(* Properties concerning generic local environment slicing ******************)
(* Basic_1: was: csubc_drop1_conf_rev *)
-lemma drops_lsubc_trans: ∀RR,RS,RP.
- gcp RR RS RP → gcr RR RS RP RP →
- ∀G,L1,K1,des. ⇩*[Ⓕ, des] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
- ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⇩*[Ⓕ, des] L2 ≡ K2.
-#RR #RS #RP #Hgcp #Hgcr #G #L1 #K1 #des #H elim H -L1 -K1 -des
+lemma drops_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
+ ∀G,L1,K1,cs. ⬇*[Ⓕ, cs] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+ ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[Ⓕ, cs] L2 ≡ K2.
+#RR #RS #RP #Hgcp #G #L1 #K1 #cs #H elim H -L1 -K1 -cs
[ /2 width=3 by drops_nil, ex2_intro/
-| #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
- elim (drop_lsubc_trans … Hgcp Hgcr … HLK1 … HK12) -Hgcp -Hgcr -K1 #K #HLK #HK2
+| #L1 #L #K1 #cs #l #m #_ #HLK1 #IHL #K2 #HK12
+ elim (drop_lsubc_trans … Hgcp … HLK1 … HK12) -Hgcp -K1 #K #HLK #HK2
elim (IHL … HLK) -IHL -HLK /3 width=5 by drops_cons, ex2_intro/
]
qed-.