(* Note: the constant 0 cannot be generalized *)
lemma lsubsv_drop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ⫃¡[h, g] L2 →
- â\88\80K1,s,e. â\87©[s, 0, e] L1 ≡ K1 →
- â\88\83â\88\83K2. G â\8a¢ K1 â«\83¡[h, g] K2 & â\87©[s, 0, e] L2 ≡ K2.
+ â\88\80K1,s,e. â¬\87[s, 0, e] L1 ≡ K1 →
+ â\88\83â\88\83K2. G â\8a¢ K1 â«\83¡[h, g] K2 & â¬\87[s, 0, e] L2 ≡ K2.
#h #g #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
(* Note: the constant 0 cannot be generalized *)
lemma lsubsv_drop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ⫃¡[h, g] L2 →
- â\88\80K2,s, e. â\87©[s, 0, e] L2 ≡ K2 →
- â\88\83â\88\83K1. G â\8a¢ K1 â«\83¡[h, g] K2 & â\87©[s, 0, e] L1 ≡ K1.
+ â\88\80K2,s, e. â¬\87[s, 0, e] L2 ≡ K2 →
+ â\88\83â\88\83K1. G â\8a¢ K1 â«\83¡[h, g] K2 & â¬\87[s, 0, e] L1 ≡ K1.
#h #g #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H