- parallel reduction for local environments: we proved the equivalence

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / equivalence / lcpcs_lcpcs.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_lcpcs.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_lcpcs.ma
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--- a/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_lcpcs.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/computation/lcprs_lcprs.ma".
-include "basic_2/conversion/lcpc_lcpc.ma".
-include "basic_2/equivalence/lcpcs_lcprs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *************)
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma lcpcs_inv_lcprs: ∀L1,L2. L1 ⊢ ⬌* L2 →
-                       ∃∃L. L1 ⊢ ➡* L & L2 ⊢ ➡* L.
-#L1 #L2 #H @(lcpcs_ind … H) -L2
-[ /3 width=3/
-| #L #L2 #_ #HL2 * #L0 #HL10 elim HL2 -HL2 #HL2 #HL0
-  [ elim (lcprs_strip … HL0 … HL2) -L #L #HL0 #HL2
-    lapply (lcprs_strap1 … HL10 … HL0) -L0 /2 width=3/
-  | lapply (lcprs_strap2 … HL2 … HL0) -L /2 width=3/
-  ]
-]
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma lcpcs_strip: ∀L,L1. L ⊢ ⬌* L1 → ∀L2. L ⊢ ⬌ L2 →
-                   ∃∃L0. L1 ⊢ ⬌ L0 & L2 ⊢ ⬌* L0.
-/3 width=3/ qed.
-
-(* Main properties **********************************************************)
-
-theorem lcpcs_trans: ∀L1,L. L1 ⊢ ⬌* L → ∀L2. L ⊢ ⬌* L2 → L1 ⊢ ⬌* L2.
-/2 width=3/ qed.
-
-theorem lcpcs_canc_sn: ∀L,L1,L2. L ⊢ ⬌* L1 → L ⊢ ⬌* L2 → L1 ⊢ ⬌* L2.
-/3 width=3 by lcpcs_trans, lcprs_comm/ qed.
-
-theorem lcpcs_canc_dx: ∀L,L1,L2. L1 ⊢ ⬌* L → L2 ⊢ ⬌* L → L1 ⊢ ⬌* L2.
-/3 width=3 by lcpcs_trans, lcprs_comm/ qed.