update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / computation / csx_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/computation/csx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2A/computation/csx_lleq.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_lleq.ma".
+include "basic_2A/computation/csx.ma".
+
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+
+(* Properties on lazy equivalence for local environments ********************)
+
+lemma csx_lleq_conf: ∀h,g,G,L1,T. ⦃G, L1⦄ ⊢ ⬊*[h, g] T →
+                     ∀L2. L1 ≡[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L1 #T #H @(csx_ind … H) -T
+/4 width=6 by csx_intro, cpx_lleq_conf_dx, lleq_cpx_trans/
+qed-.
+
+lemma csx_lleq_trans: ∀h,g,G,L1,L2,T.
+                      L1 ≡[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T → ⦃G, L1⦄ ⊢ ⬊*[h, g] T.
+/3 width=3 by csx_lleq_conf, lleq_sym/ qed-.