(* Basic_1: was: csubc_drop_conf_O *)
(* Note: the constant 0 can not be generalized *)
-lemma lsubc_drop_O1_trans: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 â\86\92 â\88\80K2,s,e. â\87©[s, 0, e] L2 ≡ K2 →
- â\88\83â\88\83K1. â\87©[s, 0, e] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
+lemma lsubc_drop_O1_trans: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 â\86\92 â\88\80K2,s,e. â¬\87[s, 0, e] L2 ≡ K2 →
+ â\88\83â\88\83K1. â¬\87[s, 0, e] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
#RP #G #L1 #L2 #H elim H -L1 -L2
[ #X #s #e #H elim (drop_inv_atom1 … H) -H /4 width=3 by drop_atom, ex2_intro/
| #I #L1 #L2 #V #_ #IHL12 #X #s #e #H
(* Basic_1: was: csubc_drop_conf_rev *)
lemma drop_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
- â\88\80G,L1,K1,d,e. â\87©[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
- â\88\83â\88\83L2. G â\8a¢ L1 â«\83[RP] L2 & â\87©[Ⓕ, d, e] L2 ≡ K2.
+ â\88\80G,L1,K1,d,e. â¬\87[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+ â\88\83â\88\83L2. G â\8a¢ L1 â«\83[RP] L2 & â¬\87[Ⓕ, d, e] L2 ≡ K2.
#RR #RS #RP #Hgcp #G #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
[ #d #e #He #X #H elim (lsubc_inv_atom1 … H) -H
>He /2 width=3 by ex2_intro/