(* Properties concerning basic local environment slicing ********************)
(* Note: the constant 0 cannot be generalized *)
-lemma lsuba_ldrop_O1_conf: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
- â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & ⇩[s, 0, e] L2 ≡ K2.
+lemma lsuba_ldrop_O1_conf: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+ â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & ⇩[s, 0, e] L2 ≡ K2.
#G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3/
| #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
qed-.
(* Note: the constant 0 cannot be generalized *)
-lemma lsuba_ldrop_O1_trans: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
- â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & ⇩[s, 0, e] L1 ≡ K1.
+lemma lsuba_ldrop_O1_trans: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+ â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & ⇩[s, 0, e] L1 ≡ K1.
#G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3/
| #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H