include "basic_2/reduction/crx_lift.ma".
include "basic_2/reduction/cix.ma".
-(* CONTEXT-SENSITIVE EXTENDED IRREDUCIBLE TERMS *****************************)
+(* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ***************)
(* Advanced properties ******************************************************)
-lemma cix_lref: ∀h,g,G,L,i. ⇩[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
+lemma cix_lref: ∀h,o,G,L,i. ⬇[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, o] 𝐈⦃#i⦄.
+#h #o #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: ∀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 â\89¡ U â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, g] 𝐈⦃U⦄.
+lemma cix_lift: ∀h,o,G,K,T. ⦃G, K⦄ ⊢ ➡[h, o] 𝐈⦃T⦄ → ∀L,c,l,k. ⬇[c, l, k] L ≡ K →
+ â\88\80U. â¬\86[l, k] T â\89¡ U â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, o] 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 â\89¡ U â\86\92 â¦\83G, Kâ¦\84 â\8a¢ â\9e¡[h, g] 𝐈⦃T⦄.
+lemma cix_inv_lift: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ➡[h, o] 𝐈⦃U⦄ → ∀K,c,l,k. ⬇[c, l, k] L ≡ K →
+ â\88\80T. â¬\86[l, k] T â\89¡ U â\86\92 â¦\83G, Kâ¦\84 â\8a¢ â\9e¡[h, o] 𝐈⦃T⦄.
/3 width=8 by crx_lift/ qed-.