(* 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 (drop_mono … HLK … HL) -L -i #H destruct
qed.
(* Properties on relocation *************************************************)
-lemma cix_lift: â\88\80h,g,G,K,T. â¦\83G, Kâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\88â¦\83Tâ¦\84 â\86\92 â\88\80L,s,d,e. â\87©[s, d, e] L ≡ K →
- â\88\80U. â\87§[d, e] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
+lemma cix_lift: â\88\80h,g,G,K,T. â¦\83G, Kâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\88â¦\83Tâ¦\84 â\86\92 â\88\80L,s,d,e. â¬\87[s, d, e] L ≡ K →
+ â\88\80U. â¬\86[d, e] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
/3 width=8 by crx_inv_lift/ qed.
-lemma cix_inv_lift: â\88\80h,g,G,L,U. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\88â¦\83Uâ¦\84 â\86\92 â\88\80K,s,d,e. â\87©[s, d, e] L ≡ K →
- â\88\80T. â\87§[d, e] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+lemma cix_inv_lift: â\88\80h,g,G,L,U. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\88â¦\83Uâ¦\84 â\86\92 â\88\80K,s,d,e. â¬\87[s, d, e] L ≡ K →
+ â\88\80T. â¬\86[d, e] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
/3 width=8 by crx_lift/ qed-.