zero_zero_real @ one_one_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_200_add__less__zeroD,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 1.83/1.12 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 1.83/1.12 | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_201_less__numeral__extra_I1_J,axiom,
% 1.83/1.12 ord_less_real @ zero_zero_real @ one_one_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_202_space__c,axiom,
% 1.83/1.12 ( ( space @ regular_regular @ ts @ v2 @ c )
% 1.83/1.12 = ( real_Abs_real_int @ ( produc705216881l_real @ zero_zero_real @ one_one_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_203_hmlsl_Ospace__def,axiom,
% 1.83/1.12 ! [Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( space @ regular_regular @ Ts @ V @ C2 )
% 1.83/1.12 = ( real_Abs_real_int @ ( produc705216881l_real @ ( pos @ Ts @ C2 ) @ ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( regular_regular @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_204_len__c,axiom,
% 1.83/1.12 ( ( len @ regular_regular @ v2 @ ts @ c )
% 1.83/1.12 = ( real_Abs_real_int @ ( produc705216881l_real @ zero_zero_real @ one_one_real ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_205_sensors_Ospace__def,axiom,
% 1.83/1.12 ! [Sensors: cars > traffic > cars > real,Ts: traffic,V: view_e774982825t_unit,C2: cars] :
% 1.83/1.12 ( ( sensors @ Sensors )
% 1.83/1.12 => ( ( space @ Sensors @ Ts @ V @ C2 )
% 1.83/1.12 = ( real_Abs_real_int @ ( produc705216881l_real @ ( pos @ Ts @ C2 ) @ ( plus_plus_real @ ( pos @ Ts @ C2 ) @ ( Sensors @ ( own_Product_unit @ V ) @ Ts @ C2 ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_206_is__num__normalize_I1_J,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 1.83/1.12 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_207_le__numeral__extra_I3_J,axiom,
% 1.83/1.12 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_208_less__numeral__extra_I3_J,axiom,
% 1.83/1.12 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_209_le__numeral__extra_I4_J,axiom,
% 1.83/1.12 ord_less_eq_real @ one_one_real @ one_one_real ).
% 1.83/1.12
% 1.83/1.12 thf(fact_210_less__numeral__extra_I4_J,axiom,
% 1.83/1.12 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_211_real__int__class_Oshift__def,axiom,
% 1.83/1.12 ( real_shift
% 1.83/1.12 = ( ^ [R2: real_int,X3: real] : ( real_Abs_real_int @ ( produc705216881l_real @ ( plus_plus_real @ ( left @ R2 ) @ X3 ) @ ( plus_plus_real @ ( right @ R2 ) @ X3 ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_212_shift__additivity,axiom,
% 1.83/1.12 ! [R: real_int,X2: real,Y2: real] :
% 1.83/1.12 ( ( real_shift @ R @ ( plus_plus_real @ X2 @ Y2 ) )
% 1.83/1.12 = ( real_shift @ ( real_shift @ R @ X2 ) @ Y2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_213_shift__keeps__length,axiom,
% 1.83/1.12 ! [X2: real] :
% 1.83/1.12 ( real_length
% 1.83/1.12 = ( ^ [R2: real_int] : ( real_length @ ( real_shift @ R2 @ X2 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_214_shift__zero,axiom,
% 1.83/1.12 ! [R: real_int] :
% 1.83/1.12 ( ( real_shift @ R @ zero_zero_real )
% 1.83/1.12 = R ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_215_shift__left__eq__right,axiom,
% 1.83/1.12 ! [R: real_int,X2: real] : ( ord_less_eq_real @ ( left @ ( real_shift @ R @ X2 ) ) @ ( right @ ( real_shift @ R @ X2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_216_ts__rep__def,axiom,
% 1.83/1.12 ( ts_rep
% 1.83/1.12 = ( produc1876576040s_real @ po @ ( produc1230243850s_real @ re @ ( produc1348924850s_real @ cl @ ( produc795767668s_real @ dy @ ( produc1439932679s_real @ ps @ sd ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_217_order__refl,axiom,
% 1.83/1.12 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_218_order__refl,axiom,
% 1.83/1.12 ! [X2: real_int] : ( ord_less_eq_real_int @ X2 @ X2 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_219_order__refl,axiom,
% 1.83/1.12 ! [X2: view_e774982825t_unit] : ( ord_le461438217t_unit @ X2 @ X2 ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_220_clm__def,axiom,
% 1.83/1.12 ! [C: cars] :
% 1.83/1.12 ( ( cl @ C )
% 1.83/1.12 = bot_bot_nat_int ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_221_dual__order_Oantisym,axiom,
% 1.83/1.12 ! [B: real,A: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ B @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_222_dual__order_Oantisym,axiom,
% 1.83/1.12 ! [B: real_int,A: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ B @ A )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ A @ B )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_223_dual__order_Oantisym,axiom,
% 1.83/1.12 ! [B: view_e774982825t_unit,A: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ B @ A )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ A @ B )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_224_dual__order_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: real,B3: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ B3 @ A3 )
% 1.83/1.12 & ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_225_dual__order_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: real_int,B3: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ B3 @ A3 )
% 1.83/1.12 & ( ord_less_eq_real_int @ A3 @ B3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_226_dual__order_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: view_e774982825t_unit,B3: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ B3 @ A3 )
% 1.83/1.12 & ( ord_le461438217t_unit @ A3 @ B3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_227_dual__order_Otrans,axiom,
% 1.83/1.12 ! [B: real,A: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ B @ A )
% 1.83/1.12 => ( ( ord_less_eq_real @ C2 @ B )
% 1.83/1.12 => ( ord_less_eq_real @ C2 @ A ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_228_dual__order_Otrans,axiom,
% 1.83/1.12 ! [B: real_int,A: real_int,C2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ B @ A )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ C2 @ B )
% 1.83/1.12 => ( ord_less_eq_real_int @ C2 @ A ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_229_dual__order_Otrans,axiom,
% 1.83/1.12 ! [B: view_e774982825t_unit,A: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ B @ A )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ C2 @ B )
% 1.83/1.12 => ( ord_le461438217t_unit @ C2 @ A ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_230_linorder__wlog,axiom,
% 1.83/1.12 ! [P: real > real > $o,A: real,B: real] :
% 1.83/1.12 ( ! [A4: real,B4: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A4 @ B4 )
% 1.83/1.12 => ( P @ A4 @ B4 ) )
% 1.83/1.12 => ( ! [A4: real,B4: real] :
% 1.83/1.12 ( ( P @ B4 @ A4 )
% 1.83/1.12 => ( P @ A4 @ B4 ) )
% 1.83/1.12 => ( P @ A @ B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_231_dual__order_Orefl,axiom,
% 1.83/1.12 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_232_dual__order_Orefl,axiom,
% 1.83/1.12 ! [A: real_int] : ( ord_less_eq_real_int @ A @ A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_233_dual__order_Orefl,axiom,
% 1.83/1.12 ! [A: view_e774982825t_unit] : ( ord_le461438217t_unit @ A @ A ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_234_order__trans,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,Z2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_less_eq_real @ Y2 @ Z2 )
% 1.83/1.12 => ( ord_less_eq_real @ X2 @ Z2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_235_order__trans,axiom,
% 1.83/1.12 ! [X2: real_int,Y2: real_int,Z2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ Y2 @ Z2 )
% 1.83/1.12 => ( ord_less_eq_real_int @ X2 @ Z2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_236_order__trans,axiom,
% 1.83/1.12 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit,Z2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ Y2 @ Z2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ X2 @ Z2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_237_order__class_Oorder_Oantisym,axiom,
% 1.83/1.12 ! [A: real,B: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ A )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_238_order__class_Oorder_Oantisym,axiom,
% 1.83/1.12 ! [A: real_int,B: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ B @ A )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_239_order__class_Oorder_Oantisym,axiom,
% 1.83/1.12 ! [A: view_e774982825t_unit,B: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ A @ B )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ B @ A )
% 1.83/1.12 => ( A = B ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_240_ord__le__eq__trans,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ( B = C2 )
% 1.83/1.12 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_241_ord__le__eq__trans,axiom,
% 1.83/1.12 ! [A: real_int,B: real_int,C2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ A @ B )
% 1.83/1.12 => ( ( B = C2 )
% 1.83/1.12 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_242_ord__le__eq__trans,axiom,
% 1.83/1.12 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ A @ B )
% 1.83/1.12 => ( ( B = C2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_243_ord__eq__le__trans,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( A = B )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_244_ord__eq__le__trans,axiom,
% 1.83/1.12 ! [A: real_int,B: real_int,C2: real_int] :
% 1.83/1.12 ( ( A = B )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ B @ C2 )
% 1.83/1.12 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_245_ord__eq__le__trans,axiom,
% 1.83/1.12 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 1.83/1.12 ( ( A = B )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ B @ C2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_246_order__class_Oorder_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: real,B3: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A3 @ B3 )
% 1.83/1.12 & ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_247_order__class_Oorder_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: real_int,B3: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ A3 @ B3 )
% 1.83/1.12 & ( ord_less_eq_real_int @ B3 @ A3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [A3: view_e774982825t_unit,B3: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ A3 @ B3 )
% 1.83/1.12 & ( ord_le461438217t_unit @ B3 @ A3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_249_antisym__conv,axiom,
% 1.83/1.12 ! [Y2: real,X2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ Y2 @ X2 )
% 1.83/1.12 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 = ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_250_antisym__conv,axiom,
% 1.83/1.12 ! [Y2: real_int,X2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ Y2 @ X2 )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 1.83/1.12 = ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_251_antisym__conv,axiom,
% 1.83/1.12 ! [Y2: view_e774982825t_unit,X2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ Y2 @ X2 )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 1.83/1.12 = ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_252_le__cases3,axiom,
% 1.83/1.12 ! [X2: real,Y2: real,Z2: real] :
% 1.83/1.12 ( ( ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ Y2 @ Z2 ) )
% 1.83/1.12 => ( ( ( ord_less_eq_real @ Y2 @ X2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ X2 @ Z2 ) )
% 1.83/1.12 => ( ( ( ord_less_eq_real @ X2 @ Z2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ Z2 @ Y2 ) )
% 1.83/1.12 => ( ( ( ord_less_eq_real @ Z2 @ Y2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ Y2 @ X2 ) )
% 1.83/1.12 => ( ( ( ord_less_eq_real @ Y2 @ Z2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ Z2 @ X2 ) )
% 1.83/1.12 => ~ ( ( ord_less_eq_real @ Z2 @ X2 )
% 1.83/1.12 => ~ ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_253_order_Otrans,axiom,
% 1.83/1.12 ! [A: real,B: real,C2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real @ B @ C2 )
% 1.83/1.12 => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_254_order_Otrans,axiom,
% 1.83/1.12 ! [A: real_int,B: real_int,C2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ A @ B )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ B @ C2 )
% 1.83/1.12 => ( ord_less_eq_real_int @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_255_order_Otrans,axiom,
% 1.83/1.12 ! [A: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ A @ B )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ B @ C2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ A @ C2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_256_le__cases,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ~ ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_257_eq__refl,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( X2 = Y2 )
% 1.83/1.12 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_258_eq__refl,axiom,
% 1.83/1.12 ! [X2: real_int,Y2: real_int] :
% 1.83/1.12 ( ( X2 = Y2 )
% 1.83/1.12 => ( ord_less_eq_real_int @ X2 @ Y2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_259_eq__refl,axiom,
% 1.83/1.12 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
% 1.83/1.12 ( ( X2 = Y2 )
% 1.83/1.12 => ( ord_le461438217t_unit @ X2 @ Y2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_260_linear,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 | ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_261_antisym,axiom,
% 1.83/1.12 ! [X2: real,Y2: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 1.83/1.12 => ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_262_antisym,axiom,
% 1.83/1.12 ! [X2: real_int,Y2: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_less_eq_real_int @ Y2 @ X2 )
% 1.83/1.12 => ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_263_antisym,axiom,
% 1.83/1.12 ! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ X2 @ Y2 )
% 1.83/1.12 => ( ( ord_le461438217t_unit @ Y2 @ X2 )
% 1.83/1.12 => ( X2 = Y2 ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_264_eq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [X3: real,Y: real] :
% 1.83/1.12 ( ( ord_less_eq_real @ X3 @ Y )
% 1.83/1.12 & ( ord_less_eq_real @ Y @ X3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_265_eq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: real_int,Z: real_int] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [X3: real_int,Y: real_int] :
% 1.83/1.12 ( ( ord_less_eq_real_int @ X3 @ Y )
% 1.83/1.12 & ( ord_less_eq_real_int @ Y @ X3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(fact_266_eq__iff,axiom,
% 1.83/1.12 ( ( ^ [Y4: view_e774982825t_unit,Z: view_e774982825t_unit] : ( Y4 = Z ) )
% 1.83/1.12 = ( ^ [X3: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 1.83/1.12 ( ( ord_le461438217t_unit @ X3 @ Y )
% 1.83/1.12 & ( ord_le461438217t_unit @ Y @ X3 ) ) ) ) ).
% 1.83/1.12
% 1.83/1.12 thf(conj_0,conjecture,
% 1.83/1.12 ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
% 1.83/1.12 & ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) ) ) ).
% 1.83/1.12 ------------------------
% 2.11/1.15 % (9865)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/183Mi)
% 2.11/1.15 % (9866)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_9673 for (2999ds/4Mi)
% 2.11/1.15 % (9868)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/2Mi)
% 2.11/1.15 % (9868)Instruction limit reached!
% 2.11/1.15 % (9868)------------------------------
% 2.11/1.15 % (9868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.15 % (9868)Termination reason: Unknown
% 2.11/1.15 % (9868)Termination phase: shuffling
% 2.11/1.15
% 2.11/1.15 % (9868)Memory used [KB]: 1279
% 2.11/1.15 % (9868)Time elapsed: 0.002 s
% 2.11/1.15 % (9868)Instructions burned: 2 (million)
% 2.11/1.15 % (9868)------------------------------
% 2.11/1.15 % (9868)------------------------------
% 2.11/1.15 % (9869)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_9673 for (2999ds/2Mi)
% 2.11/1.15 % (9866)Instruction limit reached!
% 2.11/1.15 % (9866)------------------------------
% 2.11/1.15 % (9866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.15 % (9866)Termination reason: Unknown
% 2.11/1.15 % (9866)Termination phase: shuffling
% 2.11/1.15
% 2.11/1.15 % (9866)Memory used [KB]: 1407
% 2.11/1.15 % (9866)Time elapsed: 0.003 s
% 2.11/1.15 % (9866)Instructions burned: 6 (million)
% 2.11/1.15 % (9866)------------------------------
% 2.11/1.15 % (9866)------------------------------
% 2.11/1.15 % (9867)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_9673 for (2999ds/27Mi)
% 2.11/1.15 % (9869)Instruction limit reached!
% 2.11/1.15 % (9869)------------------------------
% 2.11/1.15 % (9869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.15 % (9869)Termination reason: Unknown
% 2.11/1.15 % (9869)Termination phase: shuffling
% 2.11/1.15
% 2.11/1.15 % (9869)Memory used [KB]: 1279
% 2.11/1.15 % (9869)Time elapsed: 0.003 s
% 2.11/1.15 % (9869)Instructions burned: 3 (million)
% 2.11/1.15 % (9869)------------------------------
% 2.11/1.15 % (9869)------------------------------
% 2.11/1.16 % (9871)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/18Mi)
% 2.11/1.16 % (9870)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_9673 for (2999ds/275Mi)
% 2.11/1.16 % (9872)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/3Mi)
% 2.11/1.16 % (9873)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_9673 for (2999ds/37Mi)
% 2.11/1.16 % (9872)Instruction limit reached!
% 2.11/1.16 % (9872)------------------------------
% 2.11/1.16 % (9872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.16 % (9872)Termination reason: Unknown
% 2.11/1.16 % (9872)Termination phase: shuffling
% 2.11/1.16
% 2.11/1.16 % (9872)Memory used [KB]: 1279
% 2.11/1.16 % (9872)Time elapsed: 0.002 s
% 2.11/1.16 % (9872)Instructions burned: 3 (million)
% 2.11/1.16 % (9872)------------------------------
% 2.11/1.16 % (9872)------------------------------
% 2.11/1.16 % (9867)Instruction limit reached!
% 2.11/1.16 % (9867)------------------------------
% 2.11/1.16 % (9867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.16 % (9867)Termination reason: Unknown
% 2.11/1.16 % (9867)Termination phase: Property scanning
% 2.11/1.16
% 2.11/1.16 % (9867)Memory used [KB]: 1663
% 2.11/1.16 % (9867)Time elapsed: 0.010 s
% 2.11/1.16 % (9867)Instructions burned: 27 (million)
% 2.11/1.16 % (9867)------------------------------
% 2.11/1.16 % (9867)------------------------------
% 2.11/1.16 % (9871)Instruction limit reached!
% 2.11/1.16 % (9871)------------------------------
% 2.11/1.16 % (9871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.16 % (9871)Termination reason: Unknown
% 2.11/1.16 % (9871)Termination phase: shuffling
% 2.11/1.16
% 2.11/1.16 % (9871)Memory used [KB]: 1535
% 2.11/1.16 % (9871)Time elapsed: 0.010 s
% 2.11/1.16 % (9871)Instructions burned: 19 (million)
% 2.11/1.16 % (9871)------------------------------
% 2.11/1.16 % (9871)------------------------------
% 2.11/1.17 % (9874)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_9673 for (2999ds/15Mi)
% 2.11/1.17 % (9875)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_9673 for (2999ds/3Mi)
% 2.11/1.17 % (9873)Instruction limit reached!
% 2.11/1.17 % (9873)------------------------------
% 2.11/1.17 % (9873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.17 % (9873)Termination reason: Unknown
% 2.11/1.17 % (9873)Termination phase: shuffling
% 2.11/1.17
% 2.11/1.17 % (9873)Memory used [KB]: 2046
% 2.11/1.17 % (9873)Time elapsed: 0.011 s
% 2.11/1.17 % (9873)Instructions burned: 38 (million)
% 2.11/1.17 % (9873)------------------------------
% 2.11/1.17 % (9873)------------------------------
% 2.11/1.17 % (9874)Instruction limit reached!
% 2.11/1.17 % (9874)------------------------------
% 2.11/1.17 % (9874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.17 % (9874)Termination reason: Unknown
% 2.11/1.17 % (9874)Termination phase: shuffling
% 2.11/1.17
% 2.11/1.17 % (9874)Memory used [KB]: 1535
% 2.11/1.17 % (9874)Time elapsed: 0.008 s
% 2.11/1.17 % (9874)Instructions burned: 15 (million)
% 2.11/1.17 % (9874)------------------------------
% 2.11/1.17 % (9874)------------------------------
% 2.11/1.17 % (9875)Instruction limit reached!
% 2.11/1.17 % (9875)------------------------------
% 2.11/1.17 % (9875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.17 % (9875)Termination reason: Unknown
% 2.11/1.17 % (9875)Termination phase: shuffling
% 2.11/1.17
% 2.11/1.17 % (9875)Memory used [KB]: 1279
% 2.11/1.17 % (9875)Time elapsed: 0.002 s
% 2.11/1.17 % (9875)Instructions burned: 3 (million)
% 2.11/1.17 % (9875)------------------------------
% 2.11/1.17 % (9875)------------------------------
% 2.11/1.17 % (9876)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_9673 for (2999ds/1041Mi)
% 2.11/1.18 % (9877)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/7Mi)
% 2.11/1.18 % (9878)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/16Mi)
% 2.11/1.18 % (9880)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_9673 for (2999ds/3Mi)
% 2.11/1.18 % (9879)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_9673 for (2999ds/3Mi)
% 2.11/1.18 % (9880)Instruction limit reached!
% 2.11/1.18 % (9880)------------------------------
% 2.11/1.18 % (9880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.18 % (9880)Termination reason: Unknown
% 2.11/1.18 % (9880)Termination phase: shuffling
% 2.11/1.18
% 2.11/1.18 % (9880)Memory used [KB]: 1279
% 2.11/1.18 % (9880)Time elapsed: 0.002 s
% 2.11/1.18 % (9880)Instructions burned: 3 (million)
% 2.11/1.18 % (9880)------------------------------
% 2.11/1.18 % (9880)------------------------------
% 2.11/1.18 % (9879)Instruction limit reached!
% 2.11/1.18 % (9879)------------------------------
% 2.11/1.18 % (9879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.18 % (9879)Termination reason: Unknown
% 2.11/1.18 % (9879)Termination phase: shuffling
% 2.11/1.18
% 2.11/1.18 % (9879)Memory used [KB]: 1279
% 2.11/1.18 % (9879)Time elapsed: 0.002 s
% 2.11/1.18 % (9879)Instructions burned: 3 (million)
% 2.11/1.18 % (9879)------------------------------
% 2.11/1.18 % (9879)------------------------------
% 2.11/1.19 % (9877)Instruction limit reached!
% 2.11/1.19 % (9877)------------------------------
% 2.11/1.19 % (9877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.19 % (9877)Termination reason: Unknown
% 2.11/1.19 % (9877)Termination phase: shuffling
% 2.11/1.19
% 2.11/1.19 % (9877)Memory used [KB]: 1407
% 2.11/1.19 % (9877)Time elapsed: 0.005 s
% 2.11/1.19 % (9877)Instructions burned: 7 (million)
% 2.11/1.19 % (9877)------------------------------
% 2.11/1.19 % (9877)------------------------------
% 2.11/1.19 % (9878)Instruction limit reached!
% 2.11/1.19 % (9878)------------------------------
% 2.11/1.19 % (9878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.19 % (9878)Termination reason: Unknown
% 2.11/1.19 % (9878)Termination phase: shuffling
% 2.11/1.19
% 2.11/1.19 % (9878)Memory used [KB]: 1535
% 2.11/1.19 % (9878)Time elapsed: 0.006 s
% 2.11/1.19 % (9878)Instructions burned: 16 (million)
% 2.11/1.19 % (9878)------------------------------
% 2.11/1.19 % (9878)------------------------------
% 2.11/1.19 % (9881)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/7Mi)
% 2.11/1.20 % (9881)Instruction limit reached!
% 2.11/1.20 % (9881)------------------------------
% 2.11/1.20 % (9881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.20 % (9881)Termination reason: Unknown
% 2.11/1.20 % (9881)Termination phase: shuffling
% 2.11/1.20
% 2.11/1.20 % (9881)Memory used [KB]: 1407
% 2.11/1.20 % (9881)Time elapsed: 0.004 s
% 2.11/1.20 % (9881)Instructions burned: 9 (million)
% 2.11/1.20 % (9881)------------------------------
% 2.11/1.20 % (9881)------------------------------
% 2.11/1.20 % (9884)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/18Mi)
% 2.11/1.20 % (9882)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/3Mi)
% 2.11/1.20 % (9882)Instruction limit reached!
% 2.11/1.20 % (9882)------------------------------
% 2.11/1.20 % (9882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.20 % (9882)Termination reason: Unknown
% 2.11/1.20 % (9882)Termination phase: shuffling
% 2.11/1.20
% 2.11/1.20 % (9882)Memory used [KB]: 1279
% 2.11/1.20 % (9882)Time elapsed: 0.002 s
% 2.11/1.20 % (9882)Instructions burned: 3 (million)
% 2.11/1.20 % (9882)------------------------------
% 2.11/1.20 % (9882)------------------------------
% 2.11/1.20 % (9884)Instruction limit reached!
% 2.11/1.20 % (9884)------------------------------
% 2.11/1.20 % (9884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.20 % (9884)Termination reason: Unknown
% 2.11/1.20 % (9884)Termination phase: shuffling
% 2.11/1.20
% 2.11/1.20 % (9884)Memory used [KB]: 1535
% 2.11/1.20 % (9884)Time elapsed: 0.007 s
% 2.11/1.20 % (9884)Instructions burned: 19 (million)
% 2.11/1.20 % (9884)------------------------------
% 2.11/1.20 % (9884)------------------------------
% 2.11/1.20 % (9883)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/4Mi)
% 2.11/1.20 % (9865)Instruction limit reached!
% 2.11/1.20 % (9865)------------------------------
% 2.11/1.20 % (9865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.20 % (9865)Termination reason: Unknown
% 2.11/1.20 % (9865)Termination phase: Saturation
% 2.11/1.20
% 2.11/1.20 % (9865)Memory used [KB]: 7036
% 2.11/1.20 % (9865)Time elapsed: 0.054 s
% 2.11/1.20 % (9865)Instructions burned: 185 (million)
% 2.11/1.20 % (9865)------------------------------
% 2.11/1.20 % (9865)------------------------------
% 2.11/1.21 % (9883)Instruction limit reached!
% 2.11/1.21 % (9883)------------------------------
% 2.11/1.21 % (9883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.21 % (9883)Termination reason: Unknown
% 2.11/1.21 % (9883)Termination phase: shuffling
% 2.11/1.21
% 2.11/1.21 % (9883)Memory used [KB]: 1279
% 2.11/1.21 % (9883)Time elapsed: 0.003 s
% 2.11/1.21 % (9883)Instructions burned: 4 (million)
% 2.11/1.21 % (9883)------------------------------
% 2.11/1.21 % (9883)------------------------------
% 2.11/1.21 % (9885)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/710Mi)
% 2.11/1.21 % (9886)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/6Mi)
% 2.11/1.21 % (9887)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/902Mi)
% 2.11/1.21 % (9886)Instruction limit reached!
% 2.11/1.21 % (9886)------------------------------
% 2.11/1.21 % (9886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.21 % (9886)Termination reason: Unknown
% 2.11/1.21 % (9886)Termination phase: shuffling
% 2.11/1.21
% 2.11/1.21 % (9886)Memory used [KB]: 1407
% 2.11/1.21 % (9886)Time elapsed: 0.005 s
% 2.11/1.21 % (9886)Instructions burned: 6 (million)
% 2.11/1.21 % (9886)------------------------------
% 2.11/1.21 % (9886)------------------------------
% 2.11/1.21 % (9888)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/21Mi)
% 2.11/1.22 % (9889)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/5Mi)
% 2.11/1.22 % (9889)Instruction limit reached!
% 2.11/1.22 % (9889)------------------------------
% 2.11/1.22 % (9889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.22 % (9889)Termination reason: Unknown
% 2.11/1.22 % (9889)Termination phase: shuffling
% 2.11/1.22
% 2.11/1.22 % (9889)Memory used [KB]: 1407
% 2.11/1.22 % (9889)Time elapsed: 0.004 s
% 2.11/1.22 % (9889)Instructions burned: 8 (million)
% 2.11/1.22 % (9889)------------------------------
% 2.11/1.22 % (9889)------------------------------
% 2.11/1.22 % (9890)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/6Mi)
% 2.11/1.22 % (9888)Instruction limit reached!
% 2.11/1.22 % (9888)------------------------------
% 2.11/1.22 % (9888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.22 % (9888)Termination reason: Unknown
% 2.11/1.22 % (9888)Termination phase: shuffling
% 2.11/1.22
% 2.11/1.22 % (9888)Memory used [KB]: 1535
% 2.11/1.22 % (9888)Time elapsed: 0.010 s
% 2.11/1.22 % (9888)Instructions burned: 22 (million)
% 2.11/1.22 % (9888)------------------------------
% 2.11/1.22 % (9888)------------------------------
% 2.11/1.22 % (9890)Instruction limit reached!
% 2.11/1.22 % (9890)------------------------------
% 2.11/1.22 % (9890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.22 % (9890)Termination reason: Unknown
% 2.11/1.22 % (9890)Termination phase: shuffling
% 2.11/1.22
% 2.11/1.22 % (9890)Memory used [KB]: 1407
% 2.11/1.22 % (9890)Time elapsed: 0.003 s
% 2.11/1.22 % (9890)Instructions burned: 7 (million)
% 2.11/1.22 % (9890)------------------------------
% 2.11/1.22 % (9890)------------------------------
% 2.11/1.23 % (9891)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/377Mi)
% 2.11/1.23 % (9893)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/19Mi)
% 2.11/1.24 % (9892)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/779Mi)
% 2.11/1.24 % (9893)Instruction limit reached!
% 2.11/1.24 % (9893)------------------------------
% 2.11/1.24 % (9893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.24 % (9893)Termination reason: Unknown
% 2.11/1.24 % (9893)Termination phase: shuffling
% 2.11/1.24
% 2.11/1.24 % (9893)Memory used [KB]: 1663
% 2.11/1.24 % (9893)Time elapsed: 0.007 s
% 2.11/1.24 % (9893)Instructions burned: 21 (million)
% 2.11/1.24 % (9893)------------------------------
% 2.11/1.24 % (9893)------------------------------
% 2.11/1.25 % (9894)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9673 for (2999ds/879Mi)
% 2.11/1.26 % (9870)Instruction limit reached!
% 2.11/1.26 % (9870)------------------------------
% 2.11/1.26 % (9870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.26 % (9870)Termination reason: Unknown
% 2.11/1.26 % (9870)Termination phase: Saturation
% 2.11/1.26
% 2.11/1.26 % (9870)Memory used [KB]: 7419
% 2.11/1.26 % (9870)Time elapsed: 0.107 s
% 2.11/1.26 % (9870)Instructions burned: 278 (million)
% 2.11/1.26 % (9870)------------------------------
% 2.11/1.26 % (9870)------------------------------
% 2.11/1.27 % (9900)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9673 for (2998ds/17Mi)
% 2.11/1.28 % (9900)Instruction limit reached!
% 2.11/1.28 % (9900)------------------------------
% 2.11/1.28 % (9900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.28 % (9900)Termination reason: Unknown
% 2.11/1.28 % (9900)Termination phase: shuffling
% 2.11/1.28
% 2.11/1.28 % (9900)Memory used [KB]: 1535
% 2.11/1.28 % (9900)Time elapsed: 0.007 s
% 2.11/1.28 % (9900)Instructions burned: 17 (million)
% 2.11/1.28 % (9900)------------------------------
% 2.11/1.28 % (9900)------------------------------
% 2.11/1.29 % (9901)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9673 for (2998ds/3Mi)
% 2.11/1.29 % (9901)Instruction limit reached!
% 2.11/1.29 % (9901)------------------------------
% 2.11/1.29 % (9901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.29 % (9901)Termination reason: Unknown
% 2.11/1.29 % (9901)Termination phase: shuffling
% 2.11/1.29
% 2.11/1.29 % (9901)Memory used [KB]: 1279
% 2.11/1.29 % (9901)Time elapsed: 0.002 s
% 2.11/1.29 % (9901)Instructions burned: 4 (million)
% 2.11/1.29 % (9901)------------------------------
% 2.11/1.29 % (9901)------------------------------
% 2.11/1.30 % (9902)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9673 for (2998ds/30Mi)
% 2.11/1.31 % (9902)Instruction limit reached!
% 2.11/1.31 % (9902)------------------------------
% 2.11/1.31 % (9902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.31 % (9902)Termination reason: Unknown
% 2.11/1.31 % (9902)Termination phase: Property scanning
% 2.11/1.31
% 2.11/1.31 % (9902)Memory used [KB]: 1663
% 2.11/1.31 % (9902)Time elapsed: 0.011 s
% 2.11/1.31 % (9902)Instructions burned: 33 (million)
% 2.11/1.31 % (9902)------------------------------
% 2.11/1.31 % (9902)------------------------------
% 2.11/1.32 % (9905)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9673 for (2998ds/127Mi)
% 2.11/1.34 % (9885)First to succeed.
% 2.11/1.34 % (9885)Refutation found. Thanks to Tanya!
% 2.11/1.34 % SZS status Theorem for DTF2THF_9673
% 2.11/1.34 % SZS output start Proof for DTF2THF_9673
% 2.11/1.34 thf(type_def_5, type, real: $tType).
% 2.11/1.34 thf(type_def_7, type, cars: $tType).
% 2.11/1.34 thf(type_def_8, type, traffic: $tType).
% 2.11/1.34 thf(type_def_9, type, view_e774982825t_unit: $tType).
% 2.11/1.34 thf(type_def_10, type, real_int: $tType).
% 2.11/1.34 thf(type_def_11, type, nat_int: $tType).
% 2.11/1.34 thf(type_def_12, type, produc427086159s_real: $tType).
% 2.11/1.34 thf(type_def_13, type, produc1622321602s_real: $tType).
% 2.11/1.34 thf(type_def_14, type, produc28608506s_real: $tType).
% 2.11/1.34 thf(type_def_15, type, produc1603581272s_real: $tType).
% 2.11/1.34 thf(type_def_16, type, produc458204144s_real: $tType).
% 2.11/1.34 thf(type_def_17, type, produc957004601l_real: $tType).
% 2.11/1.34 thf(func_def_0, type, produc458204144s_real: $tType).
% 2.11/1.34 thf(func_def_1, type, produc1603581272s_real: $tType).
% 2.11/1.34 thf(func_def_2, type, produc28608506s_real: $tType).
% 2.11/1.34 thf(func_def_3, type, produc1622321602s_real: $tType).
% 2.11/1.34 thf(func_def_4, type, produc427086159s_real: $tType).
% 2.11/1.34 thf(func_def_5, type, produc957004601l_real: $tType).
% 2.11/1.34 thf(func_def_6, type, view_e774982825t_unit: $tType).
% 2.11/1.34 thf(func_def_7, type, real_int: $tType).
% 2.11/1.34 thf(func_def_8, type, nat_int: $tType).
% 2.11/1.34 thf(func_def_9, type, traffic: $tType).
% 2.11/1.34 thf(func_def_10, type, real: $tType).
% 2.11/1.34 thf(func_def_11, type, cars: $tType).
% 2.11/1.34 thf(func_def_12, type, one_one_real: real).
% 2.11/1.34 thf(func_def_13, type, plus_plus_real: real > real > real).
% 2.11/1.34 thf(func_def_14, type, zero_zero_real: real).
% 2.11/1.34 thf(func_def_15, type, len: (cars > traffic > cars > real) > view_e774982825t_unit > traffic > cars > real_int).
% 2.11/1.34 thf(func_def_16, type, bot_bot_nat_int: nat_int).
% 2.11/1.34 thf(func_def_17, type, ord_less_real_int: real_int > real_int > $o).
% 2.11/1.34 thf(func_def_18, type, ord_less_real: real > real > $o).
% 2.11/1.34 thf(func_def_19, type, ord_less_eq_real_int: real_int > real_int > $o).
% 2.11/1.34 thf(func_def_20, type, ord_less_eq_real: real > real > $o).
% 2.11/1.34 thf(func_def_21, type, ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o).
% 2.11/1.34 thf(func_def_22, type, produc795767668s_real: (cars > real > real) > produc427086159s_real > produc1622321602s_real).
% 2.11/1.34 thf(func_def_23, type, produc1348924850s_real: (cars > nat_int) > produc1622321602s_real > produc28608506s_real).
% 2.11/1.34 thf(func_def_24, type, produc1230243850s_real: (cars > nat_int) > produc28608506s_real > produc1603581272s_real).
% 2.11/1.34 thf(func_def_25, type, produc1439932679s_real: (cars > real) > (cars > real) > produc427086159s_real).
% 2.11/1.34 thf(func_def_26, type, produc1876576040s_real: (cars > real) > produc1603581272s_real > produc458204144s_real).
% 2.11/1.34 thf(func_def_27, type, produc705216881l_real: real > real > produc957004601l_real).
% 2.11/1.34 thf(func_def_28, type, left: real_int > real).
% 2.11/1.34 thf(func_def_29, type, real_Abs_real_int: produc957004601l_real > real_int).
% 2.11/1.34 thf(func_def_30, type, real_length: real_int > real).
% 2.11/1.34 thf(func_def_31, type, real_shift: real_int > real > real_int).
% 2.11/1.34 thf(func_def_32, type, right: real_int > real).
% 2.11/1.34 thf(func_def_33, type, regular_regular: cars > traffic > cars > real).
% 2.11/1.34 thf(func_def_34, type, sensors: (cars > traffic > cars > real) > $o).
% 2.11/1.34 thf(func_def_35, type, space: (cars > traffic > cars > real) > traffic > view_e774982825t_unit > cars > real_int).
% 2.11/1.34 thf(func_def_36, type, abs_traffic: produc458204144s_real > traffic).
% 2.11/1.34 thf(func_def_37, type, physical_size: traffic > cars > real).
% 2.11/1.34 thf(func_def_38, type, pos: traffic > cars > real).
% 2.11/1.34 thf(func_def_39, type, ext_Product_unit: view_e774982825t_unit > real_int).
% 2.11/1.34 thf(func_def_40, type, hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o).
% 2.11/1.34 thf(func_def_41, type, own_Product_unit: view_e774982825t_unit > cars).
% 2.11/1.34 thf(func_def_42, type, c: cars).
% 2.11/1.34 thf(func_def_43, type, cl: cars > nat_int).
% 2.11/1.34 thf(func_def_44, type, d: cars).
% 2.11/1.34 thf(func_def_45, type, dy: cars > real > real).
% 2.11/1.34 thf(func_def_46, type, po: cars > real).
% 2.11/1.34 thf(func_def_47, type, ps: cars > real).
% 2.11/1.34 thf(func_def_48, type, re: cars > nat_int).
% 2.11/1.34 thf(func_def_49, type, sd: cars > real).
% 2.11/1.34 thf(func_def_50, type, ts: traffic).
% 2.11/1.34 thf(func_def_51, type, ts_rep: produc458204144s_real).
% 2.11/1.34 thf(func_def_52, type, v: view_e774982825t_unit).
% 2.11/1.34 thf(func_def_53, type, v2: view_e774982825t_unit).
% 2.11/1.34 thf(func_def_66, type, sK0: real > real).
% 2.11/1.34 thf(func_def_67, type, sK1: real > real).
% 2.11/1.34 thf(func_def_68, type, sK2: real > real > real).
% 2.11/1.34 thf(func_def_69, type, sK3: cars > real > real).
% 2.11/1.34 thf(func_def_71, type, ph5: !>[X0: $tType]:(X0)).
% 2.11/1.34 thf(f1793,plain,(
% 2.11/1.34 $false),
% 2.11/1.34 inference(avatar_sat_refutation,[status(thm)],[f897,f1750,f1792])).
% 2.11/1.34 thf(f1792,plain,(
% 2.11/1.34 spl4_1),
% 2.11/1.34 inference(avatar_contradiction_clause,[status(thm)],[f1791])).
% 2.11/1.34 thf(f1791,plain,(
% 2.11/1.34 $false | spl4_1),
% 2.11/1.34 inference(subsumption_resolution,[status(thm)],[f1790,f892])).
% 2.11/1.34 thf(f892,plain,(
% 2.11/1.34 ((ord_less_real @ (left @ (ext_Product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) != $true) | spl4_1),
% 2.11/1.34 inference(avatar_component_clause,[status(thm)],[f890])).
% 2.11/1.34 thf(f890,definition,(
% 2.11/1.34 spl4_1 <=> ((ord_less_real @ (left @ (ext_Product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) = $true)),
% 2.11/1.34 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 2.11/1.34 thf(f1790,plain,(
% 2.11/1.34 ((ord_less_real @ (left @ (ext_Product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) = $true)),
% 2.11/1.34 inference(subsumption_resolution,[status(thm)],[f1781,f828])).
% 2.11/1.34 thf(f828,plain,(
% 2.11/1.34 ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c))) = $true)),
% 2.11/1.34 inference(cnf_transformation,[status(thm)],[f466])).
% 2.11/1.34 thf(f466,plain,(
% 2.11/1.34 ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c))) = $true)),
% 2.11/1.34 inference(fool_elimination,[status(thm)],[f465])).
% 2.11/1.34 thf(f465,plain,(
% 2.11/1.34 (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c)))),
% 2.11/1.34 inference(rectify,[status(thm)],[f20])).
% 2.11/1.34 thf(f20,axiom,(
% 2.11/1.34 (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c)))),
% 2.11/1.34 file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_19_v_H__c)).
% 2.11/1.34 thf(f1781,plain,(
% 2.11/1.34 ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c))) != $true) | ((ord_less_real @ (left @ (ext_Product_unit @ v)) @ (right @ (space @ regular_regular @ ts @ v @ d))) = $true)),
% 2.11/1.34 inference(superposition,[status(thm)],[f806,f804])).
% 2.11/1.34 thf(f804,plain,(
% 2.11/1.34 ((len @ regular_regular @ v @ ts @ d) = (len @ regular_regular @ v @ ts @ c))),
% 2.11/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 2.11/1.34 thf(f12,axiom,(
% 2.11/1.34 ((len @ regular_regular @ v @ ts @ d) = (len @ regular_regular @ v @ ts @ c))),
% 2.11/1.34 file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_11_len__eq)).
% 2.11/1.34 thf(f806,plain,(
% 2.11/1.34 ( ! [X2 : traffic,X0 : view_e774982825t_unit,X1 : cars] : (($true != (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X0 @ X2 @ X1)))) | ((ord_less_real @ (left @ (ext_Product_unit @ X0)) @ (right @ (space @ regular_regular @ X2 @ X0 @ X1))) = $true)) )),
% 2.11/1.34 inference(cnf_transformation,[status(thm)],[f767])).
% 2.11/1.34 thf(f767,plain,(
% 2.11/1.34 ! [X0 : view_e774982825t_unit,X1 : cars,X2 : traffic] : (($true != (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X0 @ X2 @ X1)))) | (((ord_less_real @ (left @ (ext_Product_unit @ X0)) @ (right @ (space @ regular_regular @ X2 @ X0 @ X1))) = $true) & ((ord_less_real @ (left @ (space @ regular_regular @ X2 @ X0 @ X1)) @ (right @ (ext_Product_unit @ X0))) = $true)))),
% 2.11/1.34 inference(ennf_transformation,[status(thm)],[f504])).
% 2.11/1.34 thf(f504,plain,(
% 2.11/1.34 ! [X0 : view_e774982825t_unit,X1 : cars,X2 : traffic] : (($true = (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X0 @ X2 @ X1)))) => (((ord_less_real @ (left @ (ext_Product_unit @ X0)) @ (right @ (space @ regular_regular @ X2 @ X0 @ X1))) = $true) & ((ord_less_real @ (left @ (space @ regular_regular @ X2 @ X0 @ X1)) @ (right @ (ext_Product_unit @ X0))) = $true)))),
% 2.11/1.34 inference(fool_elimination,[status(thm)],[f503])).
% 2.11/1.34 thf(f503,plain,(
% 2.11/1.34 ! [X0 : view_e774982825t_unit,X1 : cars,X2 : traffic] : ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X0 @ X2 @ X1))) => ((ord_less_real @ (left @ (ext_Product_unit @ X0)) @ (right @ (space @ regular_regular @ X2 @ X0 @ X1))) & (ord_less_real @ (left @ (space @ regular_regular @ X2 @ X0 @ X1)) @ (right @ (ext_Product_unit @ X0)))))),
% 2.11/1.34 inference(rectify,[status(thm)],[f4])).
% 2.11/1.34 thf(f4,axiom,(
% 2.11/1.34 ! [X6 : view_e774982825t_unit,X5 : cars,X4 : traffic] : ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X6 @ X4 @ X5))) => ((ord_less_real @ (left @ (ext_Product_unit @ X6)) @ (right @ (space @ regular_regular @ X4 @ X6 @ X5))) & (ord_less_real @ (left @ (space @ regular_regular @ X4 @ X6 @ X5)) @ (right @ (ext_Product_unit @ X6)))))),
% 2.11/1.34 file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',fact_3_hmlsl_Olen__non__empty__inside)).
% 2.11/1.34 thf(f1750,plain,(
% 2.11/1.34 spl4_2),
% 2.11/1.34 inference(avatar_split_clause,[status(thm)],[f1749,f894])).
% 2.11/1.34 thf(f894,definition,(
% 2.11/1.34 spl4_2 <=> ((ord_less_real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext_Product_unit @ v))) = $true)),
% 2.11/1.34 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 2.11/1.34 thf(f1749,plain,(
% 2.11/1.34 ((ord_less_real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext_Product_unit @ v))) = $true)),
% 2.11/1.34 inference(subsumption_resolution,[status(thm)],[f1740,f828])).
% 2.11/1.34 thf(f1740,plain,(
% 2.11/1.34 ((ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ v @ ts @ c))) != $true) | ((ord_less_real @ (left @ (space @ regular_regular @ ts @ v @ d)) @ (right @ (ext_Product_unit @ v))) = $true)),
% 2.11/1.34 inference(superposition,[status(thm)],[f805,f804])).
% 2.11/1.34 thf(f805,plain,(
% 2.11/1.34 ( ! [X2 : traffic,X0 : view_e774982825t_unit,X1 : cars] : (($true != (ord_less_real @ zero_zero_real @ (real_length @ (len @ regular_regular @ X0 @ X2 @ X1)))) | ((ord_less_real @ (left @ (space @ regular_regular @ X2 @ X0 @ X1)) @ (right @ (ext_Product_unit @ X0))) = $true)) )),
% 2.11/1.34 inference(cnf_transformation,[status(thm)],[f767])).
% 2.11/1.34 thf(f897,plain,(
% 2.11/1.34 ~spl4_1 | ~spl4_2),
% 2.11/1.34 inference(avatar_split_clause,[status(thm)],[f837,f894,f890])).
% 2.11/1.34 thf(f837,plain,(
% 2.11/1.34 ((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)),
% 2.11/1.34 inference(cnf_transformation,[status(thm)],[f732])).
% 2.11/1.34 thf(f732,plain,(
% 2.11/1.34 ((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)),
% 2.11/1.34 inference(ennf_transformation,[status(thm)],[f616])).
% 2.11/1.34 thf(f616,plain,(
% 2.11/1.34 ~(((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))),
% 2.11/1.34 inference(fool_elimination,[status(thm)],[f615])).
% 2.11/1.34 thf(f615,plain,(
% 2.11/1.34 ~((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))))),
% 2.11/1.34 inference(rectify,[status(thm)],[f269])).
% 2.11/1.34 thf(f269,negated_conjecture,(
% 2.11/1.34 ~((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))))),
% 2.11/1.34 inference(negated_conjecture,[status(cth)],[f268])).
% 2.11/1.34 thf(f268,conjecture,(
% 2.11/1.34 (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)))),
% 2.11/1.34 file('/export/starexec/sandbox/tmp/tmp.r9zIBCLkHS/DTF2THF_9673.p',conj_0)).
% 2.11/1.34 % SZS output end Proof for DTF2THF_9673
% 2.11/1.34 % (9885)------------------------------
% 2.11/1.34 % (9885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.34 % (9885)Termination reason: Refutation
% 2.11/1.34
% 2.11/1.34 % (9885)Memory used [KB]: 7164
% 2.11/1.34 % (9885)Time elapsed: 0.131 s
% 2.11/1.34 % (9885)Instructions burned: 372 (million)
% 2.11/1.34 % (9885)------------------------------
% 2.11/1.34 % (9885)------------------------------
% 2.11/1.34 % (9864)Success in time 0.213 s
%------------------------------------------------------------------------------