- parallel reduction for local environments: we proved the equivalence

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / lfpr_fpr.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_2/reducibility/lfpr.ma".
+include "basic_2/reducibility/cfpr_cpr.ma".
+
+(* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
+
+(* Inversion lemmas on context-free parallel reduction for closures *********)
+
+lemma fpr_lfpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1⦄ ➡ ⦃L2⦄.
+#L1 #L2 #T1 #T2 #H
+elim (fpr_inv_all … H) -H /2 width=3/
+qed. 
+
+(* Inversion lemmas on context-free parallel reduction for closures *********)
+
+lemma lfpr_inv_fpr: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀T. ⦃L1, T⦄ ➡ ⦃L2, T⦄.
+#L1 #L2 * /2 width=4/
+qed-.