update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / reduction / cix_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/reduction/cix_lift.ma b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cix_lift.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cix_lift.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2A/reduction/crx_lift.ma".
+include "basic_2A/reduction/cix.ma".
+
+(* 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 (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,l,m. ⬇[s, l, m] L ≡ K →
+                ∀U. ⬆[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,l,m. ⬇[s, l, m] L ≡ K →
+                    ∀T. ⬆[l, m] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+/3 width=8 by crx_lift/ qed-.