TPTP Problem File: ITP168^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP168^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Safety_Regular problem prob_110__3347974_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : Safety_Regular/prob_110__3347974_1 [Des21]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 447 ( 124 unt; 89 typ; 0 def)
% Number of atoms : 1224 ( 307 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 3835 ( 77 ~; 27 |; 178 &;2950 @)
% ( 0 <=>; 603 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 347 ( 347 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 12 con; 0-5 aty)
% Number of variables : 1382 ( 134 ^;1140 !; 108 ?;1382 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:36:43.643
%------------------------------------------------------------------------------
% Could-be-implicit typings (12)
thf(ty_n_t__Views__Oview__Oview____ext_It__Views__Oview__Oview____ext_It__Product____Type__Ounit_J_J,type,
view_e665166499t_unit: $tType ).
thf(ty_n_t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
view_e774982825t_unit: $tType ).
thf(ty_n_t__Views__Oview__Oview____ext_It__RealInt__Oreal____int_J,type,
view_ext_real_int: $tType ).
thf(ty_n_t__Views__Oview__Oview____ext_It__NatInt__Onat____int_J,type,
view_ext_nat_int: $tType ).
thf(ty_n_t__Views__Oview__Oview____ext_It__Nat__Onat_J,type,
view_ext_nat: $tType ).
thf(ty_n_t__Product____Type__Ounit,type,
product_unit: $tType ).
thf(ty_n_t__RealInt__Oreal____int,type,
real_int: $tType ).
thf(ty_n_t__NatInt__Onat____int,type,
nat_int: $tType ).
thf(ty_n_t__Traffic__Otraffic,type,
traffic: $tType ).
thf(ty_n_t__Real__Oreal,type,
real: $tType ).
thf(ty_n_t__Cars__Ocars,type,
cars: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
% Explicit typings (77)
thf(sy_c_Fun_Ofun__upd_001t__Cars__Ocars_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
fun_up1431237090l_real: ( cars > real > real ) > cars > ( real > real ) > cars > real > real ).
thf(sy_c_Fun_Ofun__upd_001t__Cars__Ocars_001t__NatInt__Onat____int,type,
fun_upd_cars_nat_int: ( cars > nat_int ) > cars > nat_int > cars > nat_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
minus_minus_real: real > real > real ).
thf(sy_c_HOL_Odefault__class_Odefault_001t__Product____Type__Ounit,type,
defaul1399868459t_unit: product_unit ).
thf(sy_c_If_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
if_real_real: $o > ( real > real ) > ( real > real ) > real > real ).
thf(sy_c_If_001t__NatInt__Onat____int,type,
if_nat_int: $o > nat_int > nat_int > nat_int ).
thf(sy_c_Move_Otraffic_Omove,type,
move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(sy_c_NatInt_Onat__int_ON__Chop,type,
nat_N_Chop: nat_int > nat_int > nat_int > $o ).
thf(sy_c_NatInt_Onat__int_Ocard_H,type,
nat_card: nat_int > nat ).
thf(sy_c_NatInt_Onat__int_Oconsec,type,
nat_consec: nat_int > nat_int > $o ).
thf(sy_c_NatInt_Onat__int_Onot__in,type,
nat_not_in: nat > nat_int > $o ).
thf(sy_c_NatInt_Onat__int_Ounion,type,
nat_union: nat_int > nat_int > nat_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__NatInt__Onat____int,type,
bot_bot_nat_int: nat_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
bot_bot_nat: nat ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Ounit,type,
bot_bot_Product_unit: product_unit ).
thf(sy_c_Orderings_Oord__class_Oless_001t__NatInt__Onat____int,type,
ord_less_nat_int: nat_int > nat_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
ord_less_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__RealInt__Oreal____int,type,
ord_less_real_int: real_int > real_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Views__Oview__Oview____ext_It__NatInt__Onat____int_J,type,
ord_le893810930at_int: view_ext_nat_int > view_ext_nat_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Views__Oview__Oview____ext_It__Nat__Onat_J,type,
ord_le1522419062xt_nat: view_ext_nat > view_ext_nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
ord_le1993783549t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Views__Oview__Oview____ext_It__RealInt__Oreal____int_J,type,
ord_le147108278al_int: view_ext_real_int > view_ext_real_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Views__Oview__Oview____ext_It__Views__Oview__Oview____ext_It__Product____Type__Ounit_J_J,type,
ord_le750644047t_unit: view_e665166499t_unit > view_e665166499t_unit > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__NatInt__Onat____int,type,
ord_less_eq_nat_int: nat_int > nat_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Ounit,type,
ord_le1997193645t_unit: product_unit > product_unit > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__RealInt__Oreal____int,type,
ord_less_eq_real_int: real_int > real_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
ord_less_eq_real: real > real > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__NatInt__Onat____int_J,type,
ord_le1902160870at_int: view_ext_nat_int > view_ext_nat_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Nat__Onat_J,type,
ord_le1036425834xt_nat: view_ext_nat > view_ext_nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__RealInt__Oreal____int_J,type,
ord_le1863101098al_int: view_ext_real_int > view_ext_real_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Views__Oview__Oview____ext_It__Product____Type__Ounit_J_J,type,
ord_le63244867t_unit: view_e665166499t_unit > view_e665166499t_unit > $o ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_RealInt_Oreal__int_OR__Chop,type,
real_R_Chop: real_int > real_int > real_int > $o ).
thf(sy_c_RealInt_Oreal__int_Oshift,type,
real_shift: real_int > real > real_int ).
thf(sy_c_Traffic_Otraffic_Oabstract,type,
abstract: traffic > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Obraking__distance,type,
braking_distance: traffic > cars > real ).
thf(sy_c_Traffic_Otraffic_Ochange__dyn,type,
change_dyn: traffic > cars > ( real > real ) > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Oclm,type,
clm: traffic > cars > nat_int ).
thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
create_claim: traffic > cars > nat > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
create_reservation: traffic > cars > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Odyn,type,
dyn: traffic > cars > real > real ).
thf(sy_c_Traffic_Otraffic_Oevolve,type,
evolve: traffic > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
physical_size: traffic > cars > real ).
thf(sy_c_Traffic_Otraffic_Opos,type,
pos: traffic > cars > real ).
thf(sy_c_Traffic_Otraffic_Ores,type,
res: traffic > cars > nat_int ).
thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
withdraw_claim: traffic > cars > traffic > $o ).
thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
withdraw_reservation: traffic > cars > nat > traffic > $o ).
thf(sy_c_Views_Oview_Oext_001t__NatInt__Onat____int,type,
ext_nat_int: view_ext_nat_int > real_int ).
thf(sy_c_Views_Oview_Oext_001t__Nat__Onat,type,
ext_nat: view_ext_nat > real_int ).
thf(sy_c_Views_Oview_Oext_001t__Product____Type__Ounit,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(sy_c_Views_Oview_Oext_001t__RealInt__Oreal____int,type,
ext_real_int: view_ext_real_int > real_int ).
thf(sy_c_Views_Oview_Oext_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
ext_vi2102772532t_unit: view_e665166499t_unit > real_int ).
thf(sy_c_Views_Oview_Ohchop,type,
hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(sy_c_Views_Oview_Olan_001t__NatInt__Onat____int,type,
lan_nat_int: view_ext_nat_int > nat_int ).
thf(sy_c_Views_Oview_Olan_001t__Nat__Onat,type,
lan_nat: view_ext_nat > nat_int ).
thf(sy_c_Views_Oview_Olan_001t__Product____Type__Ounit,type,
lan_Product_unit: view_e774982825t_unit > nat_int ).
thf(sy_c_Views_Oview_Olan_001t__RealInt__Oreal____int,type,
lan_real_int: view_ext_real_int > nat_int ).
thf(sy_c_Views_Oview_Olan_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
lan_vi1543476748t_unit: view_e665166499t_unit > nat_int ).
thf(sy_c_Views_Oview_Omore_001t__NatInt__Onat____int,type,
more_nat_int: view_ext_nat_int > nat_int ).
thf(sy_c_Views_Oview_Omore_001t__Nat__Onat,type,
more_nat: view_ext_nat > nat ).
thf(sy_c_Views_Oview_Omore_001t__Product____Type__Ounit,type,
more_Product_unit: view_e774982825t_unit > product_unit ).
thf(sy_c_Views_Oview_Omore_001t__RealInt__Oreal____int,type,
more_real_int: view_ext_real_int > real_int ).
thf(sy_c_Views_Oview_Omore_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
more_v92543030t_unit: view_e665166499t_unit > view_e774982825t_unit ).
thf(sy_c_Views_Oview_Oown_001t__NatInt__Onat____int,type,
own_nat_int: view_ext_nat_int > cars ).
thf(sy_c_Views_Oview_Oown_001t__Nat__Onat,type,
own_nat: view_ext_nat > cars ).
thf(sy_c_Views_Oview_Oown_001t__Product____Type__Ounit,type,
own_Product_unit: view_e774982825t_unit > cars ).
thf(sy_c_Views_Oview_Oown_001t__RealInt__Oreal____int,type,
own_real_int: view_ext_real_int > cars ).
thf(sy_c_Views_Oview_Oown_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
own_vi676290681t_unit: view_e665166499t_unit > cars ).
thf(sy_c_Views_Oview_Oswitch,type,
switch: view_e774982825t_unit > cars > view_e774982825t_unit > $o ).
thf(sy_c_Views_Oview_Oview__ext_001t__Product____Type__Ounit,type,
view_e912666823t_unit: real_int > nat_int > cars > product_unit > view_e774982825t_unit ).
thf(sy_v_ts_H_H____,type,
ts: traffic ).
thf(sy_v_ts_H____,type,
ts2: traffic ).
thf(sy_v_ts_Ha____,type,
ts_a: traffic ).
thf(sy_v_ts____,type,
ts3: traffic ).
thf(sy_v_v____,type,
v: view_e774982825t_unit ).
% Relevant facts (352)
thf(fact_0_cr__res_Ohyps_I1_J,axiom,
abstract @ ts3 @ ts_a ).
% cr_res.hyps(1)
thf(fact_1_cr__res_Ohyps_I2_J,axiom,
? [C: cars] : ( create_reservation @ ts_a @ C @ ts ) ).
% cr_res.hyps(2)
thf(fact_2_local_Ohmlsl_Oglobally__4,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ! [Ts2: traffic] :
( ( abstract @ Ts @ Ts2 )
=> ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
=> ! [Ts3: traffic] :
( ( abstract @ Ts @ Ts3 )
=> ! [Ts_a: traffic] :
( ( abstract @ Ts3 @ Ts_a )
=> ( Phi @ Ts_a @ ( move @ Ts3 @ Ts_a @ ( move @ Ts @ Ts3 @ V ) ) ) ) ) ) ).
% local.hmlsl.globally_4
thf(fact_3_local_Ohmlsl_Oglobally__refl,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ! [Ts2: traffic] :
( ( abstract @ Ts @ Ts2 )
=> ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
=> ( Phi @ Ts @ V ) ) ).
% local.hmlsl.globally_refl
thf(fact_4_abs,axiom,
abstract @ ts3 @ ts2 ).
% abs
thf(fact_5__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% \<open>move ts ts' v = move ts' ts'' (move ts ts' v)\<close>
thf(fact_6_traffic_Omove__nothing,axiom,
! [Ts4: traffic,V2: view_e774982825t_unit] :
( ( move @ Ts4 @ Ts4 @ V2 )
= V2 ) ).
% traffic.move_nothing
thf(fact_7_traffic_Omove__def,axiom,
( move
= ( ^ [Ts5: traffic,Ts6: traffic,V3: view_e774982825t_unit] : ( view_e912666823t_unit @ ( real_shift @ ( ext_Product_unit @ V3 ) @ ( minus_minus_real @ ( pos @ Ts6 @ ( own_Product_unit @ V3 ) ) @ ( pos @ Ts5 @ ( own_Product_unit @ V3 ) ) ) ) @ ( lan_Product_unit @ V3 ) @ ( own_Product_unit @ V3 ) @ product_Unity ) ) ) ).
% traffic.move_def
thf(fact_8_traffic_Omove__stability__res,axiom,
! [Ts4: traffic,C2: cars,Ts7: traffic,V2: view_e774982825t_unit] :
( ( create_reservation @ Ts4 @ C2 @ Ts7 )
=> ( ( move @ Ts4 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_res
thf(fact_9_traffic_Omove__keeps__owner,axiom,
! [Ts4: traffic,Ts7: traffic] :
( own_Product_unit
= ( ^ [V3: view_e774982825t_unit] : ( own_Product_unit @ ( move @ Ts4 @ Ts7 @ V3 ) ) ) ) ).
% traffic.move_keeps_owner
thf(fact_10_traffic_Omove__trans,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic,V2: view_e774982825t_unit] :
( ( ( abstract @ Ts4 @ Ts7 )
& ( abstract @ Ts7 @ Ts8 ) )
=> ( ( move @ Ts7 @ Ts8 @ ( move @ Ts4 @ Ts7 @ V2 ) )
= ( move @ Ts4 @ Ts8 @ V2 ) ) ) ).
% traffic.move_trans
thf(fact_11_traffic_Omove__keeps__lanes,axiom,
! [Ts4: traffic,Ts7: traffic] :
( lan_Product_unit
= ( ^ [V3: view_e774982825t_unit] : ( lan_Product_unit @ ( move @ Ts4 @ Ts7 @ V3 ) ) ) ) ).
% traffic.move_keeps_lanes
thf(fact_12_traffic_Omove__stability__clm,axiom,
! [Ts4: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_e774982825t_unit] :
( ( create_claim @ Ts4 @ C2 @ N @ Ts7 )
=> ( ( move @ Ts4 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_clm
thf(fact_13_traffic_Omove__stability__wdc,axiom,
! [Ts4: traffic,C2: cars,Ts7: traffic,V2: view_e774982825t_unit] :
( ( withdraw_claim @ Ts4 @ C2 @ Ts7 )
=> ( ( move @ Ts4 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_wdc
thf(fact_14_traffic_Omove__stability__wdr,axiom,
! [Ts4: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_e774982825t_unit] :
( ( withdraw_reservation @ Ts4 @ C2 @ N @ Ts7 )
=> ( ( move @ Ts4 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_wdr
thf(fact_15_local_Ohmlsl_Ohchop__assoc,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ? [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( hchop @ U @ X @ Y )
& ( Psi @ Ts @ X )
& ( Chi @ Ts @ Y ) ) ) )
= ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ? [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( hchop @ W @ X @ Y )
& ( Phi @ Ts @ X )
& ( Psi @ Ts @ Y ) )
& ( Chi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_assoc
thf(fact_16_local_Ohmlsl_Ohchop__disj__distr1,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( ( Psi @ Ts @ U )
| ( Chi @ Ts @ U ) ) ) )
= ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( Psi @ Ts @ U ) )
| ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( Chi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_disj_distr1
thf(fact_17_local_Ohmlsl_Ohchop__disj__distr2,axiom,
! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( ( Psi @ Ts @ W )
| ( Chi @ Ts @ W ) )
& ( Phi @ Ts @ U ) ) )
= ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Psi @ Ts @ W )
& ( Phi @ Ts @ U ) )
| ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( Chi @ Ts @ W )
& ( Phi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_disj_distr2
thf(fact_18_local_Ohmlsl_Ohchop__weaken2,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V @ Va @ U2 )
& ( Phi @ Ts @ U2 ) ) ) ).
% local.hmlsl.hchop_weaken2
thf(fact_19_local_Ohmlsl_Ohchop__weaken1,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_e774982825t_unit] :
( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va @ X_1 )
& ( Phi @ Ts @ Va ) ) ) ).
% local.hmlsl.hchop_weaken1
thf(fact_20_local_Ohmlsl_Ohchop__weaken,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V @ Va @ U2 )
& ? [Vb: view_e774982825t_unit] :
( ? [X_1: view_e774982825t_unit] : ( hchop @ U2 @ Vb @ X_1 )
& ( Phi @ Ts @ Vb ) ) ) ) ).
% local.hmlsl.hchop_weaken
thf(fact_21_local_Ohmlsl_Ohchop__neg2,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ~ ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V @ Va @ U2 )
& ( Phi @ Ts @ U2 ) )
=> ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V @ Va @ U2 )
& ~ ( Phi @ Ts @ U2 ) ) ) ).
% local.hmlsl.hchop_neg2
thf(fact_22_local_Ohmlsl_Ohchop__neg1,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ~ ? [Va: view_e774982825t_unit] :
( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va @ X_1 )
& ( Phi @ Ts @ Va ) )
=> ? [Va: view_e774982825t_unit] :
( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va @ X_1 )
& ~ ( Phi @ Ts @ Va ) ) ) ).
% local.hmlsl.hchop_neg1
thf(fact_23_ext__inject,axiom,
! [Ext: real_int,Lan: nat_int,Own: cars,More: product_unit,Ext2: real_int,Lan2: nat_int,Own2: cars,More2: product_unit] :
( ( ( view_e912666823t_unit @ Ext @ Lan @ Own @ More )
= ( view_e912666823t_unit @ Ext2 @ Lan2 @ Own2 @ More2 ) )
= ( ( Ext = Ext2 )
& ( Lan = Lan2 )
& ( Own = Own2 )
& ( More = More2 ) ) ) ).
% ext_inject
thf(fact_24_cases,axiom,
! [R: view_e774982825t_unit] :
~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars] :
( R
!= ( view_e912666823t_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) ) ).
% cases
thf(fact_25_induct,axiom,
! [P: view_e774982825t_unit > $o,R: view_e774982825t_unit] :
( ! [Ext3: real_int,Lan3: nat_int,Own3: cars] : ( P @ ( view_e912666823t_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) )
=> ( P @ R ) ) ).
% induct
thf(fact_26_traffic_Ocr__clm,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts4 @ Ts7 )
=> ( ? [C3: cars,N2: nat] : ( create_claim @ Ts7 @ C3 @ N2 @ Ts8 )
=> ( abstract @ Ts4 @ Ts8 ) ) ) ).
% traffic.cr_clm
thf(fact_27_traffic_Owd__clm,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts4 @ Ts7 )
=> ( ? [C3: cars] : ( withdraw_claim @ Ts7 @ C3 @ Ts8 )
=> ( abstract @ Ts4 @ Ts8 ) ) ) ).
% traffic.wd_clm
thf(fact_28_traffic_Owd__res,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts4 @ Ts7 )
=> ( ? [C3: cars,N2: nat] : ( withdraw_reservation @ Ts7 @ C3 @ N2 @ Ts8 )
=> ( abstract @ Ts4 @ Ts8 ) ) ) ).
% traffic.wd_res
thf(fact_29_traffic_Ocr__res,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts4 @ Ts7 )
=> ( ? [C3: cars] : ( create_reservation @ Ts7 @ C3 @ Ts8 )
=> ( abstract @ Ts4 @ Ts8 ) ) ) ).
% traffic.cr_res
thf(fact_30_select__convs_I3_J,axiom,
! [Ext: real_int,Lan: nat_int,Own: cars,More: product_unit] :
( ( own_Product_unit @ ( view_e912666823t_unit @ Ext @ Lan @ Own @ More ) )
= Own ) ).
% select_convs(3)
thf(fact_31_select__convs_I2_J,axiom,
! [Ext: real_int,Lan: nat_int,Own: cars,More: product_unit] :
( ( lan_Product_unit @ ( view_e912666823t_unit @ Ext @ Lan @ Own @ More ) )
= Lan ) ).
% select_convs(2)
thf(fact_32_view_Ohorizontal__chop__empty__right,axiom,
! [V: view_e774982825t_unit] :
? [X_1: view_e774982825t_unit] : ( hchop @ V @ V @ X_1 ) ).
% view.horizontal_chop_empty_right
thf(fact_33_view_Ohorizontal__chop__empty__left,axiom,
! [V: view_e774982825t_unit] :
? [U2: view_e774982825t_unit] : ( hchop @ V @ U2 @ V ) ).
% view.horizontal_chop_empty_left
thf(fact_34_view_Ohorizontal__chop__assoc2,axiom,
! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( hchop @ V1 @ V32 @ V4 ) )
=> ? [V5: view_e774982825t_unit] :
( ( hchop @ V2 @ V32 @ V5 )
& ( hchop @ V5 @ V4 @ V22 ) ) ) ).
% view.horizontal_chop_assoc2
thf(fact_35_view_Ohorizontal__chop__assoc1,axiom,
! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( hchop @ V22 @ V32 @ V4 ) )
=> ? [V5: view_e774982825t_unit] :
( ( hchop @ V2 @ V5 @ V4 )
& ( hchop @ V5 @ V1 @ V32 ) ) ) ).
% view.horizontal_chop_assoc1
thf(fact_36_view_Ohorizontal__chop1,axiom,
! [V2: view_e774982825t_unit] :
? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% view.horizontal_chop1
thf(fact_37_traffic_Oabstract_Orefl,axiom,
! [Ts4: traffic] : ( abstract @ Ts4 @ Ts4 ) ).
% traffic.abstract.refl
thf(fact_38_traffic_Oabs__trans,axiom,
! [Ts1: traffic,Ts22: traffic,Ts0: traffic] :
( ( abstract @ Ts1 @ Ts22 )
=> ( ( abstract @ Ts0 @ Ts1 )
=> ( abstract @ Ts0 @ Ts22 ) ) ) ).
% traffic.abs_trans
thf(fact_39_induct__scheme,axiom,
! [P: view_e774982825t_unit > $o,R: view_e774982825t_unit] :
( ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: product_unit] : ( P @ ( view_e912666823t_unit @ Ext3 @ Lan3 @ Own3 @ More3 ) )
=> ( P @ R ) ) ).
% induct_scheme
thf(fact_40_cases__scheme,axiom,
! [R: view_e774982825t_unit] :
~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: product_unit] :
( R
!= ( view_e912666823t_unit @ Ext3 @ Lan3 @ Own3 @ More3 ) ) ).
% cases_scheme
thf(fact_41_traffic_Oalways__create__res,axiom,
! [C2: cars,Ts: traffic] :
? [X_1: traffic] : ( create_reservation @ Ts @ C2 @ X_1 ) ).
% traffic.always_create_res
thf(fact_42_view_Ohorizontal__chop__own__trans,axiom,
! [V2: view_e774982825t_unit,U3: view_e774982825t_unit,W2: view_e774982825t_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ( own_Product_unit @ U3 )
= ( own_Product_unit @ W2 ) ) ) ).
% view.horizontal_chop_own_trans
thf(fact_43_select__convs_I1_J,axiom,
! [Ext: real_int,Lan: nat_int,Own: cars,More: product_unit] :
( ( ext_Product_unit @ ( view_e912666823t_unit @ Ext @ Lan @ Own @ More ) )
= Ext ) ).
% select_convs(1)
thf(fact_44_traffic_Ocreate__reservation__def,axiom,
( create_reservation
= ( ^ [Ts5: traffic,C4: cars,Ts6: traffic] :
( ( ( pos @ Ts6 )
= ( pos @ Ts5 ) )
& ( ( res @ Ts6 )
= ( fun_upd_cars_nat_int @ ( res @ Ts5 ) @ C4 @ ( nat_union @ ( res @ Ts5 @ C4 ) @ ( clm @ Ts5 @ C4 ) ) ) )
& ( ( dyn @ Ts6 )
= ( dyn @ Ts5 ) )
& ( ( clm @ Ts6 )
= ( fun_upd_cars_nat_int @ ( clm @ Ts5 ) @ C4 @ bot_bot_nat_int ) )
& ( ( physical_size @ Ts6 )
= ( physical_size @ Ts5 ) )
& ( ( braking_distance @ Ts6 )
= ( braking_distance @ Ts5 ) ) ) ) ) ).
% traffic.create_reservation_def
thf(fact_45_traffic_Oabstract_Oinducts,axiom,
! [Ts4: traffic,X2: traffic,P: traffic > $o] :
( ( abstract @ Ts4 @ X2 )
=> ( ( P @ Ts4 )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ( evolve @ Ts2 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars] : ( create_reservation @ Ts2 @ C @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( P @ X2 ) ) ) ) ) ) ) ) ).
% traffic.abstract.inducts
thf(fact_46_traffic_Oabstract_Osimps,axiom,
( abstract
= ( ^ [Ts5: traffic,A: traffic] :
( ( A = Ts5 )
| ? [Ts6: traffic,Ts10: traffic] :
( ( A = Ts10 )
& ( abstract @ Ts5 @ Ts6 )
& ( evolve @ Ts6 @ Ts10 ) )
| ? [Ts6: traffic,Ts10: traffic] :
( ( A = Ts10 )
& ( abstract @ Ts5 @ Ts6 )
& ? [C4: cars,N4: nat] : ( create_claim @ Ts6 @ C4 @ N4 @ Ts10 ) )
| ? [Ts6: traffic,Ts10: traffic] :
( ( A = Ts10 )
& ( abstract @ Ts5 @ Ts6 )
& ? [C4: cars] : ( withdraw_claim @ Ts6 @ C4 @ Ts10 ) )
| ? [Ts6: traffic,Ts10: traffic] :
( ( A = Ts10 )
& ( abstract @ Ts5 @ Ts6 )
& ? [C4: cars] : ( create_reservation @ Ts6 @ C4 @ Ts10 ) )
| ? [Ts6: traffic,Ts10: traffic] :
( ( A = Ts10 )
& ( abstract @ Ts5 @ Ts6 )
& ? [C4: cars,N4: nat] : ( withdraw_reservation @ Ts6 @ C4 @ N4 @ Ts10 ) ) ) ) ) ).
% traffic.abstract.simps
thf(fact_47_traffic_Oabstract_Ocases,axiom,
! [Ts4: traffic,A2: traffic] :
( ( abstract @ Ts4 @ A2 )
=> ( ( A2 != Ts4 )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ~ ( evolve @ Ts2 @ A2 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ~ ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ A2 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ~ ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ A2 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ~ ? [C: cars] : ( create_reservation @ Ts2 @ C @ A2 ) )
=> ~ ! [Ts2: traffic] :
( ( abstract @ Ts4 @ Ts2 )
=> ~ ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ A2 ) ) ) ) ) ) ) ) ).
% traffic.abstract.cases
thf(fact_48_surjective,axiom,
! [R: view_e774982825t_unit] :
( R
= ( view_e912666823t_unit @ ( ext_Product_unit @ R ) @ ( lan_Product_unit @ R ) @ ( own_Product_unit @ R ) @ ( more_Product_unit @ R ) ) ) ).
% surjective
thf(fact_49_traffic_Owithdraw__clm__eq__res,axiom,
! [Ts4: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( withdraw_claim @ Ts4 @ D @ Ts7 )
=> ( ( res @ Ts4 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.withdraw_clm_eq_res
thf(fact_50_traffic_Ocreate__clm__eq__res,axiom,
! [Ts4: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
( ( create_claim @ Ts4 @ D @ N @ Ts7 )
=> ( ( res @ Ts4 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_clm_eq_res
thf(fact_51_traffic_Ocreate__res__subseteq1__neq,axiom,
! [Ts4: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( ( create_reservation @ Ts4 @ D @ Ts7 )
& ( D != C2 ) )
=> ( ( res @ Ts4 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq1_neq
thf(fact_52_traffic_Ocreate__res__subseteq2__neq,axiom,
! [Ts4: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( ( create_reservation @ Ts4 @ D @ Ts7 )
& ( D != C2 ) )
=> ( ( clm @ Ts4 @ C2 )
= ( clm @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq2_neq
thf(fact_53_traffic_Oevolve__trans,axiom,
! [Ts0: traffic,Ts1: traffic,Ts22: traffic] :
( ( evolve @ Ts0 @ Ts1 )
=> ( ( evolve @ Ts1 @ Ts22 )
=> ( evolve @ Ts0 @ Ts22 ) ) ) ).
% traffic.evolve_trans
thf(fact_54_traffic_Oevolve_Orefl,axiom,
! [Ts4: traffic] : ( evolve @ Ts4 @ Ts4 ) ).
% traffic.evolve.refl
thf(fact_55_traffic_Owithdraw__claim__def,axiom,
( withdraw_claim
= ( ^ [Ts5: traffic,C4: cars,Ts6: traffic] :
( ( ( pos @ Ts6 )
= ( pos @ Ts5 ) )
& ( ( res @ Ts6 )
= ( res @ Ts5 ) )
& ( ( dyn @ Ts6 )
= ( dyn @ Ts5 ) )
& ( ( physical_size @ Ts6 )
= ( physical_size @ Ts5 ) )
& ( ( braking_distance @ Ts6 )
= ( braking_distance @ Ts5 ) )
& ( ( clm @ Ts6 )
= ( fun_upd_cars_nat_int @ ( clm @ Ts5 ) @ C4 @ bot_bot_nat_int ) ) ) ) ) ).
% traffic.withdraw_claim_def
thf(fact_56_traffic_Oevolve,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts4 @ Ts7 )
=> ( ( evolve @ Ts7 @ Ts8 )
=> ( abstract @ Ts4 @ Ts8 ) ) ) ).
% traffic.evolve
thf(fact_57_select__convs_I4_J,axiom,
! [Ext: real_int,Lan: nat_int,Own: cars,More: product_unit] :
( ( more_Product_unit @ ( view_e912666823t_unit @ Ext @ Lan @ Own @ More ) )
= More ) ).
% select_convs(4)
thf(fact_58_equality,axiom,
! [R: view_e774982825t_unit,R2: view_e774982825t_unit] :
( ( ( ext_Product_unit @ R )
= ( ext_Product_unit @ R2 ) )
=> ( ( ( lan_Product_unit @ R )
= ( lan_Product_unit @ R2 ) )
=> ( ( ( own_Product_unit @ R )
= ( own_Product_unit @ R2 ) )
=> ( ( ( more_Product_unit @ R )
= ( more_Product_unit @ R2 ) )
=> ( R = R2 ) ) ) ) ) ).
% equality
thf(fact_59_fun__upd__upd,axiom,
! [F: cars > nat_int,X2: cars,Y2: nat_int,Z: nat_int] :
( ( fun_upd_cars_nat_int @ ( fun_upd_cars_nat_int @ F @ X2 @ Y2 ) @ X2 @ Z )
= ( fun_upd_cars_nat_int @ F @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_60_fun__upd__upd,axiom,
! [F: cars > real > real,X2: cars,Y2: real > real,Z: real > real] :
( ( fun_up1431237090l_real @ ( fun_up1431237090l_real @ F @ X2 @ Y2 ) @ X2 @ Z )
= ( fun_up1431237090l_real @ F @ X2 @ Z ) ) ).
% fun_upd_upd
thf(fact_61_fun__upd__triv,axiom,
! [F: cars > nat_int,X2: cars] :
( ( fun_upd_cars_nat_int @ F @ X2 @ ( F @ X2 ) )
= F ) ).
% fun_upd_triv
thf(fact_62_fun__upd__triv,axiom,
! [F: cars > real > real,X2: cars] :
( ( fun_up1431237090l_real @ F @ X2 @ ( F @ X2 ) )
= F ) ).
% fun_upd_triv
thf(fact_63_fun__upd__apply,axiom,
( fun_upd_cars_nat_int
= ( ^ [F2: cars > nat_int,X: cars,Y: nat_int,Z2: cars] : ( if_nat_int @ ( Z2 = X ) @ Y @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_64_fun__upd__apply,axiom,
( fun_up1431237090l_real
= ( ^ [F2: cars > real > real,X: cars,Y: real > real,Z2: cars] : ( if_real_real @ ( Z2 = X ) @ Y @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_65_un__empty__absorb1,axiom,
! [I: nat_int] :
( ( nat_union @ I @ bot_bot_nat_int )
= I ) ).
% un_empty_absorb1
thf(fact_66_un__empty__absorb2,axiom,
! [I: nat_int] :
( ( nat_union @ bot_bot_nat_int @ I )
= I ) ).
% un_empty_absorb2
thf(fact_67_view_Ohchop__def,axiom,
( hchop
= ( ^ [V3: view_e774982825t_unit,U: view_e774982825t_unit,W: view_e774982825t_unit] :
( ( real_R_Chop @ ( ext_Product_unit @ V3 ) @ ( ext_Product_unit @ U ) @ ( ext_Product_unit @ W ) )
& ( ( lan_Product_unit @ V3 )
= ( lan_Product_unit @ U ) )
& ( ( lan_Product_unit @ V3 )
= ( lan_Product_unit @ W ) )
& ( ( own_Product_unit @ V3 )
= ( own_Product_unit @ U ) )
& ( ( own_Product_unit @ V3 )
= ( own_Product_unit @ W ) )
& ( ( more_Product_unit @ V3 )
= ( more_Product_unit @ W ) )
& ( ( more_Product_unit @ V3 )
= ( more_Product_unit @ U ) ) ) ) ) ).
% view.hchop_def
thf(fact_68_fun__upd__idem__iff,axiom,
! [F: cars > nat_int,X2: cars,Y2: nat_int] :
( ( ( fun_upd_cars_nat_int @ F @ X2 @ Y2 )
= F )
= ( ( F @ X2 )
= Y2 ) ) ).
% fun_upd_idem_iff
thf(fact_69_fun__upd__idem__iff,axiom,
! [F: cars > real > real,X2: cars,Y2: real > real] :
( ( ( fun_up1431237090l_real @ F @ X2 @ Y2 )
= F )
= ( ( F @ X2 )
= Y2 ) ) ).
% fun_upd_idem_iff
thf(fact_70_fun__upd__twist,axiom,
! [A2: cars,C2: cars,M: cars > nat_int,B: nat_int,D: nat_int] :
( ( A2 != C2 )
=> ( ( fun_upd_cars_nat_int @ ( fun_upd_cars_nat_int @ M @ A2 @ B ) @ C2 @ D )
= ( fun_upd_cars_nat_int @ ( fun_upd_cars_nat_int @ M @ C2 @ D ) @ A2 @ B ) ) ) ).
% fun_upd_twist
thf(fact_71_fun__upd__twist,axiom,
! [A2: cars,C2: cars,M: cars > real > real,B: real > real,D: real > real] :
( ( A2 != C2 )
=> ( ( fun_up1431237090l_real @ ( fun_up1431237090l_real @ M @ A2 @ B ) @ C2 @ D )
= ( fun_up1431237090l_real @ ( fun_up1431237090l_real @ M @ C2 @ D ) @ A2 @ B ) ) ) ).
% fun_upd_twist
thf(fact_72_fun__upd__other,axiom,
! [Z: cars,X2: cars,F: cars > nat_int,Y2: nat_int] :
( ( Z != X2 )
=> ( ( fun_upd_cars_nat_int @ F @ X2 @ Y2 @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_73_fun__upd__other,axiom,
! [Z: cars,X2: cars,F: cars > real > real,Y2: real > real] :
( ( Z != X2 )
=> ( ( fun_up1431237090l_real @ F @ X2 @ Y2 @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_74_fun__upd__same,axiom,
! [F: cars > nat_int,X2: cars,Y2: nat_int] :
( ( fun_upd_cars_nat_int @ F @ X2 @ Y2 @ X2 )
= Y2 ) ).
% fun_upd_same
thf(fact_75_fun__upd__same,axiom,
! [F: cars > real > real,X2: cars,Y2: real > real] :
( ( fun_up1431237090l_real @ F @ X2 @ Y2 @ X2 )
= Y2 ) ).
% fun_upd_same
thf(fact_76_fun__upd__idem,axiom,
! [F: cars > nat_int,X2: cars,Y2: nat_int] :
( ( ( F @ X2 )
= Y2 )
=> ( ( fun_upd_cars_nat_int @ F @ X2 @ Y2 )
= F ) ) ).
% fun_upd_idem
thf(fact_77_fun__upd__idem,axiom,
! [F: cars > real > real,X2: cars,Y2: real > real] :
( ( ( F @ X2 )
= Y2 )
=> ( ( fun_up1431237090l_real @ F @ X2 @ Y2 )
= F ) ) ).
% fun_upd_idem
thf(fact_78_fun__upd__eqD,axiom,
! [F: cars > nat_int,X2: cars,Y2: nat_int,G: cars > nat_int,Z: nat_int] :
( ( ( fun_upd_cars_nat_int @ F @ X2 @ Y2 )
= ( fun_upd_cars_nat_int @ G @ X2 @ Z ) )
=> ( Y2 = Z ) ) ).
% fun_upd_eqD
thf(fact_79_fun__upd__eqD,axiom,
! [F: cars > real > real,X2: cars,Y2: real > real,G: cars > real > real,Z: real > real] :
( ( ( fun_up1431237090l_real @ F @ X2 @ Y2 )
= ( fun_up1431237090l_real @ G @ X2 @ Z ) )
=> ( Y2 = Z ) ) ).
% fun_upd_eqD
thf(fact_80_fun__upd__def,axiom,
( fun_upd_cars_nat_int
= ( ^ [F2: cars > nat_int,A: cars,B2: nat_int,X: cars] : ( if_nat_int @ ( X = A ) @ B2 @ ( F2 @ X ) ) ) ) ).
% fun_upd_def
thf(fact_81_fun__upd__def,axiom,
( fun_up1431237090l_real
= ( ^ [F2: cars > real > real,A: cars,B2: real > real,X: cars] : ( if_real_real @ ( X = A ) @ B2 @ ( F2 @ X ) ) ) ) ).
% fun_upd_def
thf(fact_82_traffic_Ochange__dyn__def,axiom,
( change_dyn
= ( ^ [Ts5: traffic,C4: cars,F2: real > real,Ts6: traffic] :
( ( ( pos @ Ts6 )
= ( pos @ Ts5 ) )
& ( ( res @ Ts6 )
= ( res @ Ts5 ) )
& ( ( clm @ Ts6 )
= ( clm @ Ts5 ) )
& ( ( dyn @ Ts6 )
= ( fun_up1431237090l_real @ ( dyn @ Ts5 ) @ C4 @ F2 ) )
& ( ( physical_size @ Ts6 )
= ( physical_size @ Ts5 ) ) ) ) ) ).
% traffic.change_dyn_def
thf(fact_83_local_Ohmlsl_Owidth__hchop__stable,axiom,
! [X2: nat,Ts: traffic,V: view_e774982825t_unit] :
( ( ( nat_card @ ( lan_Product_unit @ V ) )
= X2 )
= ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ( ( nat_card @ ( lan_Product_unit @ W ) )
= X2 )
& ( ( nat_card @ ( lan_Product_unit @ U ) )
= X2 ) ) ) ) ).
% local.hmlsl.width_hchop_stable
thf(fact_84_chop__singleton__right,axiom,
! [R3: real_int] :
? [X_1: real_int] : ( real_R_Chop @ R3 @ R3 @ X_1 ) ).
% chop_singleton_right
thf(fact_85_real__int__class_Ochop__always__possible,axiom,
! [R3: real_int] :
? [S: real_int,X_1: real_int] : ( real_R_Chop @ R3 @ S @ X_1 ) ).
% real_int_class.chop_always_possible
thf(fact_86_chop__singleton__left,axiom,
! [R3: real_int] :
? [S: real_int] : ( real_R_Chop @ R3 @ S @ R3 ) ).
% chop_singleton_left
thf(fact_87_view_Oswitch__def,axiom,
( switch
= ( ^ [V3: view_e774982825t_unit,C4: cars,W: view_e774982825t_unit] :
( ( ( ext_Product_unit @ V3 )
= ( ext_Product_unit @ W ) )
& ( ( lan_Product_unit @ V3 )
= ( lan_Product_unit @ W ) )
& ( ( own_Product_unit @ W )
= C4 )
& ( ( more_Product_unit @ V3 )
= ( more_Product_unit @ W ) ) ) ) ) ).
% view.switch_def
thf(fact_88_local_Ohmlsl_Oat__conj__distr,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( ( Phi @ Ts @ V6 )
& ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
& ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_conj_distr
thf(fact_89_local_Ohmlsl_Oat__disj__dist,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( ( Phi @ Ts @ V6 )
| ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
| ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_disj_dist
thf(fact_90_local_Ohmlsl_Oat__exists,axiom,
! [Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( Phi @ Ts @ V )
=> ? [X3: cars] :
! [V7: view_e774982825t_unit] :
( ( switch @ V @ X3 @ V7 )
=> ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_exists
thf(fact_91_local_Ohmlsl_Oat__neg,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ~ ( Phi @ Ts @ V6 ) ) )
= ( ~ ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_neg
thf(fact_92_local_Ohmlsl_Oat__neg_H,axiom,
! [V2: view_e774982825t_unit,C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts4: traffic] :
( ( ~ ! [V6: view_e774982825t_unit] :
( ( switch @ V2 @ C2 @ V6 )
=> ( Phi @ Ts4 @ V6 ) ) )
= ( ! [V6: view_e774982825t_unit] :
( ( switch @ V2 @ C2 @ V6 )
=> ~ ( Phi @ Ts4 @ V6 ) ) ) ) ).
% local.hmlsl.at_neg'
thf(fact_93_local_Ohmlsl_Oat__neg1,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ! [V5: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V5 )
=> ~ ( Phi @ Ts @ V5 ) )
=> ~ ! [V5: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) ) ) ).
% local.hmlsl.at_neg1
thf(fact_94_local_Ohmlsl_Oat__neg2,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ~ ! [V7: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) )
=> ! [V7: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V7 )
=> ~ ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_neg2
thf(fact_95_local_Ohmlsl_Oat__neg__neg,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) ) )
= ( ~ ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ~ ( Phi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_neg_neg
thf(fact_96_local_Ohmlsl_Oat__neg__neg1,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ! [V5: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) )
=> ~ ! [V5: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V5 )
=> ~ ( Phi @ Ts @ V5 ) ) ) ).
% local.hmlsl.at_neg_neg1
thf(fact_97_local_Ohmlsl_Oat__neg__neg2,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ~ ! [V7: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V7 )
=> ~ ( Phi @ Ts @ V7 ) )
=> ! [V7: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_neg_neg2
thf(fact_98_local_Ohmlsl_Oat__hchop__dist,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ( ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V @ W @ U )
& ! [V6: view_e774982825t_unit] :
( ( switch @ W @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
& ! [V6: view_e774982825t_unit] :
( ( switch @ U @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V6 )
=> ? [W: view_e774982825t_unit,U: view_e774982825t_unit] :
( ( hchop @ V6 @ W @ U )
& ( Phi @ Ts @ W )
& ( Psi @ Ts @ U ) ) ) ) ) ).
% local.hmlsl.at_hchop_dist
thf(fact_99_local_Ohmlsl_Oat__hchop__dist1,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ! [V5: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V5 )
=> ? [Va2: view_e774982825t_unit,U4: view_e774982825t_unit] :
( ( hchop @ V5 @ Va2 @ U4 )
& ( Phi @ Ts @ Va2 )
& ( Psi @ Ts @ U4 ) ) )
=> ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V @ Va @ U2 )
& ! [V7: view_e774982825t_unit] :
( ( switch @ Va @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) )
& ! [V7: view_e774982825t_unit] :
( ( switch @ U2 @ C2 @ V7 )
=> ( Psi @ Ts @ V7 ) ) ) ) ).
% local.hmlsl.at_hchop_dist1
thf(fact_100_local_Ohmlsl_Oat__hchop__dist2,axiom,
! [C2: cars,Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Ts: traffic,V: view_e774982825t_unit] :
( ? [Va2: view_e774982825t_unit,U4: view_e774982825t_unit] :
( ( hchop @ V @ Va2 @ U4 )
& ! [V5: view_e774982825t_unit] :
( ( switch @ Va2 @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) )
& ! [V5: view_e774982825t_unit] :
( ( switch @ U4 @ C2 @ V5 )
=> ( Psi @ Ts @ V5 ) ) )
=> ! [V7: view_e774982825t_unit] :
( ( switch @ V @ C2 @ V7 )
=> ? [Va: view_e774982825t_unit,U2: view_e774982825t_unit] :
( ( hchop @ V7 @ Va @ U2 )
& ( Phi @ Ts @ Va )
& ( Psi @ Ts @ U2 ) ) ) ) ).
% local.hmlsl.at_hchop_dist2
thf(fact_101_view_Oswitch__always__exists,axiom,
! [V2: view_e774982825t_unit,C3: cars] :
? [X_1: view_e774982825t_unit] : ( switch @ V2 @ C3 @ X_1 ) ).
% view.switch_always_exists
thf(fact_102_view_Oswitch__triangle,axiom,
! [V2: view_e774982825t_unit,C2: cars,U3: view_e774982825t_unit,D: cars,W2: view_e774982825t_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ V2 @ D @ W2 ) )
=> ( switch @ U3 @ D @ W2 ) ) ).
% view.switch_triangle
thf(fact_103_view_Oswitch__unique,axiom,
! [V2: view_e774982825t_unit,C2: cars,U3: view_e774982825t_unit,W2: view_e774982825t_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ V2 @ C2 @ W2 ) )
=> ( U3 = W2 ) ) ).
% view.switch_unique
thf(fact_104_view_Oswitch__exists,axiom,
! [V2: view_e774982825t_unit] :
? [C: cars,X_1: view_e774982825t_unit] : ( switch @ V2 @ C @ X_1 ) ).
% view.switch_exists
thf(fact_105_view_Oswitch__trans,axiom,
! [V2: view_e774982825t_unit,C2: cars,U3: view_e774982825t_unit,D: cars,W2: view_e774982825t_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ U3 @ D @ W2 ) )
=> ( switch @ V2 @ D @ W2 ) ) ).
% view.switch_trans
thf(fact_106_view_Oswitch__hchop1,axiom,
! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,C2: cars,V8: view_e774982825t_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( switch @ V2 @ C2 @ V8 ) )
=> ? [V12: view_e774982825t_unit,V23: view_e774982825t_unit] :
( ( switch @ V1 @ C2 @ V12 )
& ( switch @ V22 @ C2 @ V23 )
& ( hchop @ V8 @ V12 @ V23 ) ) ) ).
% view.switch_hchop1
thf(fact_107_view_Oswitch__hchop2,axiom,
! [V8: view_e774982825t_unit,V13: view_e774982825t_unit,V24: view_e774982825t_unit,V2: view_e774982825t_unit,C2: cars] :
( ( ( hchop @ V8 @ V13 @ V24 )
& ( switch @ V2 @ C2 @ V8 ) )
=> ? [V14: view_e774982825t_unit,V25: view_e774982825t_unit] :
( ( switch @ V14 @ C2 @ V13 )
& ( switch @ V25 @ C2 @ V24 )
& ( hchop @ V2 @ V14 @ V25 ) ) ) ).
% view.switch_hchop2
thf(fact_108_view_Oswitch__refl,axiom,
! [V2: view_e774982825t_unit] : ( switch @ V2 @ ( own_Product_unit @ V2 ) @ V2 ) ).
% view.switch_refl
thf(fact_109_view_Oswitch__symm,axiom,
! [V2: view_e774982825t_unit,C2: cars,U3: view_e774982825t_unit] :
( ( switch @ V2 @ C2 @ U3 )
=> ( switch @ U3 @ ( own_Product_unit @ V2 ) @ V2 ) ) ).
% view.switch_symm
thf(fact_110_view_Oswitch__origin,axiom,
! [V2: view_e774982825t_unit] :
? [U2: view_e774982825t_unit] : ( switch @ U2 @ ( own_Product_unit @ V2 ) @ V2 ) ).
% view.switch_origin
thf(fact_111_view_Ohorizontal__chop__width__stable,axiom,
! [V2: view_e774982825t_unit,U3: view_e774982825t_unit,W2: view_e774982825t_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ( ( nat_card @ ( lan_Product_unit @ V2 ) )
= ( nat_card @ ( lan_Product_unit @ U3 ) ) )
& ( ( nat_card @ ( lan_Product_unit @ V2 ) )
= ( nat_card @ ( lan_Product_unit @ W2 ) ) ) ) ) ).
% view.horizontal_chop_width_stable
thf(fact_112_traffic_Ochange,axiom,
! [Ts4: traffic,Ts7: traffic,Ts8: traffic] :
( ? [C3: cars,F3: real > real] : ( change_dyn @ Ts4 @ C3 @ F3 @ Ts7 )
=> ( ( evolve @ Ts7 @ Ts8 )
=> ( evolve @ Ts4 @ Ts8 ) ) ) ).
% traffic.change
thf(fact_113_old_Ounit_Oexhaust,axiom,
! [Y2: product_unit] : Y2 = product_Unity ).
% old.unit.exhaust
thf(fact_114_old_Ounit_Oinducts,axiom,
! [P: product_unit > $o,Unit: product_unit] :
( ( P @ product_Unity )
=> ( P @ Unit ) ) ).
% old.unit.inducts
thf(fact_115_unit__all__impI,axiom,
! [P: product_unit > $o,Q: product_unit > $o] :
( ( ( P @ product_Unity )
=> ( Q @ product_Unity ) )
=> ! [X4: product_unit] :
( ( P @ X4 )
=> ( Q @ X4 ) ) ) ).
% unit_all_impI
thf(fact_116_eq__sym__Unity__conv,axiom,
! [X2: $o] :
( ( X2
= ( product_Unity = product_Unity ) )
= X2 ) ).
% eq_sym_Unity_conv
thf(fact_117_bot__unit__def,axiom,
bot_bot_Product_unit = product_Unity ).
% bot_unit_def
thf(fact_118_traffic_Ocreate__res__subseteq2,axiom,
! [Ts4: traffic,C2: cars,Ts7: traffic] :
( ( create_reservation @ Ts4 @ C2 @ Ts7 )
=> ( ord_less_eq_nat_int @ ( clm @ Ts4 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq2
thf(fact_119_order__refl,axiom,
! [X2: nat_int] : ( ord_less_eq_nat_int @ X2 @ X2 ) ).
% order_refl
thf(fact_120_order__refl,axiom,
! [X2: view_e774982825t_unit] : ( ord_le461438217t_unit @ X2 @ X2 ) ).
% order_refl
thf(fact_121_order__refl,axiom,
! [X2: real_int] : ( ord_less_eq_real_int @ X2 @ X2 ) ).
% order_refl
thf(fact_122_order__refl,axiom,
! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% order_refl
thf(fact_123_order__subst1,axiom,
! [A2: nat_int,F: nat_int > nat_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_124_order__subst1,axiom,
! [A2: nat_int,F: real_int > nat_int,B: real_int,C2: real_int] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_125_order__subst1,axiom,
! [A2: nat_int,F: nat > nat_int,B: nat,C2: nat] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_126_order__subst1,axiom,
! [A2: real_int,F: nat_int > real_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_127_order__subst1,axiom,
! [A2: real_int,F: real_int > real_int,B: real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_128_order__subst1,axiom,
! [A2: real_int,F: nat > real_int,B: nat,C2: nat] :
( ( ord_less_eq_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_129_order__subst1,axiom,
! [A2: nat,F: nat_int > nat,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_130_order__subst1,axiom,
! [A2: nat,F: real_int > nat,B: real_int,C2: real_int] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_131_order__subst1,axiom,
! [A2: nat,F: nat > nat,B: nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_132_order__subst1,axiom,
! [A2: nat_int,F: view_e774982825t_unit > nat_int,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_le461438217t_unit @ B @ C2 )
=> ( ! [X3: view_e774982825t_unit,Y3: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_133_order__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_134_order__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > real_int,C2: real_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_eq_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_135_order__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat,C2: nat] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_136_order__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > nat_int,C2: nat_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_137_order__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_eq_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_138_order__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > nat,C2: nat] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_139_order__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat_int,C2: nat_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_140_order__subst2,axiom,
! [A2: nat,B: nat,F: nat > real_int,C2: real_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_141_order__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_142_order__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_le461438217t_unit @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_le461438217t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le461438217t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_143_ord__eq__le__subst,axiom,
! [A2: nat_int,F: nat_int > nat_int,B: nat_int,C2: nat_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_144_ord__eq__le__subst,axiom,
! [A2: real_int,F: nat_int > real_int,B: nat_int,C2: nat_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_145_ord__eq__le__subst,axiom,
! [A2: nat,F: nat_int > nat,B: nat_int,C2: nat_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_146_ord__eq__le__subst,axiom,
! [A2: nat_int,F: real_int > nat_int,B: real_int,C2: real_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_147_ord__eq__le__subst,axiom,
! [A2: real_int,F: real_int > real_int,B: real_int,C2: real_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_148_ord__eq__le__subst,axiom,
! [A2: nat,F: real_int > nat,B: real_int,C2: real_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_149_ord__eq__le__subst,axiom,
! [A2: nat_int,F: nat > nat_int,B: nat,C2: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_150_ord__eq__le__subst,axiom,
! [A2: real_int,F: nat > real_int,B: nat,C2: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_151_ord__eq__le__subst,axiom,
! [A2: nat,F: nat > nat,B: nat,C2: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_152_ord__eq__le__subst,axiom,
! [A2: view_e774982825t_unit,F: nat_int > view_e774982825t_unit,B: nat_int,C2: nat_int] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_le461438217t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le461438217t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_153_ord__le__eq__subst,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_154_ord__le__eq__subst,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > real_int,C2: real_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_155_ord__le__eq__subst,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat,C2: nat] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_156_ord__le__eq__subst,axiom,
! [A2: real_int,B: real_int,F: real_int > nat_int,C2: nat_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_157_ord__le__eq__subst,axiom,
! [A2: real_int,B: real_int,F: real_int > real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_158_ord__le__eq__subst,axiom,
! [A2: real_int,B: real_int,F: real_int > nat,C2: nat] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_159_ord__le__eq__subst,axiom,
! [A2: nat,B: nat,F: nat > nat_int,C2: nat_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_160_ord__le__eq__subst,axiom,
! [A2: nat,B: nat,F: nat > real_int,C2: real_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_161_ord__le__eq__subst,axiom,
! [A2: nat,B: nat,F: nat > nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_162_ord__le__eq__subst,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ( F @ B )
= C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_le461438217t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le461438217t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_163_eq__iff,axiom,
( ( ^ [Y4: nat_int,Z3: nat_int] : Y4 = Z3 )
= ( ^ [X: nat_int,Y: nat_int] :
( ( ord_less_eq_nat_int @ X @ Y )
& ( ord_less_eq_nat_int @ Y @ X ) ) ) ) ).
% eq_iff
thf(fact_164_eq__iff,axiom,
( ( ^ [Y4: view_e774982825t_unit,Z3: view_e774982825t_unit] : Y4 = Z3 )
= ( ^ [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X @ Y )
& ( ord_le461438217t_unit @ Y @ X ) ) ) ) ).
% eq_iff
thf(fact_165_eq__iff,axiom,
( ( ^ [Y4: real_int,Z3: real_int] : Y4 = Z3 )
= ( ^ [X: real_int,Y: real_int] :
( ( ord_less_eq_real_int @ X @ Y )
& ( ord_less_eq_real_int @ Y @ X ) ) ) ) ).
% eq_iff
thf(fact_166_eq__iff,axiom,
( ( ^ [Y4: nat,Z3: nat] : Y4 = Z3 )
= ( ^ [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
& ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% eq_iff
thf(fact_167_antisym,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( ord_less_eq_nat_int @ X2 @ Y2 )
=> ( ( ord_less_eq_nat_int @ Y2 @ X2 )
=> ( X2 = Y2 ) ) ) ).
% antisym
thf(fact_168_antisym,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X2 @ Y2 )
=> ( ( ord_le461438217t_unit @ Y2 @ X2 )
=> ( X2 = Y2 ) ) ) ).
% antisym
thf(fact_169_antisym,axiom,
! [X2: real_int,Y2: real_int] :
( ( ord_less_eq_real_int @ X2 @ Y2 )
=> ( ( ord_less_eq_real_int @ Y2 @ X2 )
=> ( X2 = Y2 ) ) ) ).
% antisym
thf(fact_170_antisym,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ( ord_less_eq_nat @ Y2 @ X2 )
=> ( X2 = Y2 ) ) ) ).
% antisym
thf(fact_171_linear,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
| ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% linear
thf(fact_172_eq__refl,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( X2 = Y2 )
=> ( ord_less_eq_nat_int @ X2 @ Y2 ) ) ).
% eq_refl
thf(fact_173_eq__refl,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ( X2 = Y2 )
=> ( ord_le461438217t_unit @ X2 @ Y2 ) ) ).
% eq_refl
thf(fact_174_eq__refl,axiom,
! [X2: real_int,Y2: real_int] :
( ( X2 = Y2 )
=> ( ord_less_eq_real_int @ X2 @ Y2 ) ) ).
% eq_refl
thf(fact_175_eq__refl,axiom,
! [X2: nat,Y2: nat] :
( ( X2 = Y2 )
=> ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% eq_refl
thf(fact_176_le__cases,axiom,
! [X2: nat,Y2: nat] :
( ~ ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% le_cases
thf(fact_177_order_Otrans,axiom,
! [A2: nat_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ord_less_eq_nat_int @ A2 @ C2 ) ) ) ).
% order.trans
thf(fact_178_order_Otrans,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A2 @ B )
=> ( ( ord_le461438217t_unit @ B @ C2 )
=> ( ord_le461438217t_unit @ A2 @ C2 ) ) ) ).
% order.trans
thf(fact_179_order_Otrans,axiom,
! [A2: real_int,B: real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ord_less_eq_real_int @ A2 @ C2 ) ) ) ).
% order.trans
thf(fact_180_order_Otrans,axiom,
! [A2: nat,B: nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% order.trans
thf(fact_181_le__cases3,axiom,
! [X2: nat,Y2: nat,Z: nat] :
( ( ( ord_less_eq_nat @ X2 @ Y2 )
=> ~ ( ord_less_eq_nat @ Y2 @ Z ) )
=> ( ( ( ord_less_eq_nat @ Y2 @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ Z ) )
=> ( ( ( ord_less_eq_nat @ X2 @ Z )
=> ~ ( ord_less_eq_nat @ Z @ Y2 ) )
=> ( ( ( ord_less_eq_nat @ Z @ Y2 )
=> ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
=> ( ( ( ord_less_eq_nat @ Y2 @ Z )
=> ~ ( ord_less_eq_nat @ Z @ X2 ) )
=> ~ ( ( ord_less_eq_nat @ Z @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% le_cases3
thf(fact_182_antisym__conv,axiom,
! [Y2: nat_int,X2: nat_int] :
( ( ord_less_eq_nat_int @ Y2 @ X2 )
=> ( ( ord_less_eq_nat_int @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv
thf(fact_183_antisym__conv,axiom,
! [Y2: view_e774982825t_unit,X2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ Y2 @ X2 )
=> ( ( ord_le461438217t_unit @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv
thf(fact_184_antisym__conv,axiom,
! [Y2: real_int,X2: real_int] :
( ( ord_less_eq_real_int @ Y2 @ X2 )
=> ( ( ord_less_eq_real_int @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv
thf(fact_185_antisym__conv,axiom,
! [Y2: nat,X2: nat] :
( ( ord_less_eq_nat @ Y2 @ X2 )
=> ( ( ord_less_eq_nat @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv
thf(fact_186_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y4: nat_int,Z3: nat_int] : Y4 = Z3 )
= ( ^ [A: nat_int,B2: nat_int] :
( ( ord_less_eq_nat_int @ A @ B2 )
& ( ord_less_eq_nat_int @ B2 @ A ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_187_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y4: view_e774982825t_unit,Z3: view_e774982825t_unit] : Y4 = Z3 )
= ( ^ [A: view_e774982825t_unit,B2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A @ B2 )
& ( ord_le461438217t_unit @ B2 @ A ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_188_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y4: real_int,Z3: real_int] : Y4 = Z3 )
= ( ^ [A: real_int,B2: real_int] :
( ( ord_less_eq_real_int @ A @ B2 )
& ( ord_less_eq_real_int @ B2 @ A ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_189_order__class_Oorder_Oeq__iff,axiom,
( ( ^ [Y4: nat,Z3: nat] : Y4 = Z3 )
= ( ^ [A: nat,B2: nat] :
( ( ord_less_eq_nat @ A @ B2 )
& ( ord_less_eq_nat @ B2 @ A ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_190_ord__eq__le__trans,axiom,
! [A2: nat_int,B: nat_int,C2: nat_int] :
( ( A2 = B )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ord_less_eq_nat_int @ A2 @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_191_ord__eq__le__trans,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( A2 = B )
=> ( ( ord_le461438217t_unit @ B @ C2 )
=> ( ord_le461438217t_unit @ A2 @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_192_ord__eq__le__trans,axiom,
! [A2: real_int,B: real_int,C2: real_int] :
( ( A2 = B )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ord_less_eq_real_int @ A2 @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_193_ord__eq__le__trans,axiom,
! [A2: nat,B: nat,C2: nat] :
( ( A2 = B )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_194_ord__le__eq__trans,axiom,
! [A2: nat_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( B = C2 )
=> ( ord_less_eq_nat_int @ A2 @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_195_ord__le__eq__trans,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A2 @ B )
=> ( ( B = C2 )
=> ( ord_le461438217t_unit @ A2 @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_196_ord__le__eq__trans,axiom,
! [A2: real_int,B: real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( B = C2 )
=> ( ord_less_eq_real_int @ A2 @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_197_ord__le__eq__trans,axiom,
! [A2: nat,B: nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( B = C2 )
=> ( ord_less_eq_nat @ A2 @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_198_order__class_Oorder_Oantisym,axiom,
! [A2: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ B @ A2 )
=> ( A2 = B ) ) ) ).
% order_class.order.antisym
thf(fact_199_order__class_Oorder_Oantisym,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A2 @ B )
=> ( ( ord_le461438217t_unit @ B @ A2 )
=> ( A2 = B ) ) ) ).
% order_class.order.antisym
thf(fact_200_order__class_Oorder_Oantisym,axiom,
! [A2: real_int,B: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_eq_real_int @ B @ A2 )
=> ( A2 = B ) ) ) ).
% order_class.order.antisym
thf(fact_201_order__class_Oorder_Oantisym,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ A2 )
=> ( A2 = B ) ) ) ).
% order_class.order.antisym
thf(fact_202_order__trans,axiom,
! [X2: nat_int,Y2: nat_int,Z: nat_int] :
( ( ord_less_eq_nat_int @ X2 @ Y2 )
=> ( ( ord_less_eq_nat_int @ Y2 @ Z )
=> ( ord_less_eq_nat_int @ X2 @ Z ) ) ) ).
% order_trans
thf(fact_203_order__trans,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit,Z: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X2 @ Y2 )
=> ( ( ord_le461438217t_unit @ Y2 @ Z )
=> ( ord_le461438217t_unit @ X2 @ Z ) ) ) ).
% order_trans
thf(fact_204_order__trans,axiom,
! [X2: real_int,Y2: real_int,Z: real_int] :
( ( ord_less_eq_real_int @ X2 @ Y2 )
=> ( ( ord_less_eq_real_int @ Y2 @ Z )
=> ( ord_less_eq_real_int @ X2 @ Z ) ) ) ).
% order_trans
thf(fact_205_order__trans,axiom,
! [X2: nat,Y2: nat,Z: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ( ord_less_eq_nat @ Y2 @ Z )
=> ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% order_trans
thf(fact_206_dual__order_Orefl,axiom,
! [A2: nat_int] : ( ord_less_eq_nat_int @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_207_dual__order_Orefl,axiom,
! [A2: view_e774982825t_unit] : ( ord_le461438217t_unit @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_208_dual__order_Orefl,axiom,
! [A2: real_int] : ( ord_less_eq_real_int @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_209_dual__order_Orefl,axiom,
! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_210_linorder__wlog,axiom,
! [P: nat > nat > $o,A2: nat,B: nat] :
( ! [A3: nat,B3: nat] :
( ( ord_less_eq_nat @ A3 @ B3 )
=> ( P @ A3 @ B3 ) )
=> ( ! [A3: nat,B3: nat] :
( ( P @ B3 @ A3 )
=> ( P @ A3 @ B3 ) )
=> ( P @ A2 @ B ) ) ) ).
% linorder_wlog
thf(fact_211_dual__order_Otrans,axiom,
! [B: nat_int,A2: nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ B @ A2 )
=> ( ( ord_less_eq_nat_int @ C2 @ B )
=> ( ord_less_eq_nat_int @ C2 @ A2 ) ) ) ).
% dual_order.trans
thf(fact_212_dual__order_Otrans,axiom,
! [B: view_e774982825t_unit,A2: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ B @ A2 )
=> ( ( ord_le461438217t_unit @ C2 @ B )
=> ( ord_le461438217t_unit @ C2 @ A2 ) ) ) ).
% dual_order.trans
thf(fact_213_dual__order_Otrans,axiom,
! [B: real_int,A2: real_int,C2: real_int] :
( ( ord_less_eq_real_int @ B @ A2 )
=> ( ( ord_less_eq_real_int @ C2 @ B )
=> ( ord_less_eq_real_int @ C2 @ A2 ) ) ) ).
% dual_order.trans
thf(fact_214_dual__order_Otrans,axiom,
! [B: nat,A2: nat,C2: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C2 @ B )
=> ( ord_less_eq_nat @ C2 @ A2 ) ) ) ).
% dual_order.trans
thf(fact_215_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: nat_int,Z3: nat_int] : Y4 = Z3 )
= ( ^ [A: nat_int,B2: nat_int] :
( ( ord_less_eq_nat_int @ B2 @ A )
& ( ord_less_eq_nat_int @ A @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_216_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: view_e774982825t_unit,Z3: view_e774982825t_unit] : Y4 = Z3 )
= ( ^ [A: view_e774982825t_unit,B2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ B2 @ A )
& ( ord_le461438217t_unit @ A @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_217_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: real_int,Z3: real_int] : Y4 = Z3 )
= ( ^ [A: real_int,B2: real_int] :
( ( ord_less_eq_real_int @ B2 @ A )
& ( ord_less_eq_real_int @ A @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_218_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: nat,Z3: nat] : Y4 = Z3 )
= ( ^ [A: nat,B2: nat] :
( ( ord_less_eq_nat @ B2 @ A )
& ( ord_less_eq_nat @ A @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_219_dual__order_Oantisym,axiom,
! [B: nat_int,A2: nat_int] :
( ( ord_less_eq_nat_int @ B @ A2 )
=> ( ( ord_less_eq_nat_int @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_220_dual__order_Oantisym,axiom,
! [B: view_e774982825t_unit,A2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ B @ A2 )
=> ( ( ord_le461438217t_unit @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_221_dual__order_Oantisym,axiom,
! [B: real_int,A2: real_int] :
( ( ord_less_eq_real_int @ B @ A2 )
=> ( ( ord_less_eq_real_int @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_222_dual__order_Oantisym,axiom,
! [B: nat,A2: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_223_less__eq__view__ext__def,axiom,
( ord_le1902160870at_int
= ( ^ [V9: view_ext_nat_int,V10: view_ext_nat_int] :
( ( ord_less_eq_real_int @ ( ext_nat_int @ V9 ) @ ( ext_nat_int @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_nat_int @ V9 ) @ ( lan_nat_int @ V10 ) )
& ( ( own_nat_int @ V9 )
= ( own_nat_int @ V10 ) )
& ( ord_less_eq_nat_int @ ( more_nat_int @ V9 ) @ ( more_nat_int @ V10 ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_224_less__eq__view__ext__def,axiom,
( ord_le63244867t_unit
= ( ^ [V9: view_e665166499t_unit,V10: view_e665166499t_unit] :
( ( ord_less_eq_real_int @ ( ext_vi2102772532t_unit @ V9 ) @ ( ext_vi2102772532t_unit @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_vi1543476748t_unit @ V9 ) @ ( lan_vi1543476748t_unit @ V10 ) )
& ( ( own_vi676290681t_unit @ V9 )
= ( own_vi676290681t_unit @ V10 ) )
& ( ord_le461438217t_unit @ ( more_v92543030t_unit @ V9 ) @ ( more_v92543030t_unit @ V10 ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_225_less__eq__view__ext__def,axiom,
( ord_le1863101098al_int
= ( ^ [V9: view_ext_real_int,V10: view_ext_real_int] :
( ( ord_less_eq_real_int @ ( ext_real_int @ V9 ) @ ( ext_real_int @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_real_int @ V9 ) @ ( lan_real_int @ V10 ) )
& ( ( own_real_int @ V9 )
= ( own_real_int @ V10 ) )
& ( ord_less_eq_real_int @ ( more_real_int @ V9 ) @ ( more_real_int @ V10 ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_226_less__eq__view__ext__def,axiom,
( ord_le1036425834xt_nat
= ( ^ [V9: view_ext_nat,V10: view_ext_nat] :
( ( ord_less_eq_real_int @ ( ext_nat @ V9 ) @ ( ext_nat @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_nat @ V9 ) @ ( lan_nat @ V10 ) )
& ( ( own_nat @ V9 )
= ( own_nat @ V10 ) )
& ( ord_less_eq_nat @ ( more_nat @ V9 ) @ ( more_nat @ V10 ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_227_less__eq__view__ext__def,axiom,
( ord_le461438217t_unit
= ( ^ [V9: view_e774982825t_unit,V10: view_e774982825t_unit] :
( ( ord_less_eq_real_int @ ( ext_Product_unit @ V9 ) @ ( ext_Product_unit @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_Product_unit @ V9 ) @ ( lan_Product_unit @ V10 ) )
& ( ( own_Product_unit @ V9 )
= ( own_Product_unit @ V10 ) )
& ( ord_le1997193645t_unit @ ( more_Product_unit @ V9 ) @ ( more_Product_unit @ V10 ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_228_bot_Oextremum,axiom,
! [A2: product_unit] : ( ord_le1997193645t_unit @ bot_bot_Product_unit @ A2 ) ).
% bot.extremum
thf(fact_229_bot_Oextremum,axiom,
! [A2: nat_int] : ( ord_less_eq_nat_int @ bot_bot_nat_int @ A2 ) ).
% bot.extremum
thf(fact_230_bot_Oextremum,axiom,
! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% bot.extremum
thf(fact_231_bot_Oextremum__unique,axiom,
! [A2: product_unit] :
( ( ord_le1997193645t_unit @ A2 @ bot_bot_Product_unit )
= ( A2 = bot_bot_Product_unit ) ) ).
% bot.extremum_unique
thf(fact_232_bot_Oextremum__unique,axiom,
! [A2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ bot_bot_nat_int )
= ( A2 = bot_bot_nat_int ) ) ).
% bot.extremum_unique
thf(fact_233_bot_Oextremum__unique,axiom,
! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
= ( A2 = bot_bot_nat ) ) ).
% bot.extremum_unique
thf(fact_234_bot_Oextremum__uniqueI,axiom,
! [A2: product_unit] :
( ( ord_le1997193645t_unit @ A2 @ bot_bot_Product_unit )
=> ( A2 = bot_bot_Product_unit ) ) ).
% bot.extremum_uniqueI
thf(fact_235_bot_Oextremum__uniqueI,axiom,
! [A2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ bot_bot_nat_int )
=> ( A2 = bot_bot_nat_int ) ) ).
% bot.extremum_uniqueI
thf(fact_236_bot_Oextremum__uniqueI,axiom,
! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
=> ( A2 = bot_bot_nat ) ) ).
% bot.extremum_uniqueI
thf(fact_237_traffic_Ocreate__res__subseteq1,axiom,
! [Ts4: traffic,C2: cars,Ts7: traffic] :
( ( create_reservation @ Ts4 @ C2 @ Ts7 )
=> ( ord_less_eq_nat_int @ ( res @ Ts4 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq1
thf(fact_238_traffic_Owithdraw__res__subseteq,axiom,
! [Ts4: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
( ( withdraw_reservation @ Ts4 @ D @ N @ Ts7 )
=> ( ord_less_eq_nat_int @ ( res @ Ts7 @ C2 ) @ ( res @ Ts4 @ C2 ) ) ) ).
% traffic.withdraw_res_subseteq
thf(fact_239_default__unit__def,axiom,
defaul1399868459t_unit = product_Unity ).
% default_unit_def
thf(fact_240_less__view__ext__def,axiom,
( ord_le1993783549t_unit
= ( ^ [V9: view_e774982825t_unit,V10: view_e774982825t_unit] :
( ( ord_less_eq_real_int @ ( ext_Product_unit @ V9 ) @ ( ext_Product_unit @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_Product_unit @ V9 ) @ ( lan_Product_unit @ V10 ) )
& ( ( own_Product_unit @ V10 )
= ( own_Product_unit @ V9 ) )
& ( ord_le1997193645t_unit @ ( more_Product_unit @ V9 ) @ ( more_Product_unit @ V10 ) )
& ~ ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V10 ) @ ( ext_Product_unit @ V9 ) )
& ( ord_less_eq_nat_int @ ( lan_Product_unit @ V10 ) @ ( lan_Product_unit @ V9 ) )
& ( ( own_Product_unit @ V10 )
= ( own_Product_unit @ V9 ) )
& ( ord_le1997193645t_unit @ ( more_Product_unit @ V10 ) @ ( more_Product_unit @ V9 ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_241_less__view__ext__def,axiom,
( ord_le893810930at_int
= ( ^ [V9: view_ext_nat_int,V10: view_ext_nat_int] :
( ( ord_less_eq_real_int @ ( ext_nat_int @ V9 ) @ ( ext_nat_int @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_nat_int @ V9 ) @ ( lan_nat_int @ V10 ) )
& ( ( own_nat_int @ V10 )
= ( own_nat_int @ V9 ) )
& ( ord_less_eq_nat_int @ ( more_nat_int @ V9 ) @ ( more_nat_int @ V10 ) )
& ~ ( ( ord_less_eq_real_int @ ( ext_nat_int @ V10 ) @ ( ext_nat_int @ V9 ) )
& ( ord_less_eq_nat_int @ ( lan_nat_int @ V10 ) @ ( lan_nat_int @ V9 ) )
& ( ( own_nat_int @ V10 )
= ( own_nat_int @ V9 ) )
& ( ord_less_eq_nat_int @ ( more_nat_int @ V10 ) @ ( more_nat_int @ V9 ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_242_less__view__ext__def,axiom,
( ord_le750644047t_unit
= ( ^ [V9: view_e665166499t_unit,V10: view_e665166499t_unit] :
( ( ord_less_eq_real_int @ ( ext_vi2102772532t_unit @ V9 ) @ ( ext_vi2102772532t_unit @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_vi1543476748t_unit @ V9 ) @ ( lan_vi1543476748t_unit @ V10 ) )
& ( ( own_vi676290681t_unit @ V10 )
= ( own_vi676290681t_unit @ V9 ) )
& ( ord_le461438217t_unit @ ( more_v92543030t_unit @ V9 ) @ ( more_v92543030t_unit @ V10 ) )
& ~ ( ( ord_less_eq_real_int @ ( ext_vi2102772532t_unit @ V10 ) @ ( ext_vi2102772532t_unit @ V9 ) )
& ( ord_less_eq_nat_int @ ( lan_vi1543476748t_unit @ V10 ) @ ( lan_vi1543476748t_unit @ V9 ) )
& ( ( own_vi676290681t_unit @ V10 )
= ( own_vi676290681t_unit @ V9 ) )
& ( ord_le461438217t_unit @ ( more_v92543030t_unit @ V10 ) @ ( more_v92543030t_unit @ V9 ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_243_less__view__ext__def,axiom,
( ord_le147108278al_int
= ( ^ [V9: view_ext_real_int,V10: view_ext_real_int] :
( ( ord_less_eq_real_int @ ( ext_real_int @ V9 ) @ ( ext_real_int @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_real_int @ V9 ) @ ( lan_real_int @ V10 ) )
& ( ( own_real_int @ V10 )
= ( own_real_int @ V9 ) )
& ( ord_less_eq_real_int @ ( more_real_int @ V9 ) @ ( more_real_int @ V10 ) )
& ~ ( ( ord_less_eq_real_int @ ( ext_real_int @ V10 ) @ ( ext_real_int @ V9 ) )
& ( ord_less_eq_nat_int @ ( lan_real_int @ V10 ) @ ( lan_real_int @ V9 ) )
& ( ( own_real_int @ V10 )
= ( own_real_int @ V9 ) )
& ( ord_less_eq_real_int @ ( more_real_int @ V10 ) @ ( more_real_int @ V9 ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_244_less__view__ext__def,axiom,
( ord_le1522419062xt_nat
= ( ^ [V9: view_ext_nat,V10: view_ext_nat] :
( ( ord_less_eq_real_int @ ( ext_nat @ V9 ) @ ( ext_nat @ V10 ) )
& ( ord_less_eq_nat_int @ ( lan_nat @ V9 ) @ ( lan_nat @ V10 ) )
& ( ( own_nat @ V10 )
= ( own_nat @ V9 ) )
& ( ord_less_eq_nat @ ( more_nat @ V9 ) @ ( more_nat @ V10 ) )
& ~ ( ( ord_less_eq_real_int @ ( ext_nat @ V10 ) @ ( ext_nat @ V9 ) )
& ( ord_less_eq_nat_int @ ( lan_nat @ V10 ) @ ( lan_nat @ V9 ) )
& ( ( own_nat @ V10 )
= ( own_nat @ V9 ) )
& ( ord_less_eq_nat @ ( more_nat @ V10 ) @ ( more_nat @ V9 ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_245_diff__mono,axiom,
! [A2: real,B: real,D: real,C2: real] :
( ( ord_less_eq_real @ A2 @ B )
=> ( ( ord_less_eq_real @ D @ C2 )
=> ( ord_less_eq_real @ ( minus_minus_real @ A2 @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% diff_mono
thf(fact_246_leD,axiom,
! [Y2: nat_int,X2: nat_int] :
( ( ord_less_eq_nat_int @ Y2 @ X2 )
=> ~ ( ord_less_nat_int @ X2 @ Y2 ) ) ).
% leD
thf(fact_247_leD,axiom,
! [Y2: view_e774982825t_unit,X2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ Y2 @ X2 )
=> ~ ( ord_le1993783549t_unit @ X2 @ Y2 ) ) ).
% leD
thf(fact_248_leD,axiom,
! [Y2: real_int,X2: real_int] :
( ( ord_less_eq_real_int @ Y2 @ X2 )
=> ~ ( ord_less_real_int @ X2 @ Y2 ) ) ).
% leD
thf(fact_249_leD,axiom,
! [Y2: nat,X2: nat] :
( ( ord_less_eq_nat @ Y2 @ X2 )
=> ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% leD
thf(fact_250_leI,axiom,
! [X2: nat,Y2: nat] :
( ~ ( ord_less_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% leI
thf(fact_251_le__less,axiom,
( ord_less_eq_nat_int
= ( ^ [X: nat_int,Y: nat_int] :
( ( ord_less_nat_int @ X @ Y )
| ( X = Y ) ) ) ) ).
% le_less
thf(fact_252_le__less,axiom,
( ord_le461438217t_unit
= ( ^ [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( ord_le1993783549t_unit @ X @ Y )
| ( X = Y ) ) ) ) ).
% le_less
thf(fact_253_le__less,axiom,
( ord_less_eq_real_int
= ( ^ [X: real_int,Y: real_int] :
( ( ord_less_real_int @ X @ Y )
| ( X = Y ) ) ) ) ).
% le_less
thf(fact_254_le__less,axiom,
( ord_less_eq_nat
= ( ^ [X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
| ( X = Y ) ) ) ) ).
% le_less
thf(fact_255_less__le,axiom,
( ord_less_nat_int
= ( ^ [X: nat_int,Y: nat_int] :
( ( ord_less_eq_nat_int @ X @ Y )
& ( X != Y ) ) ) ) ).
% less_le
thf(fact_256_less__le,axiom,
( ord_le1993783549t_unit
= ( ^ [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X @ Y )
& ( X != Y ) ) ) ) ).
% less_le
thf(fact_257_less__le,axiom,
( ord_less_real_int
= ( ^ [X: real_int,Y: real_int] :
( ( ord_less_eq_real_int @ X @ Y )
& ( X != Y ) ) ) ) ).
% less_le
thf(fact_258_less__le,axiom,
( ord_less_nat
= ( ^ [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
& ( X != Y ) ) ) ) ).
% less_le
thf(fact_259_order__le__less__subst1,axiom,
! [A2: nat_int,F: nat_int > nat_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_260_order__le__less__subst1,axiom,
! [A2: nat_int,F: nat > nat_int,B: nat,C2: nat] :
( ( ord_less_eq_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_261_order__le__less__subst1,axiom,
! [A2: view_e774982825t_unit,F: nat_int > view_e774982825t_unit,B: nat_int,C2: nat_int] :
( ( ord_le461438217t_unit @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_le1993783549t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_262_order__le__less__subst1,axiom,
! [A2: view_e774982825t_unit,F: nat > view_e774982825t_unit,B: nat,C2: nat] :
( ( ord_le461438217t_unit @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_le1993783549t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_263_order__le__less__subst1,axiom,
! [A2: real_int,F: nat_int > real_int,B: nat_int,C2: nat_int] :
( ( ord_less_eq_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_264_order__le__less__subst1,axiom,
! [A2: real_int,F: nat > real_int,B: nat,C2: nat] :
( ( ord_less_eq_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_265_order__le__less__subst1,axiom,
! [A2: nat,F: nat_int > nat,B: nat_int,C2: nat_int] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_266_order__le__less__subst1,axiom,
! [A2: nat,F: nat > nat,B: nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_267_order__le__less__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat_int,C2: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_268_order__le__less__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > real_int,C2: real_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_269_order__le__less__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat,C2: nat] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_less_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_270_order__le__less__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > nat_int,C2: nat_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_271_order__le__less__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_272_order__le__less__subst2,axiom,
! [A2: real_int,B: real_int,F: real_int > nat,C2: nat] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_273_order__le__less__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat_int,C2: nat_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_274_order__le__less__subst2,axiom,
! [A2: nat,B: nat,F: nat > real_int,C2: real_int] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_275_order__le__less__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_276_order__le__less__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( ord_le1993783549t_unit @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_le461438217t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_le_less_subst2
thf(fact_277_order__less__le__subst1,axiom,
! [A2: nat_int,F: nat_int > nat_int,B: nat_int,C2: nat_int] :
( ( ord_less_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_278_order__less__le__subst1,axiom,
! [A2: real_int,F: nat_int > real_int,B: nat_int,C2: nat_int] :
( ( ord_less_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_279_order__less__le__subst1,axiom,
! [A2: nat,F: nat_int > nat,B: nat_int,C2: nat_int] :
( ( ord_less_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_280_order__less__le__subst1,axiom,
! [A2: nat_int,F: real_int > nat_int,B: real_int,C2: real_int] :
( ( ord_less_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_281_order__less__le__subst1,axiom,
! [A2: real_int,F: real_int > real_int,B: real_int,C2: real_int] :
( ( ord_less_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_282_order__less__le__subst1,axiom,
! [A2: nat,F: real_int > nat,B: real_int,C2: real_int] :
( ( ord_less_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_real_int @ B @ C2 )
=> ( ! [X3: real_int,Y3: real_int] :
( ( ord_less_eq_real_int @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_283_order__less__le__subst1,axiom,
! [A2: nat_int,F: nat > nat_int,B: nat,C2: nat] :
( ( ord_less_nat_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_284_order__less__le__subst1,axiom,
! [A2: real_int,F: nat > real_int,B: nat,C2: nat] :
( ( ord_less_real_int @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_285_order__less__le__subst1,axiom,
! [A2: nat,F: nat > nat,B: nat,C2: nat] :
( ( ord_less_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_eq_nat @ X3 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_286_order__less__le__subst1,axiom,
! [A2: view_e774982825t_unit,F: nat_int > view_e774982825t_unit,B: nat_int,C2: nat_int] :
( ( ord_le1993783549t_unit @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat_int @ B @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_eq_nat_int @ X3 @ Y3 )
=> ( ord_le461438217t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ A2 @ ( F @ C2 ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_287_order__less__le__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat_int,C2: nat_int] :
( ( ord_less_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_288_order__less__le__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat_int,C2: nat_int] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_nat_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_289_order__less__le__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_nat_int @ A2 @ B )
=> ( ( ord_le461438217t_unit @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_le1993783549t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_290_order__less__le__subst2,axiom,
! [A2: nat,B: nat,F: nat > view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_le461438217t_unit @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_le1993783549t_unit @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_le1993783549t_unit @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_291_order__less__le__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > real_int,C2: real_int] :
( ( ord_less_nat_int @ A2 @ B )
=> ( ( ord_less_eq_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_292_order__less__le__subst2,axiom,
! [A2: nat,B: nat,F: nat > real_int,C2: real_int] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_real_int @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_real_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_real_int @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_293_order__less__le__subst2,axiom,
! [A2: nat_int,B: nat_int,F: nat_int > nat,C2: nat] :
( ( ord_less_nat_int @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat_int,Y3: nat_int] :
( ( ord_less_nat_int @ X3 @ Y3 )
=> ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_294_order__less__le__subst2,axiom,
! [A2: nat,B: nat,F: nat > nat,C2: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
=> ( ! [X3: nat,Y3: nat] :
( ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
=> ( ord_less_nat @ ( F @ A2 ) @ C2 ) ) ) ) ).
% order_less_le_subst2
thf(fact_295_not__le,axiom,
! [X2: nat,Y2: nat] :
( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
= ( ord_less_nat @ Y2 @ X2 ) ) ).
% not_le
thf(fact_296_not__less,axiom,
! [X2: nat,Y2: nat] :
( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
= ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% not_less
thf(fact_297_le__neq__trans,axiom,
! [A2: nat_int,B: nat_int] :
( ( ord_less_eq_nat_int @ A2 @ B )
=> ( ( A2 != B )
=> ( ord_less_nat_int @ A2 @ B ) ) ) ).
% le_neq_trans
thf(fact_298_le__neq__trans,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A2 @ B )
=> ( ( A2 != B )
=> ( ord_le1993783549t_unit @ A2 @ B ) ) ) ).
% le_neq_trans
thf(fact_299_le__neq__trans,axiom,
! [A2: real_int,B: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( A2 != B )
=> ( ord_less_real_int @ A2 @ B ) ) ) ).
% le_neq_trans
thf(fact_300_le__neq__trans,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( A2 != B )
=> ( ord_less_nat @ A2 @ B ) ) ) ).
% le_neq_trans
thf(fact_301_antisym__conv1,axiom,
! [X2: nat_int,Y2: nat_int] :
( ~ ( ord_less_nat_int @ X2 @ Y2 )
=> ( ( ord_less_eq_nat_int @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv1
thf(fact_302_antisym__conv1,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ~ ( ord_le1993783549t_unit @ X2 @ Y2 )
=> ( ( ord_le461438217t_unit @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv1
thf(fact_303_antisym__conv1,axiom,
! [X2: real_int,Y2: real_int] :
( ~ ( ord_less_real_int @ X2 @ Y2 )
=> ( ( ord_less_eq_real_int @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv1
thf(fact_304_antisym__conv1,axiom,
! [X2: nat,Y2: nat] :
( ~ ( ord_less_nat @ X2 @ Y2 )
=> ( ( ord_less_eq_nat @ X2 @ Y2 )
= ( X2 = Y2 ) ) ) ).
% antisym_conv1
thf(fact_305_antisym__conv2,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( ord_less_eq_nat_int @ X2 @ Y2 )
=> ( ( ~ ( ord_less_nat_int @ X2 @ Y2 ) )
= ( X2 = Y2 ) ) ) ).
% antisym_conv2
thf(fact_306_antisym__conv2,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X2 @ Y2 )
=> ( ( ~ ( ord_le1993783549t_unit @ X2 @ Y2 ) )
= ( X2 = Y2 ) ) ) ).
% antisym_conv2
thf(fact_307_antisym__conv2,axiom,
! [X2: real_int,Y2: real_int] :
( ( ord_less_eq_real_int @ X2 @ Y2 )
=> ( ( ~ ( ord_less_real_int @ X2 @ Y2 ) )
= ( X2 = Y2 ) ) ) ).
% antisym_conv2
thf(fact_308_antisym__conv2,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
= ( X2 = Y2 ) ) ) ).
% antisym_conv2
thf(fact_309_less__imp__le,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( ord_less_nat_int @ X2 @ Y2 )
=> ( ord_less_eq_nat_int @ X2 @ Y2 ) ) ).
% less_imp_le
thf(fact_310_less__imp__le,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ( ord_le1993783549t_unit @ X2 @ Y2 )
=> ( ord_le461438217t_unit @ X2 @ Y2 ) ) ).
% less_imp_le
thf(fact_311_less__imp__le,axiom,
! [X2: real_int,Y2: real_int] :
( ( ord_less_real_int @ X2 @ Y2 )
=> ( ord_less_eq_real_int @ X2 @ Y2 ) ) ).
% less_imp_le
thf(fact_312_less__imp__le,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% less_imp_le
thf(fact_313_le__less__trans,axiom,
! [X2: nat_int,Y2: nat_int,Z: nat_int] :
( ( ord_less_eq_nat_int @ X2 @ Y2 )
=> ( ( ord_less_nat_int @ Y2 @ Z )
=> ( ord_less_nat_int @ X2 @ Z ) ) ) ).
% le_less_trans
thf(fact_314_le__less__trans,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit,Z: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X2 @ Y2 )
=> ( ( ord_le1993783549t_unit @ Y2 @ Z )
=> ( ord_le1993783549t_unit @ X2 @ Z ) ) ) ).
% le_less_trans
thf(fact_315_le__less__trans,axiom,
! [X2: real_int,Y2: real_int,Z: real_int] :
( ( ord_less_eq_real_int @ X2 @ Y2 )
=> ( ( ord_less_real_int @ Y2 @ Z )
=> ( ord_less_real_int @ X2 @ Z ) ) ) ).
% le_less_trans
thf(fact_316_le__less__trans,axiom,
! [X2: nat,Y2: nat,Z: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ( ord_less_nat @ Y2 @ Z )
=> ( ord_less_nat @ X2 @ Z ) ) ) ).
% le_less_trans
thf(fact_317_less__le__trans,axiom,
! [X2: nat_int,Y2: nat_int,Z: nat_int] :
( ( ord_less_nat_int @ X2 @ Y2 )
=> ( ( ord_less_eq_nat_int @ Y2 @ Z )
=> ( ord_less_nat_int @ X2 @ Z ) ) ) ).
% less_le_trans
thf(fact_318_less__le__trans,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit,Z: view_e774982825t_unit] :
( ( ord_le1993783549t_unit @ X2 @ Y2 )
=> ( ( ord_le461438217t_unit @ Y2 @ Z )
=> ( ord_le1993783549t_unit @ X2 @ Z ) ) ) ).
% less_le_trans
thf(fact_319_less__le__trans,axiom,
! [X2: real_int,Y2: real_int,Z: real_int] :
( ( ord_less_real_int @ X2 @ Y2 )
=> ( ( ord_less_eq_real_int @ Y2 @ Z )
=> ( ord_less_real_int @ X2 @ Z ) ) ) ).
% less_le_trans
thf(fact_320_less__le__trans,axiom,
! [X2: nat,Y2: nat,Z: nat] :
( ( ord_less_nat @ X2 @ Y2 )
=> ( ( ord_less_eq_nat @ Y2 @ Z )
=> ( ord_less_nat @ X2 @ Z ) ) ) ).
% less_le_trans
thf(fact_321_le__less__linear,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
| ( ord_less_nat @ Y2 @ X2 ) ) ).
% le_less_linear
thf(fact_322_le__imp__less__or__eq,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( ord_less_eq_nat_int @ X2 @ Y2 )
=> ( ( ord_less_nat_int @ X2 @ Y2 )
| ( X2 = Y2 ) ) ) ).
% le_imp_less_or_eq
thf(fact_323_le__imp__less__or__eq,axiom,
! [X2: view_e774982825t_unit,Y2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X2 @ Y2 )
=> ( ( ord_le1993783549t_unit @ X2 @ Y2 )
| ( X2 = Y2 ) ) ) ).
% le_imp_less_or_eq
thf(fact_324_le__imp__less__or__eq,axiom,
! [X2: real_int,Y2: real_int] :
( ( ord_less_eq_real_int @ X2 @ Y2 )
=> ( ( ord_less_real_int @ X2 @ Y2 )
| ( X2 = Y2 ) ) ) ).
% le_imp_less_or_eq
thf(fact_325_le__imp__less__or__eq,axiom,
! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ( ord_less_nat @ X2 @ Y2 )
| ( X2 = Y2 ) ) ) ).
% le_imp_less_or_eq
thf(fact_326_less__le__not__le,axiom,
( ord_less_nat_int
= ( ^ [X: nat_int,Y: nat_int] :
( ( ord_less_eq_nat_int @ X @ Y )
& ~ ( ord_less_eq_nat_int @ Y @ X ) ) ) ) ).
% less_le_not_le
thf(fact_327_less__le__not__le,axiom,
( ord_le1993783549t_unit
= ( ^ [X: view_e774982825t_unit,Y: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ X @ Y )
& ~ ( ord_le461438217t_unit @ Y @ X ) ) ) ) ).
% less_le_not_le
thf(fact_328_less__le__not__le,axiom,
( ord_less_real_int
= ( ^ [X: real_int,Y: real_int] :
( ( ord_less_eq_real_int @ X @ Y )
& ~ ( ord_less_eq_real_int @ Y @ X ) ) ) ) ).
% less_le_not_le
thf(fact_329_less__le__not__le,axiom,
( ord_less_nat
= ( ^ [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
& ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% less_le_not_le
thf(fact_330_not__le__imp__less,axiom,
! [Y2: nat,X2: nat] :
( ~ ( ord_less_eq_nat @ Y2 @ X2 )
=> ( ord_less_nat @ X2 @ Y2 ) ) ).
% not_le_imp_less
thf(fact_331_order_Ostrict__trans1,axiom,
! [A2: view_e774982825t_unit,B: view_e774982825t_unit,C2: view_e774982825t_unit] :
( ( ord_le461438217t_unit @ A2 @ B )
=> ( ( ord_le1993783549t_unit @ B @ C2 )
=> ( ord_le1993783549t_unit @ A2 @ C2 ) ) ) ).
% order.strict_trans1
thf(fact_332_order_Ostrict__trans1,axiom,
! [A2: real_int,B: real_int,C2: real_int] :
( ( ord_less_eq_real_int @ A2 @ B )
=> ( ( ord_less_real_int @ B @ C2 )
=> ( ord_less_real_int @ A2 @ C2 ) ) ) ).
% order.strict_trans1
thf(fact_333_order_Ostrict__trans1,axiom,
! [A2: nat,B: nat,C2: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat @ B @ C2 )
=> ( ord_less_nat @ A2 @ C2 ) ) ) ).
% order.strict_trans1
thf(fact_334_view_Ohorizontal__chop__leq2,axiom,
! [V2: view_e774982825t_unit,U3: view_e774982825t_unit,W2: view_e774982825t_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ord_le461438217t_unit @ W2 @ V2 ) ) ).
% view.horizontal_chop_leq2
thf(fact_335_view_Ohorizontal__chop__leq1,axiom,
! [V2: view_e774982825t_unit,U3: view_e774982825t_unit,W2: view_e774982825t_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ord_le461438217t_unit @ U3 @ V2 ) ) ).
% view.horizontal_chop_leq1
thf(fact_336_view_Oswitch__leq,axiom,
! [U5: view_e774982825t_unit,U3: view_e774982825t_unit,V2: view_e774982825t_unit,C2: cars] :
( ( ( ord_le461438217t_unit @ U5 @ U3 )
& ( switch @ V2 @ C2 @ U3 ) )
=> ? [V5: view_e774982825t_unit] :
( ( switch @ V5 @ C2 @ U5 )
& ( ord_le461438217t_unit @ V5 @ V2 ) ) ) ).
% view.switch_leq
thf(fact_337_chop__leq2,axiom,
! [R: real_int,S2: real_int,T: real_int] :
( ( real_R_Chop @ R @ S2 @ T )
=> ( ord_less_eq_real_int @ T @ R ) ) ).
% chop_leq2
thf(fact_338_chop__leq1,axiom,
! [R: real_int,S2: real_int,T: real_int] :
( ( real_R_Chop @ R @ S2 @ T )
=> ( ord_less_eq_real_int @ S2 @ R ) ) ).
% chop_leq1
thf(fact_339_card__subset__le,axiom,
! [I: nat_int,I2: nat_int] :
( ( ord_less_eq_nat_int @ I @ I2 )
=> ( ord_less_eq_nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% card_subset_le
thf(fact_340_traffic_Oclm__consec__res,axiom,
! [Ts4: traffic,C2: cars] :
( ( ( clm @ Ts4 @ C2 )
!= bot_bot_nat_int )
=> ( ( nat_consec @ ( clm @ Ts4 @ C2 ) @ ( res @ Ts4 @ C2 ) )
| ( nat_consec @ ( res @ Ts4 @ C2 ) @ ( clm @ Ts4 @ C2 ) ) ) ) ).
% traffic.clm_consec_res
thf(fact_341_card__subset__less,axiom,
! [I: nat_int,I2: nat_int] :
( ( ord_less_nat_int @ I @ I2 )
=> ( ord_less_nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% card_subset_less
thf(fact_342_consec__intermediate2,axiom,
! [I: nat_int,J: nat_int,K: nat_int] :
( ( ( nat_consec @ I @ J )
& ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
=> ( nat_consec @ J @ K ) ) ).
% consec_intermediate2
thf(fact_343_consec__intermediate1,axiom,
! [J: nat_int,K: nat_int,I: nat_int] :
( ( ( nat_consec @ J @ K )
& ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
=> ( nat_consec @ I @ J ) ) ).
% consec_intermediate1
thf(fact_344_consec__assoc2,axiom,
! [I: nat_int,J: nat_int,K: nat_int] :
( ( ( nat_consec @ I @ J )
& ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
=> ( nat_consec @ I @ ( nat_union @ J @ K ) ) ) ).
% consec_assoc2
thf(fact_345_consec__assoc1,axiom,
! [J: nat_int,K: nat_int,I: nat_int] :
( ( ( nat_consec @ J @ K )
& ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
=> ( nat_consec @ ( nat_union @ I @ J ) @ K ) ) ).
% consec_assoc1
thf(fact_346_un__assoc,axiom,
! [I: nat_int,J: nat_int,K: nat_int] :
( ( ( nat_consec @ I @ J )
& ( nat_consec @ J @ K ) )
=> ( ( nat_union @ ( nat_union @ I @ J ) @ K )
= ( nat_union @ I @ ( nat_union @ J @ K ) ) ) ) ).
% un_assoc
thf(fact_347_consec__assoc__mult,axiom,
! [I22: nat_int,I1: nat_int,I3: nat_int,I4: nat_int] :
( ( ( ( I22 = bot_bot_nat_int )
| ( nat_consec @ I1 @ I22 ) )
& ( ( I3 = bot_bot_nat_int )
| ( nat_consec @ I3 @ I4 ) )
& ( nat_consec @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) ) )
=> ( ( nat_union @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) )
= ( nat_union @ ( nat_union @ I1 @ ( nat_union @ I22 @ I3 ) ) @ I4 ) ) ) ).
% consec_assoc_mult
thf(fact_348_un__subset2,axiom,
! [I: nat_int,J: nat_int] :
( ( nat_consec @ I @ J )
=> ( ord_less_eq_nat_int @ J @ ( nat_union @ I @ J ) ) ) ).
% un_subset2
thf(fact_349_un__subset1,axiom,
! [I: nat_int,J: nat_int] :
( ( nat_consec @ I @ J )
=> ( ord_less_eq_nat_int @ I @ ( nat_union @ I @ J ) ) ) ).
% un_subset1
thf(fact_350_nchop__def,axiom,
( nat_N_Chop
= ( ^ [I5: nat_int,J2: nat_int,K2: nat_int] :
( ( I5
= ( nat_union @ J2 @ K2 ) )
& ( ( J2 = bot_bot_nat_int )
| ( K2 = bot_bot_nat_int )
| ( nat_consec @ J2 @ K2 ) ) ) ) ) ).
% nchop_def
thf(fact_351_consec__un__not__elem2,axiom,
! [I: nat_int,J: nat_int,N: nat] :
( ( ( nat_consec @ I @ J )
& ( nat_not_in @ N @ ( nat_union @ I @ J ) ) )
=> ( nat_not_in @ N @ J ) ) ).
% consec_un_not_elem2
% Helper facts (5)
thf(help_If_2_1_If_001t__NatInt__Onat____int_T,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( if_nat_int @ $false @ X2 @ Y2 )
= Y2 ) ).
thf(help_If_1_1_If_001t__NatInt__Onat____int_T,axiom,
! [X2: nat_int,Y2: nat_int] :
( ( if_nat_int @ $true @ X2 @ Y2 )
= X2 ) ).
thf(help_If_3_1_If_001_062_It__Real__Oreal_Mt__Real__Oreal_J_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001_062_It__Real__Oreal_Mt__Real__Oreal_J_T,axiom,
! [X2: real > real,Y2: real > real] :
( ( if_real_real @ $false @ X2 @ Y2 )
= Y2 ) ).
thf(help_If_1_1_If_001_062_It__Real__Oreal_Mt__Real__Oreal_J_T,axiom,
! [X2: real > real,Y2: real > real] :
( ( if_real_real @ $true @ X2 @ Y2 )
= X2 ) ).
% Conjectures (1)
thf(conj_0,conjecture,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ) ).
%------------------------------------------------------------------------------