(* Properties with generic slicing for local environments *******************)
lemma fqup_drops_succ: ∀b,G,K,T,i,L,U. ⬇*[↑i] L ≘ K → ⬆*[↑i] T ≘ U →
- â¦\83G,L,Uâ¦\84 â\8a\90+[b] ⦃G,K,T⦄.
+ â¦\83G,L,Uâ¦\84 â¬\82+[b] ⦃G,K,T⦄.
#b #G #K #T #i elim i -i
[ #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
#I #Y #HY #H destruct <(drops_fwd_isid … HY) -K //
qed.
lemma fqup_drops_strap1: ∀b,G1,G2,L1,K1,K2,T1,T2,U1,i. ⬇*[i] L1 ≘ K1 → ⬆*[i] T1 ≘ U1 →
- â¦\83G1,K1,T1â¦\84 â\8a\90[b] â¦\83G2,K2,T2â¦\84 â\86\92 â¦\83G1,L1,U1â¦\84 â\8a\90+[b] ⦃G2,K2,T2⦄.
+ â¦\83G1,K1,T1â¦\84 â¬\82[b] â¦\83G2,K2,T2â¦\84 â\86\92 â¦\83G1,L1,U1â¦\84 â¬\82+[b] ⦃G2,K2,T2⦄.
#b #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 *
[ #HLK1 #HTU1 #HT12
>(drops_fwd_isid … HLK1) -L1 //
]
qed-.
-lemma fqup_lref: â\88\80b,I,G,L,K,V,i. â¬\87*[i] L â\89\98 K.â\93\91{I}V â\86\92 â¦\83G,L,#iâ¦\84 â\8a\90+[b] ⦃G,K,V⦄.
+lemma fqup_lref: â\88\80b,I,G,L,K,V,i. â¬\87*[i] L â\89\98 K.â\93\91{I}V â\86\92 â¦\83G,L,#iâ¦\84 â¬\82+[b] ⦃G,K,V⦄.
/2 width=6 by fqup_drops_strap1/ qed.