-lemma drop_lsubc_trans: ∀RR,RS,RP.
- acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
- ∀G,L1,K1,d,e. ⇩[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
- ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⇩[Ⓕ, d, e] L2 ≡ K2.
-#RR #RS #RP #Hacp #Hacr #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/
+lemma drop_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
+ ∀G,L1,K1,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+ ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇[Ⓕ, l, k] L2 ≡ K2.
+#RR #RS #RP #Hgcp #G #L1 #K1 #l #k #H elim H -L1 -K1 -l -k
+[ #l #k #Hm #X #H elim (lsubc_inv_atom1 … H) -H
+ >Hm /2 width=3 by ex2_intro/