- parallel reduction for local environments: we proved the equivalence

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / lcprs_lcprs.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_lcprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_lcprs.ma
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--- a/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_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_lcpr.ma".
-include "basic_2/computation/lcprs_cprs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
-
-(* Advanced properties ******************************************************)
-
-lemma lcprs_strip: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡ L2 →
-                   ∃∃L0. L1 ⊢ ➡ L0 & L2 ⊢ ➡* L0.
-/3 width=3/ qed.
-
-(* Main properties **********************************************************)
-
-theorem lcprs_conf: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡* L2 →
-                    ∃∃L0. L1 ⊢ ➡* L0 & L2 ⊢ ➡* L0.
-/3 width=3/ qed.
-
-theorem lcprs_trans: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
-/2 width=3/ qed.
-
-lemma lcprs_pair: ∀L1,L2. L1 ⊢ ➡* L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
-                  ∀I. L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
-#L1 #L2 #H @(lcprs_ind … H) -L2 /2 width=1/
-#L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
-@(lcprs_trans … (L.ⓑ{I}V1)) /2 width=1/
-qed.