(* PARALLEL SUBSTITUTION ON LOCAL ENVIRONMENTS ******************************)
-lemma ltps_tps_conf_ge: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\89« U2 →
- â\88\80L1,d1,e1. L0 [d1, e1] â\89« L1 → d1 + e1 ≤ d2 →
- L1 â\8a¢ T2 [d2, e2] â\89« U2.
+lemma ltps_tps_conf_ge: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\96¶ U2 →
+ â\88\80L1,d1,e1. L0 [d1, e1] â\96¶ L1 → d1 + e1 ≤ d2 →
+ L1 â\8a¢ T2 [d2, e2] â\96¶ U2.
#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
[ //
| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01 #Hde1d2
qed.
(* Basic_1: was: subst1_subst1_back *)
-lemma ltps_tps_conf: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\89« U2 →
- â\88\80L1,d1,e1. L0 [d1, e1] â\89« L1 →
- â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\89« T &
- L1 â\8a¢ U2 [d1, e1] â\89« T.
+lemma ltps_tps_conf: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\96¶ U2 →
+ â\88\80L1,d1,e1. L0 [d1, e1] â\96¶ L1 →
+ â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\96¶ T &
+ L1 â\8a¢ U2 [d1, e1] â\96¶ T.
#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
[ /2 width=3/
| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01
]
qed.
-lemma ltps_tps_trans_ge: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\89« U2 →
- â\88\80L1,d1,e1. L1 [d1, e1] â\89« L0 → d1 + e1 ≤ d2 →
- L1 â\8a¢ T2 [d2, e2] â\89« U2.
+lemma ltps_tps_trans_ge: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\96¶ U2 →
+ â\88\80L1,d1,e1. L1 [d1, e1] â\96¶ L0 → d1 + e1 ≤ d2 →
+ L1 â\8a¢ T2 [d2, e2] â\96¶ U2.
#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
[ //
| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10 #Hde1d2
qed.
(* Basic_1: was: subst1_subst1 *)
-lemma ltps_tps_trans: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\89« U2 →
- â\88\80L1,d1,e1. L1 [d1, e1] â\89« L0 →
- â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\89« T &
- L0 â\8a¢ T [d1, e1] â\89« U2.
+lemma ltps_tps_trans: â\88\80L0,T2,U2,d2,e2. L0 â\8a¢ T2 [d2, e2] â\96¶ U2 →
+ â\88\80L1,d1,e1. L1 [d1, e1] â\96¶ L0 →
+ â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\96¶ T &
+ L0 â\8a¢ T [d1, e1] â\96¶ U2.
#L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
[ /2 width=3/
| #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10