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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2A/reduction/crx_lift.ma".
16 include "basic_2A/reduction/cix.ma".
18 (* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ***************)
20 (* Advanced properties ******************************************************)
22 lemma cix_lref: ∀h,g,G,L,i. ⬇[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃#i⦄.
23 #h #g #G #L #i #HL #H elim (crx_inv_lref … H) -h #I #K #V #HLK
24 lapply (drop_mono … HLK … HL) -L -i #H destruct
27 (* Properties on relocation *************************************************)
29 lemma cix_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ∀L,s,l,m. ⬇[s, l, m] L ≡ K →
30 ∀U. ⬆[l, m] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄.
31 /3 width=8 by crx_inv_lift/ qed.
33 lemma cix_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃U⦄ → ∀K,s,l,m. ⬇[s, l, m] L ≡ K →
34 ∀T. ⬆[l, m] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
35 /3 width=8 by crx_lift/ qed-.