update in lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_cix.ma b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_cix.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/cpx_cix.ma".
+include "basic_2A/reduction/cnx_crx.ma".
+
+(* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
+
+(* Main properties on irreducibility ****************************************)
+
+theorem cix_cnx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄.
+/2 width=6 by cpx_fwd_cix/ qed.
+
+(* Main inversion lemmas on irreducibility **********************************)
+
+theorem cnx_inv_cix: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+/2 width=7 by cnx_inv_crx/ qed-.