(* Properties with generic slicing for local environments *******************)
-lemma fqup_drops_succ: â\88\80b,G,K,T,i,L,U. â¬\87*[⫯i] L â\89¡ K â\86\92 â¬\86*[⫯i] T â\89¡ U →
+lemma fqup_drops_succ: â\88\80b,G,K,T,i,L,U. â¬\87*[â\86\91i] L â\89\98 K â\86\92 â¬\86*[â\86\91i] T â\89\98 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
/3 width=2 by fqu_fqup, fqu_drop/
| #l #IH #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
#I #Y #HY #H destruct
- elim (lifts_split_trans â\80¦ HTU â\80¦ (ð\9d\90\94â\9d´â«¯l❵) (𝐔❴1❵)) -HTU
+ elim (lifts_split_trans â\80¦ HTU â\80¦ (ð\9d\90\94â\9d´â\86\91l❵) (𝐔❴1❵)) -HTU
/4 width=5 by fqup_strap2, fqu_drop/
]
qed.
-lemma fqup_drops_strap1: â\88\80b,G1,G2,L1,K1,K2,T1,T2,U1,i. â¬\87*[i] L1 â\89¡ K1 â\86\92 â¬\86*[i] T1 â\89¡ U1 →
+lemma fqup_drops_strap1: â\88\80b,G1,G2,L1,K1,K2,T1,T2,U1,i. â¬\87*[i] L1 â\89\98 K1 â\86\92 â¬\86*[i] T1 â\89\98 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: â\88\80b,I,G,L,K,V,i. â¬\87*[i] L â\89¡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊐+[b] ⦃G, K, V⦄.
+lemma fqup_lref: â\88\80b,I,G,L,K,V,i. â¬\87*[i] L â\89\98 K.ⓑ{I}V → ⦃G, L, #i⦄ ⊐+[b] ⦃G, K, V⦄.
/2 width=6 by fqup_drops_strap1/ qed.