- parallel reduction for local environments: we proved the equivalence

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / lcprs.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 COMPUTATION ON LOCAL ENVIRONMENTS *************)
-
-definition lcprs: relation lenv ≝ TC … lcpr.
-
-interpretation
-  "context-sensitive parallel computation (environment)"
-  'CPRedStar L1 L2 = (lcprs L1 L2).
-
-(* Basic eliminators ********************************************************)
-
-lemma lcprs_ind: ∀L1. ∀R:predicate lenv. R L1 →
-                 (∀L,L2. L1 ⊢ ➡* L → L ⊢ ➡ L2 → R L → R L2) →
-                 ∀L2. L1 ⊢ ➡* L2 → R L2.
-#L1 #R #HL1 #IHL1 #L2 #HL12
-@(TC_star_ind … HL1 IHL1 … HL12) //
-qed-.
-
-lemma lcprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
-                    (∀L1,L. L1 ⊢ ➡ L → L ⊢ ➡* L2 → R L → R L1) →
-                    ∀L1. L1 ⊢ ➡* L2 → R L1.
-#L2 #R #HL2 #IHL2 #L1 #HL12
-@(TC_star_ind_dx … HL2 IHL2 … HL12) //
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma lcprs_refl: ∀L. L ⊢ ➡* L.
-/2 width=1/ qed.
-
-lemma lcprs_strap1: ∀L1,L,L2.
-                    L1 ⊢ ➡* L → L ⊢ ➡ L2 → L1 ⊢ ➡* L2.
-/2 width=3/ qed.
-
-lemma lcprs_strap2: ∀L1,L,L2.
-                    L1 ⊢ ➡ L → L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
-/2 width=3/ qed.