- parallel reduction for local environments: we proved the equivalence

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / conversion / lcpc.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/lcpr.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **************)
-
-definition lcpc: relation lenv ≝
-   λL1,L2. L1 ⊢ ➡ L2 ∨ L2 ⊢ ➡ L1.
-
-interpretation
-   "context-sensitive parallel conversion (local environment)"
-   'CPConv L1 L2 = (lcpc L1 L2).
-
-(* Basic properties *********************************************************)
-
-lemma lcpc_refl: ∀L. L ⊢ ⬌ L.
-/2 width=1/ qed.
-
-lemma lcpc_sym: ∀L1,L2. L1 ⊢ ⬌ L2 → L2 ⊢ ⬌ L1.
-#L1 #L2 * /2 width=1/
-qed.
-
-lemma lcpc_lcpr: ∀L1,L2. L1 ⊢ ⬌ L2 → ∃∃L. L1 ⊢ ➡ L & L2 ⊢ ➡ L.
-#L1 #L2 * /2 width=3/
-qed.