(* Properties with generic slicing for local environments *******************)
-lemma fqup_drops_succ: ∀b,G,K,T,i,L,U. ⇩*[↑i] L ≘ K → ⇧*[↑i] T ≘ U →
+lemma fqup_drops_succ: ∀b,G,K,T,i,L,U. ⇩[↑i] L ≘ K → ⇧[↑i] T ≘ U →
❪G,L,U❫ ⬂+[b] ❪G,K,T❫.
#b #G #K #T #i elim i -i
[ #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
]
qed.
-lemma fqup_drops_strap1: ∀b,G1,G2,L1,K1,K2,T1,T2,U1,i. ⇩*[i] L1 ≘ K1 → ⇧*[i] T1 ≘ U1 →
+lemma fqup_drops_strap1: ∀b,G1,G2,L1,K1,K2,T1,T2,U1,i. ⇩[i] L1 ≘ K1 → ⇧[i] T1 ≘ U1 →
❪G1,K1,T1❫ ⬂[b] ❪G2,K2,T2❫ → ❪G1,L1,U1❫ ⬂+[b] ❪G2,K2,T2❫.
#b #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 *
[ #HLK1 #HTU1 #HT12
]
qed-.
-lemma fqup_lref: ∀b,I,G,L,K,V,i. ⇩*[i] L ≘ K.ⓑ[I]V → ❪G,L,#i❫ ⬂+[b] ❪G,K,V❫.
+lemma fqup_lref: ∀b,I,G,L,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,L,#i❫ ⬂+[b] ❪G,K,V❫.
/2 width=6 by fqup_drops_strap1/ qed.