TPTP Problem File: ITP168^2.p
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%------------------------------------------------------------------------------
% File : ITP168^2 : 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 : 0.33 v8.1.0, 0.25 v7.5.0
% Syntax : Number of formulae : 381 ( 114 unt; 67 typ; 0 def)
% Number of atoms : 937 ( 222 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 3532 ( 81 ~; 27 |; 140 &;2816 @)
% ( 0 <=>; 468 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 234 ( 234 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 8 con; 0-6 aty)
% Number of variables : 1170 ( 78 ^; 948 !; 113 ?;1170 :)
% ( 31 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 16:21:50.823
%------------------------------------------------------------------------------
% Could-be-implicit typings (8)
thf(ty_t_Views_Oview_Oview__ext,type,
view_ext: $tType > $tType ).
thf(ty_t_Product__Type_Ounit,type,
product_unit: $tType ).
thf(ty_t_RealInt_Oreal__int,type,
real_int: $tType ).
thf(ty_t_Traffic_Otraffic,type,
traffic: $tType ).
thf(ty_t_NatInt_Onat__int,type,
nat_int: $tType ).
thf(ty_t_Real_Oreal,type,
real: $tType ).
thf(ty_t_Cars_Ocars,type,
cars: $tType ).
thf(ty_t_Nat_Onat,type,
nat: $tType ).
% Explicit typings (59)
thf(sy_cl_HOL_Otype,type,
type:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ominus,type,
minus:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Obot,type,
bot:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Oord,type,
ord:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Oorder,type,
order:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ogroup__add,type,
group_add:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Ono__bot,type,
no_bot:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Ono__top,type,
no_top:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Olinorder,type,
linorder:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Opreorder,type,
preorder:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Oorder__bot,type,
order_bot:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Owellorder,type,
wellorder:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Odense__order,type,
dense_order:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Odense__linorder,type,
dense_linorder:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Oordered__ab__group__add,type,
ordered_ab_group_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
cancel146912293up_add:
!>[A: $tType] : $o ).
thf(sy_c_Fun_Ofun__upd,type,
fun_upd:
!>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
thf(sy_c_Groups_Ominus__class_Ominus,type,
minus_minus:
!>[A: $tType] : ( A > A > A ) ).
thf(sy_c_HOL_Odefault__class_Odefault,type,
default_default:
!>[A: $tType] : A ).
thf(sy_c_If,type,
if:
!>[A: $tType] : ( $o > A > A > A ) ).
thf(sy_c_Move_Otraffic_Omove,type,
move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_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,type,
bot_bot:
!>[A: $tType] : A ).
thf(sy_c_Orderings_Oord__class_Oless,type,
ord_less:
!>[A: $tType] : ( A > A > $o ) ).
thf(sy_c_Orderings_Oord__class_Oless__eq,type,
ord_less_eq:
!>[A: $tType] : ( A > A > $o ) ).
thf(sy_c_Orderings_Oorder__class_OGreatest,type,
order_Greatest:
!>[A: $tType] : ( ( A > $o ) > A ) ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
product_rec_unit:
!>[T: $tType] : ( T > product_unit > T ) ).
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,type,
ext:
!>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
thf(sy_c_Views_Oview_Ohchop,type,
hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
thf(sy_c_Views_Oview_Olan,type,
lan:
!>[Z: $tType] : ( ( view_ext @ Z ) > nat_int ) ).
thf(sy_c_Views_Oview_Omore,type,
more:
!>[Z: $tType] : ( ( view_ext @ Z ) > Z ) ).
thf(sy_c_Views_Oview_Oown,type,
own:
!>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
thf(sy_c_Views_Oview_Oswitch,type,
switch: ( view_ext @ product_unit ) > cars > ( view_ext @ product_unit ) > $o ).
thf(sy_c_Views_Oview_Oview__ext,type,
view_ext2:
!>[Z: $tType] : ( real_int > nat_int > cars > Z > ( view_ext @ Z ) ) ).
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_ext @ product_unit ).
% Relevant facts (256)
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_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_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__all__iff,axiom,
! [A: $tType,B: $tType,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [Ts4: traffic] :
( ( abstract @ Ts @ Ts4 )
=> ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) )
= ( ! [X: B,Ts4: traffic] :
( ( abstract @ Ts @ Ts4 )
=> ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) ) ) ).
% local.hmlsl.globally_all_iff
thf(fact_4_local_Ohmlsl_Oglobally__all__iff_H,axiom,
! [A: $tType,B: $tType,Ts5: traffic,Phi: traffic > ( view_ext @ product_unit ) > $o,V2: view_ext @ product_unit] :
( ( ! [Ts4: traffic] :
( ( abstract @ Ts5 @ Ts4 )
=> ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) )
= ( ! [X: B,Ts4: traffic] :
( ( abstract @ Ts5 @ Ts4 )
=> ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) ) ) ).
% local.hmlsl.globally_all_iff'
thf(fact_5_local_Ohmlsl_Oglobally__refl,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ! [Ts2: traffic] :
( ( abstract @ Ts @ Ts2 )
=> ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
=> ( Phi @ Ts @ V ) ) ).
% local.hmlsl.globally_refl
thf(fact_6_abs,axiom,
abstract @ ts3 @ ts2 ).
% abs
thf(fact_7__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_8_traffic_Omove__nothing,axiom,
! [Ts5: traffic,V2: view_ext @ product_unit] :
( ( move @ Ts5 @ Ts5 @ V2 )
= V2 ) ).
% traffic.move_nothing
thf(fact_9_traffic_Omove__def,axiom,
( move
= ( ^ [Ts6: traffic,Ts4: traffic,V3: view_ext @ product_unit] : ( view_ext2 @ product_unit @ ( real_shift @ ( ext @ product_unit @ V3 ) @ ( minus_minus @ real @ ( pos @ Ts4 @ ( own @ product_unit @ V3 ) ) @ ( pos @ Ts6 @ ( own @ product_unit @ V3 ) ) ) ) @ ( lan @ product_unit @ V3 ) @ ( own @ product_unit @ V3 ) @ product_Unity ) ) ) ).
% traffic.move_def
thf(fact_10_traffic_Omove__stability__res,axiom,
! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
( ( create_reservation @ Ts5 @ C2 @ Ts7 )
=> ( ( move @ Ts5 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_res
thf(fact_11_traffic_Omove__keeps__owner,axiom,
! [Ts5: traffic,Ts7: traffic] :
( ( own @ product_unit )
= ( ^ [V3: view_ext @ product_unit] : ( own @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% traffic.move_keeps_owner
thf(fact_12_traffic_Omove__trans,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic,V2: view_ext @ product_unit] :
( ( ( abstract @ Ts5 @ Ts7 )
& ( abstract @ Ts7 @ Ts8 ) )
=> ( ( move @ Ts7 @ Ts8 @ ( move @ Ts5 @ Ts7 @ V2 ) )
= ( move @ Ts5 @ Ts8 @ V2 ) ) ) ).
% traffic.move_trans
thf(fact_13_traffic_Omove__keeps__lanes,axiom,
! [Ts5: traffic,Ts7: traffic] :
( ( lan @ product_unit )
= ( ^ [V3: view_ext @ product_unit] : ( lan @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% traffic.move_keeps_lanes
thf(fact_14_traffic_Omove__stability__clm,axiom,
! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
( ( create_claim @ Ts5 @ C2 @ N @ Ts7 )
=> ( ( move @ Ts5 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_clm
thf(fact_15_traffic_Omove__stability__wdc,axiom,
! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
( ( withdraw_claim @ Ts5 @ C2 @ Ts7 )
=> ( ( move @ Ts5 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_wdc
thf(fact_16_traffic_Omove__stability__wdr,axiom,
! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
( ( withdraw_reservation @ Ts5 @ C2 @ N @ Ts7 )
=> ( ( move @ Ts5 @ Ts7 @ V2 )
= V2 ) ) ).
% traffic.move_stability_wdr
thf(fact_17_local_Ohmlsl_Ohchop__assoc,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
( ( hchop @ U @ X @ Y )
& ( Psi @ Ts @ X )
& ( Chi @ Ts @ Y ) ) ) )
= ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
( ( hchop @ W @ X @ Y )
& ( Phi @ Ts @ X )
& ( Psi @ Ts @ Y ) )
& ( Chi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_assoc
thf(fact_18_local_Ohmlsl_Ohchop__disj__distr1,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( ( Psi @ Ts @ U )
| ( Chi @ Ts @ U ) ) ) )
= ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( Psi @ Ts @ U ) )
| ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Phi @ Ts @ W )
& ( Chi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_disj_distr1
thf(fact_19_local_Ohmlsl_Ohchop__disj__distr2,axiom,
! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( ( Psi @ Ts @ W )
| ( Chi @ Ts @ W ) )
& ( Phi @ Ts @ U ) ) )
= ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Psi @ Ts @ W )
& ( Phi @ Ts @ U ) )
| ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( Chi @ Ts @ W )
& ( Phi @ Ts @ U ) ) ) ) ).
% local.hmlsl.hchop_disj_distr2
thf(fact_20_local_Ohmlsl_Ohchop__weaken2,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V @ Va @ U2 )
& ( Phi @ Ts @ U2 ) ) ) ).
% local.hmlsl.hchop_weaken2
thf(fact_21_local_Ohmlsl_Ohchop__weaken1,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_ext @ product_unit] :
( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
& ( Phi @ Ts @ Va ) ) ) ).
% local.hmlsl.hchop_weaken1
thf(fact_22_local_Ohmlsl_Ohchop__weaken,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( Phi @ Ts @ V )
=> ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V @ Va @ U2 )
& ? [Vb: view_ext @ product_unit] :
( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb @ X_1 )
& ( Phi @ Ts @ Vb ) ) ) ) ).
% local.hmlsl.hchop_weaken
thf(fact_23_local_Ohmlsl_Ohchop__neg2,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ~ ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V @ Va @ U2 )
& ( Phi @ Ts @ U2 ) )
=> ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V @ Va @ U2 )
& ~ ( Phi @ Ts @ U2 ) ) ) ).
% local.hmlsl.hchop_neg2
thf(fact_24_local_Ohmlsl_Ohchop__neg1,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ~ ? [Va: view_ext @ product_unit] :
( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
& ( Phi @ Ts @ Va ) )
=> ? [Va: view_ext @ product_unit] :
( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
& ~ ( Phi @ Ts @ Va ) ) ) ).
% local.hmlsl.hchop_neg1
thf(fact_25_ext__inject,axiom,
! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z,Ext2: real_int,Lan2: nat_int,Own2: cars,More2: Z] :
( ( ( view_ext2 @ Z @ Ext @ Lan @ Own @ More )
= ( view_ext2 @ Z @ Ext2 @ Lan2 @ Own2 @ More2 ) )
= ( ( Ext = Ext2 )
& ( Lan = Lan2 )
& ( Own = Own2 )
& ( More = More2 ) ) ) ).
% ext_inject
thf(fact_26_cases,axiom,
! [R: view_ext @ product_unit] :
~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars] :
( R
!= ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) ) ).
% cases
thf(fact_27_induct,axiom,
! [P: ( view_ext @ product_unit ) > $o,R: view_ext @ product_unit] :
( ! [Ext3: real_int,Lan3: nat_int,Own3: cars] : ( P @ ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) )
=> ( P @ R ) ) ).
% induct
thf(fact_28_traffic_Ocr__clm,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts5 @ Ts7 )
=> ( ? [C3: cars,N2: nat] : ( create_claim @ Ts7 @ C3 @ N2 @ Ts8 )
=> ( abstract @ Ts5 @ Ts8 ) ) ) ).
% traffic.cr_clm
thf(fact_29_traffic_Owd__clm,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts5 @ Ts7 )
=> ( ? [C3: cars] : ( withdraw_claim @ Ts7 @ C3 @ Ts8 )
=> ( abstract @ Ts5 @ Ts8 ) ) ) ).
% traffic.wd_clm
thf(fact_30_traffic_Owd__res,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts5 @ Ts7 )
=> ( ? [C3: cars,N2: nat] : ( withdraw_reservation @ Ts7 @ C3 @ N2 @ Ts8 )
=> ( abstract @ Ts5 @ Ts8 ) ) ) ).
% traffic.wd_res
thf(fact_31_minus__apply,axiom,
! [B: $tType,A: $tType] :
( ( minus @ B )
=> ( ( minus_minus @ ( A > B ) )
= ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% minus_apply
thf(fact_32_traffic_Ocr__res,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts5 @ Ts7 )
=> ( ? [C3: cars] : ( create_reservation @ Ts7 @ C3 @ Ts8 )
=> ( abstract @ Ts5 @ Ts8 ) ) ) ).
% traffic.cr_res
thf(fact_33_select__convs_I3_J,axiom,
! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
( ( own @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
= Own ) ).
% select_convs(3)
thf(fact_34_select__convs_I2_J,axiom,
! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
( ( lan @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
= Lan ) ).
% select_convs(2)
thf(fact_35_fun__diff__def,axiom,
! [B: $tType,A: $tType] :
( ( minus @ B )
=> ( ( minus_minus @ ( A > B ) )
= ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% fun_diff_def
thf(fact_36_view_Ohorizontal__chop__empty__right,axiom,
! [V: view_ext @ product_unit] :
? [X_1: view_ext @ product_unit] : ( hchop @ V @ V @ X_1 ) ).
% view.horizontal_chop_empty_right
thf(fact_37_view_Ohorizontal__chop__empty__left,axiom,
! [V: view_ext @ product_unit] :
? [U2: view_ext @ product_unit] : ( hchop @ V @ U2 @ V ) ).
% view.horizontal_chop_empty_left
thf(fact_38_view_Ohorizontal__chop__assoc2,axiom,
! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( hchop @ V1 @ V32 @ V4 ) )
=> ? [V5: view_ext @ product_unit] :
( ( hchop @ V2 @ V32 @ V5 )
& ( hchop @ V5 @ V4 @ V22 ) ) ) ).
% view.horizontal_chop_assoc2
thf(fact_39_view_Ohorizontal__chop__assoc1,axiom,
! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( hchop @ V22 @ V32 @ V4 ) )
=> ? [V5: view_ext @ product_unit] :
( ( hchop @ V2 @ V5 @ V4 )
& ( hchop @ V5 @ V1 @ V32 ) ) ) ).
% view.horizontal_chop_assoc1
thf(fact_40_view_Ohorizontal__chop1,axiom,
! [V2: view_ext @ product_unit] :
? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% view.horizontal_chop1
thf(fact_41_traffic_Oabstract_Orefl,axiom,
! [Ts5: traffic] : ( abstract @ Ts5 @ Ts5 ) ).
% traffic.abstract.refl
thf(fact_42_traffic_Oabs__trans,axiom,
! [Ts1: traffic,Ts22: traffic,Ts0: traffic] :
( ( abstract @ Ts1 @ Ts22 )
=> ( ( abstract @ Ts0 @ Ts1 )
=> ( abstract @ Ts0 @ Ts22 ) ) ) ).
% traffic.abs_trans
thf(fact_43_induct__scheme,axiom,
! [Z: $tType,P: ( view_ext @ Z ) > $o,R: view_ext @ Z] :
( ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] : ( P @ ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) )
=> ( P @ R ) ) ).
% induct_scheme
thf(fact_44_cases__scheme,axiom,
! [Z: $tType,R: view_ext @ Z] :
~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] :
( R
!= ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) ) ).
% cases_scheme
thf(fact_45_ext,axiom,
! [B: $tType,A: $tType,F: A > B,G: A > B] :
( ! [X2: A] :
( ( F @ X2 )
= ( G @ X2 ) )
=> ( F = G ) ) ).
% ext
thf(fact_46_traffic_Oalways__create__res,axiom,
! [C2: cars,Ts: traffic] :
? [X_1: traffic] : ( create_reservation @ Ts @ C2 @ X_1 ) ).
% traffic.always_create_res
thf(fact_47_view_Ohorizontal__chop__own__trans,axiom,
! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ( own @ product_unit @ U3 )
= ( own @ product_unit @ W2 ) ) ) ).
% view.horizontal_chop_own_trans
thf(fact_48_select__convs_I1_J,axiom,
! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
( ( ext @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
= Ext ) ).
% select_convs(1)
thf(fact_49_traffic_Ocreate__reservation__def,axiom,
( create_reservation
= ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
( ( ( pos @ Ts4 )
= ( pos @ Ts6 ) )
& ( ( res @ Ts4 )
= ( fun_upd @ cars @ nat_int @ ( res @ Ts6 ) @ C4 @ ( nat_union @ ( res @ Ts6 @ C4 ) @ ( clm @ Ts6 @ C4 ) ) ) )
& ( ( dyn @ Ts4 )
= ( dyn @ Ts6 ) )
& ( ( clm @ Ts4 )
= ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) )
& ( ( physical_size @ Ts4 )
= ( physical_size @ Ts6 ) )
& ( ( braking_distance @ Ts4 )
= ( braking_distance @ Ts6 ) ) ) ) ) ).
% traffic.create_reservation_def
thf(fact_50_traffic_Oabstract_Oinducts,axiom,
! [Ts5: traffic,X3: traffic,P: traffic > $o] :
( ( abstract @ Ts5 @ X3 )
=> ( ( P @ Ts5 )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ( evolve @ Ts2 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars] : ( create_reservation @ Ts2 @ C @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( ! [Ts2: traffic,Ts9: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ( ( P @ Ts2 )
=> ( ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ Ts9 )
=> ( P @ Ts9 ) ) ) )
=> ( P @ X3 ) ) ) ) ) ) ) ) ).
% traffic.abstract.inducts
thf(fact_51_traffic_Oabstract_Osimps,axiom,
( abstract
= ( ^ [Ts6: traffic,A3: traffic] :
( ( A3 = Ts6 )
| ? [Ts4: traffic,Ts10: traffic] :
( ( A3 = Ts10 )
& ( abstract @ Ts6 @ Ts4 )
& ( evolve @ Ts4 @ Ts10 ) )
| ? [Ts4: traffic,Ts10: traffic] :
( ( A3 = Ts10 )
& ( abstract @ Ts6 @ Ts4 )
& ? [C4: cars,N4: nat] : ( create_claim @ Ts4 @ C4 @ N4 @ Ts10 ) )
| ? [Ts4: traffic,Ts10: traffic] :
( ( A3 = Ts10 )
& ( abstract @ Ts6 @ Ts4 )
& ? [C4: cars] : ( withdraw_claim @ Ts4 @ C4 @ Ts10 ) )
| ? [Ts4: traffic,Ts10: traffic] :
( ( A3 = Ts10 )
& ( abstract @ Ts6 @ Ts4 )
& ? [C4: cars] : ( create_reservation @ Ts4 @ C4 @ Ts10 ) )
| ? [Ts4: traffic,Ts10: traffic] :
( ( A3 = Ts10 )
& ( abstract @ Ts6 @ Ts4 )
& ? [C4: cars,N4: nat] : ( withdraw_reservation @ Ts4 @ C4 @ N4 @ Ts10 ) ) ) ) ) ).
% traffic.abstract.simps
thf(fact_52_traffic_Oabstract_Ocases,axiom,
! [Ts5: traffic,A4: traffic] :
( ( abstract @ Ts5 @ A4 )
=> ( ( A4 != Ts5 )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ~ ( evolve @ Ts2 @ A4 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ~ ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ A4 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ~ ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ A4 ) )
=> ( ! [Ts2: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ~ ? [C: cars] : ( create_reservation @ Ts2 @ C @ A4 ) )
=> ~ ! [Ts2: traffic] :
( ( abstract @ Ts5 @ Ts2 )
=> ~ ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ A4 ) ) ) ) ) ) ) ) ).
% traffic.abstract.cases
thf(fact_53_surjective,axiom,
! [Z: $tType,R: view_ext @ Z] :
( R
= ( view_ext2 @ Z @ ( ext @ Z @ R ) @ ( lan @ Z @ R ) @ ( own @ Z @ R ) @ ( more @ Z @ R ) ) ) ).
% surjective
thf(fact_54_traffic_Owithdraw__clm__eq__res,axiom,
! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( withdraw_claim @ Ts5 @ D @ Ts7 )
=> ( ( res @ Ts5 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.withdraw_clm_eq_res
thf(fact_55_traffic_Ocreate__clm__eq__res,axiom,
! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
( ( create_claim @ Ts5 @ D @ N @ Ts7 )
=> ( ( res @ Ts5 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_clm_eq_res
thf(fact_56_traffic_Ocreate__res__subseteq1__neq,axiom,
! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( ( create_reservation @ Ts5 @ D @ Ts7 )
& ( D != C2 ) )
=> ( ( res @ Ts5 @ C2 )
= ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq1_neq
thf(fact_57_traffic_Ocreate__res__subseteq2__neq,axiom,
! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
( ( ( create_reservation @ Ts5 @ D @ Ts7 )
& ( D != C2 ) )
=> ( ( clm @ Ts5 @ C2 )
= ( clm @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq2_neq
thf(fact_58_traffic_Oevolve__trans,axiom,
! [Ts0: traffic,Ts1: traffic,Ts22: traffic] :
( ( evolve @ Ts0 @ Ts1 )
=> ( ( evolve @ Ts1 @ Ts22 )
=> ( evolve @ Ts0 @ Ts22 ) ) ) ).
% traffic.evolve_trans
thf(fact_59_traffic_Oevolve_Orefl,axiom,
! [Ts5: traffic] : ( evolve @ Ts5 @ Ts5 ) ).
% traffic.evolve.refl
thf(fact_60_traffic_Owithdraw__claim__def,axiom,
( withdraw_claim
= ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
( ( ( pos @ Ts4 )
= ( pos @ Ts6 ) )
& ( ( res @ Ts4 )
= ( res @ Ts6 ) )
& ( ( dyn @ Ts4 )
= ( dyn @ Ts6 ) )
& ( ( physical_size @ Ts4 )
= ( physical_size @ Ts6 ) )
& ( ( braking_distance @ Ts4 )
= ( braking_distance @ Ts6 ) )
& ( ( clm @ Ts4 )
= ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) ) ) ) ) ).
% traffic.withdraw_claim_def
thf(fact_61_traffic_Oevolve,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ( abstract @ Ts5 @ Ts7 )
=> ( ( evolve @ Ts7 @ Ts8 )
=> ( abstract @ Ts5 @ Ts8 ) ) ) ).
% traffic.evolve
thf(fact_62_select__convs_I4_J,axiom,
! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
( ( more @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
= More ) ).
% select_convs(4)
thf(fact_63_equality,axiom,
! [Z: $tType,R: view_ext @ Z,R2: view_ext @ Z] :
( ( ( ext @ Z @ R )
= ( ext @ Z @ R2 ) )
=> ( ( ( lan @ Z @ R )
= ( lan @ Z @ R2 ) )
=> ( ( ( own @ Z @ R )
= ( own @ Z @ R2 ) )
=> ( ( ( more @ Z @ R )
= ( more @ Z @ R2 ) )
=> ( R = R2 ) ) ) ) ) ).
% equality
thf(fact_64_fun__upd__upd,axiom,
! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,Z2: B] :
( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X3 @ Y2 ) @ X3 @ Z2 )
= ( fun_upd @ A @ B @ F @ X3 @ Z2 ) ) ).
% fun_upd_upd
thf(fact_65_fun__upd__triv,axiom,
! [B: $tType,A: $tType,F: A > B,X3: A] :
( ( fun_upd @ A @ B @ F @ X3 @ ( F @ X3 ) )
= F ) ).
% fun_upd_triv
thf(fact_66_fun__upd__apply,axiom,
! [A: $tType,B: $tType] :
( ( fun_upd @ B @ A )
= ( ^ [F2: B > A,X: B,Y: A,Z3: B] : ( if @ A @ ( Z3 = X ) @ Y @ ( F2 @ Z3 ) ) ) ) ).
% fun_upd_apply
thf(fact_67_bot__apply,axiom,
! [C5: $tType,D2: $tType] :
( ( bot @ C5 )
=> ( ( bot_bot @ ( D2 > C5 ) )
= ( ^ [X: D2] : ( bot_bot @ C5 ) ) ) ) ).
% bot_apply
thf(fact_68_un__empty__absorb1,axiom,
! [I: nat_int] :
( ( nat_union @ I @ ( bot_bot @ nat_int ) )
= I ) ).
% un_empty_absorb1
thf(fact_69_un__empty__absorb2,axiom,
! [I: nat_int] :
( ( nat_union @ ( bot_bot @ nat_int ) @ I )
= I ) ).
% un_empty_absorb2
thf(fact_70_view_Ohchop__def,axiom,
( hchop
= ( ^ [V3: view_ext @ product_unit,U: view_ext @ product_unit,W: view_ext @ product_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_71_bot__fun__def,axiom,
! [B: $tType,A: $tType] :
( ( bot @ B )
=> ( ( bot_bot @ ( A > B ) )
= ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% bot_fun_def
thf(fact_72_fun__upd__idem__iff,axiom,
! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B] :
( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
= F )
= ( ( F @ X3 )
= Y2 ) ) ).
% fun_upd_idem_iff
thf(fact_73_fun__upd__twist,axiom,
! [A: $tType,B: $tType,A4: A,C2: A,M: A > B,B3: B,D: B] :
( ( A4 != C2 )
=> ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A4 @ B3 ) @ C2 @ D )
= ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A4 @ B3 ) ) ) ).
% fun_upd_twist
thf(fact_74_fun__upd__other,axiom,
! [B: $tType,A: $tType,Z2: A,X3: A,F: A > B,Y2: B] :
( ( Z2 != X3 )
=> ( ( fun_upd @ A @ B @ F @ X3 @ Y2 @ Z2 )
= ( F @ Z2 ) ) ) ).
% fun_upd_other
thf(fact_75_fun__upd__same,axiom,
! [B: $tType,A: $tType,F: B > A,X3: B,Y2: A] :
( ( fun_upd @ B @ A @ F @ X3 @ Y2 @ X3 )
= Y2 ) ).
% fun_upd_same
thf(fact_76_fun__upd__idem,axiom,
! [A: $tType,B: $tType,F: B > A,X3: B,Y2: A] :
( ( ( F @ X3 )
= Y2 )
=> ( ( fun_upd @ B @ A @ F @ X3 @ Y2 )
= F ) ) ).
% fun_upd_idem
thf(fact_77_fun__upd__eqD,axiom,
! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,G: A > B,Z2: B] :
( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
= ( fun_upd @ A @ B @ G @ X3 @ Z2 ) )
=> ( Y2 = Z2 ) ) ).
% fun_upd_eqD
thf(fact_78_fun__upd__def,axiom,
! [B: $tType,A: $tType] :
( ( fun_upd @ A @ B )
= ( ^ [F2: A > B,A3: A,B4: B,X: A] : ( if @ B @ ( X = A3 ) @ B4 @ ( F2 @ X ) ) ) ) ).
% fun_upd_def
thf(fact_79_traffic_Ochange__dyn__def,axiom,
( change_dyn
= ( ^ [Ts6: traffic,C4: cars,F2: real > real,Ts4: traffic] :
( ( ( pos @ Ts4 )
= ( pos @ Ts6 ) )
& ( ( res @ Ts4 )
= ( res @ Ts6 ) )
& ( ( clm @ Ts4 )
= ( clm @ Ts6 ) )
& ( ( dyn @ Ts4 )
= ( fun_upd @ cars @ ( real > real ) @ ( dyn @ Ts6 ) @ C4 @ F2 ) )
& ( ( physical_size @ Ts4 )
= ( physical_size @ Ts6 ) ) ) ) ) ).
% traffic.change_dyn_def
thf(fact_80_local_Ohmlsl_Owidth__hchop__stable,axiom,
! [X3: nat,Ts: traffic,V: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ V ) )
= X3 )
= ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ( ( nat_card @ ( lan @ product_unit @ W ) )
= X3 )
& ( ( nat_card @ ( lan @ product_unit @ U ) )
= X3 ) ) ) ) ).
% local.hmlsl.width_hchop_stable
thf(fact_81_chop__singleton__right,axiom,
! [R3: real_int] :
? [X_1: real_int] : ( real_R_Chop @ R3 @ R3 @ X_1 ) ).
% chop_singleton_right
thf(fact_82_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_83_chop__singleton__left,axiom,
! [R3: real_int] :
? [S: real_int] : ( real_R_Chop @ R3 @ S @ R3 ) ).
% chop_singleton_left
thf(fact_84_view_Oswitch__def,axiom,
( switch
= ( ^ [V3: view_ext @ product_unit,C4: cars,W: view_ext @ product_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_85_local_Ohmlsl_Oat__conj__distr,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( ( Phi @ Ts @ V6 )
& ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
& ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_conj_distr
thf(fact_86_local_Ohmlsl_Oat__disj__dist,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( ( Phi @ Ts @ V6 )
| ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
| ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_disj_dist
thf(fact_87_local_Ohmlsl_Oat__eq,axiom,
! [A: $tType,E: cars,C2: A,D: A,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ E @ V6 )
=> ( C2 = D ) ) )
= ( C2 = D ) ) ).
% local.hmlsl.at_eq
thf(fact_88_local_Ohmlsl_Oat__exists,axiom,
! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( Phi @ Ts @ V )
=> ? [X2: cars] :
! [V7: view_ext @ product_unit] :
( ( switch @ V @ X2 @ V7 )
=> ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_exists
thf(fact_89_local_Ohmlsl_Oat__neg,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ~ ( Phi @ Ts @ V6 ) ) )
= ( ~ ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_neg
thf(fact_90_local_Ohmlsl_Oat__neg_H,axiom,
! [V2: view_ext @ product_unit,C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts5: traffic] :
( ( ~ ! [V6: view_ext @ product_unit] :
( ( switch @ V2 @ C2 @ V6 )
=> ( Phi @ Ts5 @ V6 ) ) )
= ( ! [V6: view_ext @ product_unit] :
( ( switch @ V2 @ C2 @ V6 )
=> ~ ( Phi @ Ts5 @ V6 ) ) ) ) ).
% local.hmlsl.at_neg'
thf(fact_91_local_Ohmlsl_Oat__neg1,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ! [V5: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V5 )
=> ~ ( Phi @ Ts @ V5 ) )
=> ~ ! [V5: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) ) ) ).
% local.hmlsl.at_neg1
thf(fact_92_local_Ohmlsl_Oat__neg2,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ~ ! [V7: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) )
=> ! [V7: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V7 )
=> ~ ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_neg2
thf(fact_93_local_Ohmlsl_Oat__neg__neg,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) ) )
= ( ~ ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ~ ( Phi @ Ts @ V6 ) ) ) ) ).
% local.hmlsl.at_neg_neg
thf(fact_94_local_Ohmlsl_Oat__neg__neg1,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ! [V5: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) )
=> ~ ! [V5: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V5 )
=> ~ ( Phi @ Ts @ V5 ) ) ) ).
% local.hmlsl.at_neg_neg1
thf(fact_95_local_Ohmlsl_Oat__neg__neg2,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ~ ! [V7: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V7 )
=> ~ ( Phi @ Ts @ V7 ) )
=> ! [V7: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) ) ) ).
% local.hmlsl.at_neg_neg2
thf(fact_96_local_Ohmlsl_Oat__hchop__dist,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V @ W @ U )
& ! [V6: view_ext @ product_unit] :
( ( switch @ W @ C2 @ V6 )
=> ( Phi @ Ts @ V6 ) )
& ! [V6: view_ext @ product_unit] :
( ( switch @ U @ C2 @ V6 )
=> ( Psi @ Ts @ V6 ) ) ) )
= ( ! [V6: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V6 )
=> ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
( ( hchop @ V6 @ W @ U )
& ( Phi @ Ts @ W )
& ( Psi @ Ts @ U ) ) ) ) ) ).
% local.hmlsl.at_hchop_dist
thf(fact_97_local_Ohmlsl_Oat__hchop__dist1,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ! [V5: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V5 )
=> ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
( ( hchop @ V5 @ Va2 @ U4 )
& ( Phi @ Ts @ Va2 )
& ( Psi @ Ts @ U4 ) ) )
=> ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V @ Va @ U2 )
& ! [V7: view_ext @ product_unit] :
( ( switch @ Va @ C2 @ V7 )
=> ( Phi @ Ts @ V7 ) )
& ! [V7: view_ext @ product_unit] :
( ( switch @ U2 @ C2 @ V7 )
=> ( Psi @ Ts @ V7 ) ) ) ) ).
% local.hmlsl.at_hchop_dist1
thf(fact_98_local_Ohmlsl_Oat__hchop__dist2,axiom,
! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
( ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
( ( hchop @ V @ Va2 @ U4 )
& ! [V5: view_ext @ product_unit] :
( ( switch @ Va2 @ C2 @ V5 )
=> ( Phi @ Ts @ V5 ) )
& ! [V5: view_ext @ product_unit] :
( ( switch @ U4 @ C2 @ V5 )
=> ( Psi @ Ts @ V5 ) ) )
=> ! [V7: view_ext @ product_unit] :
( ( switch @ V @ C2 @ V7 )
=> ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
( ( hchop @ V7 @ Va @ U2 )
& ( Phi @ Ts @ Va )
& ( Psi @ Ts @ U2 ) ) ) ) ).
% local.hmlsl.at_hchop_dist2
thf(fact_99_view_Oswitch__always__exists,axiom,
! [V2: view_ext @ product_unit,C3: cars] :
? [X_1: view_ext @ product_unit] : ( switch @ V2 @ C3 @ X_1 ) ).
% view.switch_always_exists
thf(fact_100_view_Oswitch__triangle,axiom,
! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ V2 @ D @ W2 ) )
=> ( switch @ U3 @ D @ W2 ) ) ).
% view.switch_triangle
thf(fact_101_view_Oswitch__unique,axiom,
! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ V2 @ C2 @ W2 ) )
=> ( U3 = W2 ) ) ).
% view.switch_unique
thf(fact_102_view_Oswitch__exists,axiom,
! [V2: view_ext @ product_unit] :
? [C: cars,X_1: view_ext @ product_unit] : ( switch @ V2 @ C @ X_1 ) ).
% view.switch_exists
thf(fact_103_view_Oswitch__trans,axiom,
! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
( ( ( switch @ V2 @ C2 @ U3 )
& ( switch @ U3 @ D @ W2 ) )
=> ( switch @ V2 @ D @ W2 ) ) ).
% view.switch_trans
thf(fact_104_view_Oswitch__hchop1,axiom,
! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,C2: cars,V8: view_ext @ product_unit] :
( ( ( hchop @ V2 @ V1 @ V22 )
& ( switch @ V2 @ C2 @ V8 ) )
=> ? [V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
( ( switch @ V1 @ C2 @ V12 )
& ( switch @ V22 @ C2 @ V23 )
& ( hchop @ V8 @ V12 @ V23 ) ) ) ).
% view.switch_hchop1
thf(fact_105_view_Oswitch__hchop2,axiom,
! [V8: view_ext @ product_unit,V13: view_ext @ product_unit,V24: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
( ( ( hchop @ V8 @ V13 @ V24 )
& ( switch @ V2 @ C2 @ V8 ) )
=> ? [V14: view_ext @ product_unit,V25: view_ext @ product_unit] :
( ( switch @ V14 @ C2 @ V13 )
& ( switch @ V25 @ C2 @ V24 )
& ( hchop @ V2 @ V14 @ V25 ) ) ) ).
% view.switch_hchop2
thf(fact_106_view_Oswitch__refl,axiom,
! [V2: view_ext @ product_unit] : ( switch @ V2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% view.switch_refl
thf(fact_107_view_Oswitch__symm,axiom,
! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit] :
( ( switch @ V2 @ C2 @ U3 )
=> ( switch @ U3 @ ( own @ product_unit @ V2 ) @ V2 ) ) ).
% view.switch_symm
thf(fact_108_view_Oswitch__origin,axiom,
! [V2: view_ext @ product_unit] :
? [U2: view_ext @ product_unit] : ( switch @ U2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% view.switch_origin
thf(fact_109_view_Ohorizontal__chop__width__stable,axiom,
! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_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_110_traffic_Ochange,axiom,
! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
( ? [C3: cars,F3: real > real] : ( change_dyn @ Ts5 @ C3 @ F3 @ Ts7 )
=> ( ( evolve @ Ts7 @ Ts8 )
=> ( evolve @ Ts5 @ Ts8 ) ) ) ).
% traffic.change
thf(fact_111_old_Ounit_Oexhaust,axiom,
! [Y2: product_unit] : Y2 = product_Unity ).
% old.unit.exhaust
thf(fact_112_old_Ounit_Oinducts,axiom,
! [P: product_unit > $o,Unit: product_unit] :
( ( P @ product_Unity )
=> ( P @ Unit ) ) ).
% old.unit.inducts
thf(fact_113_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_114_eq__sym__Unity__conv,axiom,
! [X3: $o] :
( ( X3
= ( product_Unity = product_Unity ) )
= X3 ) ).
% eq_sym_Unity_conv
thf(fact_115_bot__unit__def,axiom,
( ( bot_bot @ product_unit )
= product_Unity ) ).
% bot_unit_def
thf(fact_116_traffic_Ocreate__res__subseteq2,axiom,
! [Ts5: traffic,C2: cars,Ts7: traffic] :
( ( create_reservation @ Ts5 @ C2 @ Ts7 )
=> ( ord_less_eq @ nat_int @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq2
thf(fact_117_order__refl,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% order_refl
thf(fact_118_le__funD,axiom,
! [B: $tType,A: $tType] :
( ( ord @ B )
=> ! [F: A > B,G: A > B,X3: A] :
( ( ord_less_eq @ ( A > B ) @ F @ G )
=> ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% le_funD
thf(fact_119_le__funE,axiom,
! [B: $tType,A: $tType] :
( ( ord @ B )
=> ! [F: A > B,G: A > B,X3: A] :
( ( ord_less_eq @ ( A > B ) @ F @ G )
=> ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% le_funE
thf(fact_120_le__funI,axiom,
! [B: $tType,A: $tType] :
( ( ord @ B )
=> ! [F: A > B,G: A > B] :
( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
=> ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% le_funI
thf(fact_121_le__fun__def,axiom,
! [B: $tType,A: $tType] :
( ( ord @ B )
=> ( ( ord_less_eq @ ( A > B ) )
= ( ^ [F2: A > B,G2: A > B] :
! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% le_fun_def
thf(fact_122_order__subst1,axiom,
! [A: $tType,B: $tType] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
=> ( ( ord_less_eq @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less_eq @ B @ X2 @ Y3 )
=> ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% order_subst1
thf(fact_123_order__subst2,axiom,
! [A: $tType,C5: $tType] :
( ( ( order @ C5 )
& ( order @ A ) )
=> ! [A4: A,B3: A,F: A > C5,C2: C5] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less_eq @ A @ X2 @ Y3 )
=> ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% order_subst2
thf(fact_124_ord__eq__le__subst,axiom,
! [A: $tType,B: $tType] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( A4
= ( F @ B3 ) )
=> ( ( ord_less_eq @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less_eq @ B @ X2 @ Y3 )
=> ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_125_ord__le__eq__subst,axiom,
! [A: $tType,B: $tType] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [A4: A,B3: A,F: A > B,C2: B] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ( F @ B3 )
= C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less_eq @ A @ X2 @ Y3 )
=> ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% ord_le_eq_subst
thf(fact_126_eq__iff,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ^ [Y4: A,Z4: A] : Y4 = Z4 )
= ( ^ [X: A,Y: A] :
( ( ord_less_eq @ A @ X @ Y )
& ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% eq_iff
thf(fact_127_antisym,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ( ord_less_eq @ A @ Y2 @ X3 )
=> ( X3 = Y2 ) ) ) ) ).
% antisym
thf(fact_128_linear,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
| ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% linear
thf(fact_129_eq__refl,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A] :
( ( X3 = Y2 )
=> ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% eq_refl
thf(fact_130_le__cases,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ~ ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% le_cases
thf(fact_131_order_Otrans,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ A @ B3 @ C2 )
=> ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% order.trans
thf(fact_132_le__cases3,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ( ord_less_eq @ A @ X3 @ Y2 )
=> ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
=> ( ( ( ord_less_eq @ A @ Y2 @ X3 )
=> ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
=> ( ( ( ord_less_eq @ A @ X3 @ Z2 )
=> ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
=> ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
=> ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
=> ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
=> ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
=> ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
=> ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% le_cases3
thf(fact_133_antisym__conv,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [Y2: A,X3: A] :
( ( ord_less_eq @ A @ Y2 @ X3 )
=> ( ( ord_less_eq @ A @ X3 @ Y2 )
= ( X3 = Y2 ) ) ) ) ).
% antisym_conv
thf(fact_134_order__class_Oorder_Oeq__iff,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ^ [Y4: A,Z4: A] : Y4 = Z4 )
= ( ^ [A3: A,B4: A] :
( ( ord_less_eq @ A @ A3 @ B4 )
& ( ord_less_eq @ A @ B4 @ A3 ) ) ) ) ) ).
% order_class.order.eq_iff
thf(fact_135_ord__eq__le__trans,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( A4 = B3 )
=> ( ( ord_less_eq @ A @ B3 @ C2 )
=> ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% ord_eq_le_trans
thf(fact_136_ord__le__eq__trans,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( B3 = C2 )
=> ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% ord_le_eq_trans
thf(fact_137_order__class_Oorder_Oantisym,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ A @ B3 @ A4 )
=> ( A4 = B3 ) ) ) ) ).
% order_class.order.antisym
thf(fact_138_order__trans,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ( ord_less_eq @ A @ Y2 @ Z2 )
=> ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% order_trans
thf(fact_139_dual__order_Orefl,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% dual_order.refl
thf(fact_140_linorder__wlog,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [P: A > A > $o,A4: A,B3: A] :
( ! [A5: A,B5: A] :
( ( ord_less_eq @ A @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: A,B5: A] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A4 @ B3 ) ) ) ) ).
% linorder_wlog
thf(fact_141_dual__order_Otrans,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less_eq @ A @ B3 @ A4 )
=> ( ( ord_less_eq @ A @ C2 @ B3 )
=> ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% dual_order.trans
thf(fact_142_dual__order_Oeq__iff,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ^ [Y4: A,Z4: A] : Y4 = Z4 )
= ( ^ [A3: A,B4: A] :
( ( ord_less_eq @ A @ B4 @ A3 )
& ( ord_less_eq @ A @ A3 @ B4 ) ) ) ) ) ).
% dual_order.eq_iff
thf(fact_143_dual__order_Oantisym,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A] :
( ( ord_less_eq @ A @ B3 @ A4 )
=> ( ( ord_less_eq @ A @ A4 @ B3 )
=> ( A4 = B3 ) ) ) ) ).
% dual_order.antisym
thf(fact_144_less__eq__view__ext__def,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less_eq @ ( view_ext @ A ) )
= ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
& ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
& ( ( own @ A @ V9 )
= ( own @ A @ V10 ) )
& ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) ) ) ) ) ) ).
% less_eq_view_ext_def
thf(fact_145_bot_Oextremum,axiom,
! [A: $tType] :
( ( order_bot @ A )
=> ! [A4: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A4 ) ) ).
% bot.extremum
thf(fact_146_bot_Oextremum__unique,axiom,
! [A: $tType] :
( ( order_bot @ A )
=> ! [A4: A] :
( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
= ( A4
= ( bot_bot @ A ) ) ) ) ).
% bot.extremum_unique
thf(fact_147_bot_Oextremum__uniqueI,axiom,
! [A: $tType] :
( ( order_bot @ A )
=> ! [A4: A] :
( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
=> ( A4
= ( bot_bot @ A ) ) ) ) ).
% bot.extremum_uniqueI
thf(fact_148_traffic_Ocreate__res__subseteq1,axiom,
! [Ts5: traffic,C2: cars,Ts7: traffic] :
( ( create_reservation @ Ts5 @ C2 @ Ts7 )
=> ( ord_less_eq @ nat_int @ ( res @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% traffic.create_res_subseteq1
thf(fact_149_traffic_Owithdraw__res__subseteq,axiom,
! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
( ( withdraw_reservation @ Ts5 @ D @ N @ Ts7 )
=> ( ord_less_eq @ nat_int @ ( res @ Ts7 @ C2 ) @ ( res @ Ts5 @ C2 ) ) ) ).
% traffic.withdraw_res_subseteq
thf(fact_150_old_Ounit_Orec,axiom,
! [T: $tType,F1: T] :
( ( product_rec_unit @ T @ F1 @ product_Unity )
= F1 ) ).
% old.unit.rec
thf(fact_151_default__unit__def,axiom,
( ( default_default @ product_unit )
= product_Unity ) ).
% default_unit_def
thf(fact_152_less__view__ext__def,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less @ ( view_ext @ A ) )
= ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
& ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
& ( ( own @ A @ V10 )
= ( own @ A @ V9 ) )
& ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) )
& ~ ( ( ord_less_eq @ real_int @ ( ext @ A @ V10 ) @ ( ext @ A @ V9 ) )
& ( ord_less_eq @ nat_int @ ( lan @ A @ V10 ) @ ( lan @ A @ V9 ) )
& ( ( own @ A @ V10 )
= ( own @ A @ V9 ) )
& ( ord_less_eq @ A @ ( more @ A @ V10 ) @ ( more @ A @ V9 ) ) ) ) ) ) ) ).
% less_view_ext_def
thf(fact_153_diff__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,D: A,C2: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ A @ D @ C2 )
=> ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% diff_mono
thf(fact_154_leD,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [Y2: A,X3: A] :
( ( ord_less_eq @ A @ Y2 @ X3 )
=> ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% leD
thf(fact_155_leI,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ~ ( ord_less @ A @ X3 @ Y2 )
=> ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% leI
thf(fact_156_le__less,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less_eq @ A )
= ( ^ [X: A,Y: A] :
( ( ord_less @ A @ X @ Y )
| ( X = Y ) ) ) ) ) ).
% le_less
thf(fact_157_less__le,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less @ A )
= ( ^ [X: A,Y: A] :
( ( ord_less_eq @ A @ X @ Y )
& ( X != Y ) ) ) ) ) ).
% less_le
thf(fact_158_order__le__less__subst1,axiom,
! [A: $tType,B: $tType] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
=> ( ( ord_less @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less @ B @ X2 @ Y3 )
=> ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_159_order__le__less__subst2,axiom,
! [A: $tType,C5: $tType] :
( ( ( order @ C5 )
& ( order @ A ) )
=> ! [A4: A,B3: A,F: A > C5,C2: C5] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less_eq @ A @ X2 @ Y3 )
=> ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% order_le_less_subst2
thf(fact_160_order__less__le__subst1,axiom,
! [A: $tType,B: $tType] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( ord_less @ A @ A4 @ ( F @ B3 ) )
=> ( ( ord_less_eq @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less_eq @ B @ X2 @ Y3 )
=> ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_161_order__less__le__subst2,axiom,
! [A: $tType,C5: $tType] :
( ( ( order @ C5 )
& ( order @ A ) )
=> ! [A4: A,B3: A,F: A > C5,C2: C5] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less @ A @ X2 @ Y3 )
=> ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% order_less_le_subst2
thf(fact_162_not__le,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
= ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% not_le
thf(fact_163_not__less,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
= ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% not_less
thf(fact_164_le__neq__trans,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( A4 != B3 )
=> ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% le_neq_trans
thf(fact_165_antisym__conv1,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ~ ( ord_less @ A @ X3 @ Y2 )
=> ( ( ord_less_eq @ A @ X3 @ Y2 )
= ( X3 = Y2 ) ) ) ) ).
% antisym_conv1
thf(fact_166_antisym__conv2,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
= ( X3 = Y2 ) ) ) ) ).
% antisym_conv2
thf(fact_167_less__imp__le,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% less_imp_le
thf(fact_168_le__less__trans,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ( ord_less @ A @ Y2 @ Z2 )
=> ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% le_less_trans
thf(fact_169_less__le__trans,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( ( ord_less_eq @ A @ Y2 @ Z2 )
=> ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% less_le_trans
thf(fact_170_dense__ge,axiom,
! [A: $tType] :
( ( dense_linorder @ A )
=> ! [Z2: A,Y2: A] :
( ! [X2: A] :
( ( ord_less @ A @ Z2 @ X2 )
=> ( ord_less_eq @ A @ Y2 @ X2 ) )
=> ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% dense_ge
thf(fact_171_dense__le,axiom,
! [A: $tType] :
( ( dense_linorder @ A )
=> ! [Y2: A,Z2: A] :
( ! [X2: A] :
( ( ord_less @ A @ X2 @ Y2 )
=> ( ord_less_eq @ A @ X2 @ Z2 ) )
=> ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% dense_le
thf(fact_172_le__less__linear,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
| ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% le_less_linear
thf(fact_173_le__imp__less__or__eq,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less_eq @ A @ X3 @ Y2 )
=> ( ( ord_less @ A @ X3 @ Y2 )
| ( X3 = Y2 ) ) ) ) ).
% le_imp_less_or_eq
thf(fact_174_less__le__not__le,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ( ( ord_less @ A )
= ( ^ [X: A,Y: A] :
( ( ord_less_eq @ A @ X @ Y )
& ~ ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% less_le_not_le
thf(fact_175_not__le__imp__less,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [Y2: A,X3: A] :
( ~ ( ord_less_eq @ A @ Y2 @ X3 )
=> ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% not_le_imp_less
thf(fact_176_order_Ostrict__trans1,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ( ord_less @ A @ B3 @ C2 )
=> ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% order.strict_trans1
thf(fact_177_order_Ostrict__trans2,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ord_less_eq @ A @ B3 @ C2 )
=> ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% order.strict_trans2
thf(fact_178_order_Oorder__iff__strict,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less_eq @ A )
= ( ^ [A3: A,B4: A] :
( ( ord_less @ A @ A3 @ B4 )
| ( A3 = B4 ) ) ) ) ) ).
% order.order_iff_strict
thf(fact_179_order_Ostrict__iff__order,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less @ A )
= ( ^ [A3: A,B4: A] :
( ( ord_less_eq @ A @ A3 @ B4 )
& ( A3 != B4 ) ) ) ) ) ).
% order.strict_iff_order
thf(fact_180_dual__order_Ostrict__trans1,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less_eq @ A @ B3 @ A4 )
=> ( ( ord_less @ A @ C2 @ B3 )
=> ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% dual_order.strict_trans1
thf(fact_181_dual__order_Ostrict__trans2,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ( ( ord_less_eq @ A @ C2 @ B3 )
=> ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% dual_order.strict_trans2
thf(fact_182_dense__ge__bounded,axiom,
! [A: $tType] :
( ( dense_linorder @ A )
=> ! [Z2: A,X3: A,Y2: A] :
( ( ord_less @ A @ Z2 @ X3 )
=> ( ! [W3: A] :
( ( ord_less @ A @ Z2 @ W3 )
=> ( ( ord_less @ A @ W3 @ X3 )
=> ( ord_less_eq @ A @ Y2 @ W3 ) ) )
=> ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% dense_ge_bounded
thf(fact_183_dense__le__bounded,axiom,
! [A: $tType] :
( ( dense_linorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( ! [W3: A] :
( ( ord_less @ A @ X3 @ W3 )
=> ( ( ord_less @ A @ W3 @ Y2 )
=> ( ord_less_eq @ A @ W3 @ Z2 ) ) )
=> ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% dense_le_bounded
thf(fact_184_order_Ostrict__implies__order,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ord_less_eq @ A @ A4 @ B3 ) ) ) ).
% order.strict_implies_order
thf(fact_185_dual__order_Oorder__iff__strict,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less_eq @ A )
= ( ^ [B4: A,A3: A] :
( ( ord_less @ A @ B4 @ A3 )
| ( A3 = B4 ) ) ) ) ) ).
% dual_order.order_iff_strict
thf(fact_186_dual__order_Ostrict__iff__order,axiom,
! [A: $tType] :
( ( order @ A )
=> ( ( ord_less @ A )
= ( ^ [B4: A,A3: A] :
( ( ord_less_eq @ A @ B4 @ A3 )
& ( A3 != B4 ) ) ) ) ) ).
% dual_order.strict_iff_order
thf(fact_187_dual__order_Ostrict__implies__order,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ( ord_less_eq @ A @ B3 @ A4 ) ) ) ).
% dual_order.strict_implies_order
thf(fact_188_order_Onot__eq__order__implies__strict,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( A4 != B3 )
=> ( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% order.not_eq_order_implies_strict
thf(fact_189_bot_Oextremum__strict,axiom,
! [A: $tType] :
( ( order_bot @ A )
=> ! [A4: A] :
~ ( ord_less @ A @ A4 @ ( bot_bot @ A ) ) ) ).
% bot.extremum_strict
thf(fact_190_bot_Onot__eq__extremum,axiom,
! [A: $tType] :
( ( order_bot @ A )
=> ! [A4: A] :
( ( A4
!= ( bot_bot @ A ) )
= ( ord_less @ A @ ( bot_bot @ A ) @ A4 ) ) ) ).
% bot.not_eq_extremum
thf(fact_191_view_Ohorizontal__chop__leq2,axiom,
! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ W2 @ V2 ) ) ).
% view.horizontal_chop_leq2
thf(fact_192_view_Ohorizontal__chop__leq1,axiom,
! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
( ( hchop @ V2 @ U3 @ W2 )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ U3 @ V2 ) ) ).
% view.horizontal_chop_leq1
thf(fact_193_view_Oswitch__leq,axiom,
! [U5: view_ext @ product_unit,U3: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ U5 @ U3 )
& ( switch @ V2 @ C2 @ U3 ) )
=> ? [V5: view_ext @ product_unit] :
( ( switch @ V5 @ C2 @ U5 )
& ( ord_less_eq @ ( view_ext @ product_unit ) @ V5 @ V2 ) ) ) ).
% view.switch_leq
thf(fact_194_dual__order_Ostrict__implies__not__eq,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ( A4 != B3 ) ) ) ).
% dual_order.strict_implies_not_eq
thf(fact_195_order_Ostrict__implies__not__eq,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( A4 != B3 ) ) ) ).
% order.strict_implies_not_eq
thf(fact_196_not__less__iff__gr__or__eq,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
= ( ( ord_less @ A @ Y2 @ X3 )
| ( X3 = Y2 ) ) ) ) ).
% not_less_iff_gr_or_eq
thf(fact_197_dual__order_Ostrict__trans,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ( ( ord_less @ A @ C2 @ B3 )
=> ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% dual_order.strict_trans
thf(fact_198_linorder__less__wlog,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [P: A > A > $o,A4: A,B3: A] :
( ! [A5: A,B5: A] :
( ( ord_less @ A @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: A] : ( P @ A5 @ A5 )
=> ( ! [A5: A,B5: A] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A4 @ B3 ) ) ) ) ) ).
% linorder_less_wlog
thf(fact_199_exists__least__iff,axiom,
! [A: $tType] :
( ( wellorder @ A )
=> ( ( ^ [P2: A > $o] :
? [X5: A] : ( P2 @ X5 ) )
= ( ^ [P3: A > $o] :
? [N4: A] :
( ( P3 @ N4 )
& ! [M2: A] :
( ( ord_less @ A @ M2 @ N4 )
=> ~ ( P3 @ M2 ) ) ) ) ) ) ).
% exists_least_iff
thf(fact_200_less__imp__not__less,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% less_imp_not_less
thf(fact_201_order_Ostrict__trans,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ord_less @ A @ B3 @ C2 )
=> ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% order.strict_trans
thf(fact_202_dual__order_Oirrefl,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A] :
~ ( ord_less @ A @ A4 @ A4 ) ) ).
% dual_order.irrefl
thf(fact_203_linorder__cases,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ~ ( ord_less @ A @ X3 @ Y2 )
=> ( ( X3 != Y2 )
=> ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% linorder_cases
thf(fact_204_less__imp__triv,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A,P: $o] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( ( ord_less @ A @ Y2 @ X3 )
=> P ) ) ) ).
% less_imp_triv
thf(fact_205_less__imp__not__eq2,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( Y2 != X3 ) ) ) ).
% less_imp_not_eq2
thf(fact_206_antisym__conv3,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [Y2: A,X3: A] :
( ~ ( ord_less @ A @ Y2 @ X3 )
=> ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
= ( X3 = Y2 ) ) ) ) ).
% antisym_conv3
thf(fact_207_less__induct,axiom,
! [A: $tType] :
( ( wellorder @ A )
=> ! [P: A > $o,A4: A] :
( ! [X2: A] :
( ! [Y5: A] :
( ( ord_less @ A @ Y5 @ X2 )
=> ( P @ Y5 ) )
=> ( P @ X2 ) )
=> ( P @ A4 ) ) ) ).
% less_induct
thf(fact_208_less__not__sym,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% less_not_sym
thf(fact_209_less__imp__not__eq,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( X3 != Y2 ) ) ) ).
% less_imp_not_eq
thf(fact_210_dual__order_Oasym,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [B3: A,A4: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% dual_order.asym
thf(fact_211_ord__less__eq__trans,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( B3 = C2 )
=> ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% ord_less_eq_trans
thf(fact_212_ord__eq__less__trans,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( A4 = B3 )
=> ( ( ord_less @ A @ B3 @ C2 )
=> ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% ord_eq_less_trans
thf(fact_213_less__irrefl,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A] :
~ ( ord_less @ A @ X3 @ X3 ) ) ).
% less_irrefl
thf(fact_214_less__linear,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
| ( X3 = Y2 )
| ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% less_linear
thf(fact_215_less__trans,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A,Z2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( ( ord_less @ A @ Y2 @ Z2 )
=> ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% less_trans
thf(fact_216_less__asym_H,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [A4: A,B3: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% less_asym'
thf(fact_217_less__asym,axiom,
! [A: $tType] :
( ( preorder @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% less_asym
thf(fact_218_less__imp__neq,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ( X3 != Y2 ) ) ) ).
% less_imp_neq
thf(fact_219_dense,axiom,
! [A: $tType] :
( ( dense_order @ A )
=> ! [X3: A,Y2: A] :
( ( ord_less @ A @ X3 @ Y2 )
=> ? [Z5: A] :
( ( ord_less @ A @ X3 @ Z5 )
& ( ord_less @ A @ Z5 @ Y2 ) ) ) ) ).
% dense
thf(fact_220_order_Oasym,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [A4: A,B3: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% order.asym
thf(fact_221_neq__iff,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( X3 != Y2 )
= ( ( ord_less @ A @ X3 @ Y2 )
| ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% neq_iff
thf(fact_222_neqE,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X3: A,Y2: A] :
( ( X3 != Y2 )
=> ( ~ ( ord_less @ A @ X3 @ Y2 )
=> ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% neqE
thf(fact_223_gt__ex,axiom,
! [A: $tType] :
( ( no_top @ A )
=> ! [X3: A] :
? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% gt_ex
thf(fact_224_lt__ex,axiom,
! [A: $tType] :
( ( no_bot @ A )
=> ! [X3: A] :
? [Y3: A] : ( ord_less @ A @ Y3 @ X3 ) ) ).
% lt_ex
thf(fact_225_order__less__subst2,axiom,
! [A: $tType,C5: $tType] :
( ( ( order @ C5 )
& ( order @ A ) )
=> ! [A4: A,B3: A,F: A > C5,C2: C5] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less @ A @ X2 @ Y3 )
=> ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% order_less_subst2
thf(fact_226_order__less__subst1,axiom,
! [A: $tType,B: $tType] :
( ( ( order @ B )
& ( order @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( ord_less @ A @ A4 @ ( F @ B3 ) )
=> ( ( ord_less @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less @ B @ X2 @ Y3 )
=> ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% order_less_subst1
thf(fact_227_ord__less__eq__subst,axiom,
! [A: $tType,B: $tType] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [A4: A,B3: A,F: A > B,C2: B] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ( F @ B3 )
= C2 )
=> ( ! [X2: A,Y3: A] :
( ( ord_less @ A @ X2 @ Y3 )
=> ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% ord_less_eq_subst
thf(fact_228_ord__eq__less__subst,axiom,
! [A: $tType,B: $tType] :
( ( ( ord @ B )
& ( ord @ A ) )
=> ! [A4: A,F: B > A,B3: B,C2: B] :
( ( A4
= ( F @ B3 ) )
=> ( ( ord_less @ B @ B3 @ C2 )
=> ( ! [X2: B,Y3: B] :
( ( ord_less @ B @ X2 @ Y3 )
=> ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
=> ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% ord_eq_less_subst
thf(fact_229_diff__strict__right__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% diff_strict_right_mono
thf(fact_230_diff__strict__left__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less @ A @ B3 @ A4 )
=> ( ord_less @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% diff_strict_left_mono
thf(fact_231_diff__eq__diff__less,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,C2: A,D: A] :
( ( ( minus_minus @ A @ A4 @ B3 )
= ( minus_minus @ A @ C2 @ D ) )
=> ( ( ord_less @ A @ A4 @ B3 )
= ( ord_less @ A @ C2 @ D ) ) ) ) ).
% diff_eq_diff_less
thf(fact_232_diff__strict__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,D: A,C2: A] :
( ( ord_less @ A @ A4 @ B3 )
=> ( ( ord_less @ A @ D @ C2 )
=> ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% diff_strict_mono
thf(fact_233_chop__leq2,axiom,
! [R: real_int,S2: real_int,T2: real_int] :
( ( real_R_Chop @ R @ S2 @ T2 )
=> ( ord_less_eq @ real_int @ T2 @ R ) ) ).
% chop_leq2
thf(fact_234_chop__leq1,axiom,
! [R: real_int,S2: real_int,T2: real_int] :
( ( real_R_Chop @ R @ S2 @ T2 )
=> ( ord_less_eq @ real_int @ S2 @ R ) ) ).
% chop_leq1
thf(fact_235_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_236_diff__eq__diff__eq,axiom,
! [A: $tType] :
( ( group_add @ A )
=> ! [A4: A,B3: A,C2: A,D: A] :
( ( ( minus_minus @ A @ A4 @ B3 )
= ( minus_minus @ A @ C2 @ D ) )
=> ( ( A4 = B3 )
= ( C2 = D ) ) ) ) ).
% diff_eq_diff_eq
thf(fact_237_diff__right__commute,axiom,
! [A: $tType] :
( ( cancel146912293up_add @ A )
=> ! [A4: A,C2: A,B3: A] :
( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B3 )
= ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B3 ) @ C2 ) ) ) ).
% diff_right_commute
thf(fact_238_diff__eq__diff__less__eq,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,C2: A,D: A] :
( ( ( minus_minus @ A @ A4 @ B3 )
= ( minus_minus @ A @ C2 @ D ) )
=> ( ( ord_less_eq @ A @ A4 @ B3 )
= ( ord_less_eq @ A @ C2 @ D ) ) ) ) ).
% diff_eq_diff_less_eq
thf(fact_239_diff__right__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [A4: A,B3: A,C2: A] :
( ( ord_less_eq @ A @ A4 @ B3 )
=> ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% diff_right_mono
thf(fact_240_diff__left__mono,axiom,
! [A: $tType] :
( ( ordered_ab_group_add @ A )
=> ! [B3: A,A4: A,C2: A] :
( ( ord_less_eq @ A @ B3 @ A4 )
=> ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% diff_left_mono
thf(fact_241_traffic_Oclm__consec__res,axiom,
! [Ts5: traffic,C2: cars] :
( ( ( clm @ Ts5 @ C2 )
!= ( bot_bot @ nat_int ) )
=> ( ( nat_consec @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts5 @ C2 ) )
| ( nat_consec @ ( res @ Ts5 @ C2 ) @ ( clm @ Ts5 @ C2 ) ) ) ) ).
% traffic.clm_consec_res
thf(fact_242_Greatest__equality,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [P: A > $o,X3: A] :
( ( P @ X3 )
=> ( ! [Y3: A] :
( ( P @ Y3 )
=> ( ord_less_eq @ A @ Y3 @ X3 ) )
=> ( ( order_Greatest @ A @ P )
= X3 ) ) ) ) ).
% Greatest_equality
thf(fact_243_GreatestI2__order,axiom,
! [A: $tType] :
( ( order @ A )
=> ! [P: A > $o,X3: A,Q: A > $o] :
( ( P @ X3 )
=> ( ! [Y3: A] :
( ( P @ Y3 )
=> ( ord_less_eq @ A @ Y3 @ X3 ) )
=> ( ! [X2: A] :
( ( P @ X2 )
=> ( ! [Y5: A] :
( ( P @ Y5 )
=> ( ord_less_eq @ A @ Y5 @ X2 ) )
=> ( Q @ X2 ) ) )
=> ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% GreatestI2_order
thf(fact_244_less__fun__def,axiom,
! [B: $tType,A: $tType] :
( ( ord @ B )
=> ( ( ord_less @ ( A > B ) )
= ( ^ [F2: A > B,G2: A > B] :
( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
& ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% less_fun_def
thf(fact_245_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_246_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_247_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_248_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_249_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_250_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_251_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_252_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_253_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_254_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_255_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
% Type constructors (54)
thf(tcon_fun___Orderings_Oorder__bot,axiom,
! [A6: $tType,A7: $tType] :
( ( order_bot @ A7 )
=> ( order_bot @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Orderings_Opreorder,axiom,
! [A6: $tType,A7: $tType] :
( ( preorder @ A7 )
=> ( preorder @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Orderings_Oorder,axiom,
! [A6: $tType,A7: $tType] :
( ( order @ A7 )
=> ( order @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Orderings_Oord,axiom,
! [A6: $tType,A7: $tType] :
( ( ord @ A7 )
=> ( ord @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Orderings_Obot,axiom,
! [A6: $tType,A7: $tType] :
( ( bot @ A7 )
=> ( bot @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Groups_Ominus,axiom,
! [A6: $tType,A7: $tType] :
( ( minus @ A7 )
=> ( minus @ ( A6 > A7 ) ) ) ).
thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
cancel146912293up_add @ nat ).
thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
wellorder @ nat ).
thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
order_bot @ nat ).
thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
preorder @ nat ).
thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
linorder @ nat ).
thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
no_top @ nat ).
thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
order @ nat ).
thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
ord @ nat ).
thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
bot @ nat ).
thf(tcon_Nat_Onat___Groups_Ominus_6,axiom,
minus @ nat ).
thf(tcon_HOL_Obool___Orderings_Oorder__bot_7,axiom,
order_bot @ $o ).
thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
preorder @ $o ).
thf(tcon_HOL_Obool___Orderings_Olinorder_9,axiom,
linorder @ $o ).
thf(tcon_HOL_Obool___Orderings_Oorder_10,axiom,
order @ $o ).
thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
ord @ $o ).
thf(tcon_HOL_Obool___Orderings_Obot_12,axiom,
bot @ $o ).
thf(tcon_HOL_Obool___Groups_Ominus_13,axiom,
minus @ $o ).
thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_14,axiom,
cancel146912293up_add @ real ).
thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
ordered_ab_group_add @ real ).
thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
dense_linorder @ real ).
thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
dense_order @ real ).
thf(tcon_Real_Oreal___Orderings_Opreorder_15,axiom,
preorder @ real ).
thf(tcon_Real_Oreal___Orderings_Olinorder_16,axiom,
linorder @ real ).
thf(tcon_Real_Oreal___Orderings_Ono__top_17,axiom,
no_top @ real ).
thf(tcon_Real_Oreal___Orderings_Ono__bot,axiom,
no_bot @ real ).
thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
group_add @ real ).
thf(tcon_Real_Oreal___Orderings_Oorder_18,axiom,
order @ real ).
thf(tcon_Real_Oreal___Orderings_Oord_19,axiom,
ord @ real ).
thf(tcon_Real_Oreal___Groups_Ominus_20,axiom,
minus @ real ).
thf(tcon_NatInt_Onat__int___Orderings_Oorder__bot_21,axiom,
order_bot @ nat_int ).
thf(tcon_NatInt_Onat__int___Orderings_Opreorder_22,axiom,
preorder @ nat_int ).
thf(tcon_NatInt_Onat__int___Orderings_Oorder_23,axiom,
order @ nat_int ).
thf(tcon_NatInt_Onat__int___Orderings_Oord_24,axiom,
ord @ nat_int ).
thf(tcon_NatInt_Onat__int___Orderings_Obot_25,axiom,
bot @ nat_int ).
thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_26,axiom,
preorder @ real_int ).
thf(tcon_RealInt_Oreal__int___Orderings_Oorder_27,axiom,
order @ real_int ).
thf(tcon_RealInt_Oreal__int___Orderings_Oord_28,axiom,
ord @ real_int ).
thf(tcon_Product__Type_Ounit___Orderings_Owellorder_29,axiom,
wellorder @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_30,axiom,
order_bot @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31,axiom,
preorder @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32,axiom,
linorder @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Oorder_33,axiom,
order @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Oord_34,axiom,
ord @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Obot_35,axiom,
bot @ product_unit ).
thf(tcon_Product__Type_Ounit___Groups_Ominus_36,axiom,
minus @ product_unit ).
thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_37,axiom,
! [A6: $tType] :
( ( order @ A6 )
=> ( preorder @ ( view_ext @ A6 ) ) ) ).
thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_38,axiom,
! [A6: $tType] :
( ( order @ A6 )
=> ( order @ ( view_ext @ A6 ) ) ) ).
thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_39,axiom,
! [A6: $tType] :
( ( order @ A6 )
=> ( ord @ ( view_ext @ A6 ) ) ) ).
% Helper facts (3)
thf(help_If_3_1_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_T,axiom,
! [A: $tType,X3: A,Y2: A] :
( ( if @ A @ $false @ X3 @ Y2 )
= Y2 ) ).
thf(help_If_1_1_T,axiom,
! [A: $tType,X3: A,Y2: A] :
( ( if @ A @ $true @ X3 @ Y2 )
= X3 ) ).
% Conjectures (1)
thf(conj_0,conjecture,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ) ).
%------------------------------------------------------------------------------