(* Advanced properties ******************************************************)
-lemma cix_lref: â\88\80h,g,G,L,i. â\87©[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃#i⦄.
+lemma cix_lref: â\88\80h,g,G,L,i. â¬\87[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃#i⦄.
#h #g #G #L #i #HL #H elim (crx_inv_lref … H) -h #I #K #V #HLK
-lapply (ldrop_mono … HLK … HL) -L -i #H destruct
+lapply (drop_mono … HLK … HL) -L -i #H destruct
qed.
(* Properties on relocation *************************************************)
-lemma cix_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ∀L,s,d,e. ⇩[s, d, e] L ≡ K →
- â\88\80U. â\87§[d, e] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
+lemma cix_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ∀L,s,l,m. ⬇[s, l, m] L ≡ K →
+ â\88\80U. â¬\86[l, m] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
/3 width=8 by crx_inv_lift/ qed.
-lemma cix_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄ → ∀K,s,d,e. ⇩[s, d, e] L ≡ K →
- â\88\80T. â\87§[d, e] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+lemma cix_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄ → ∀K,s,l,m. ⬇[s, l, m] L ≡ K →
+ â\88\80T. â¬\86[l, m] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
/3 width=8 by crx_lift/ qed-.