- parallel reduction for local environments: we proved the equivalence

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_aaa.ma
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--- a/matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_aaa.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_aaa.ma".
-include "basic_2/equivalence/cpcs_cpcs.ma".
-include "basic_2/equivalence/lcpcs_lcpcs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL EBVIRONMENTS *************)
-
-(* Main properties about atomic arity assignment on terms *******************)
-
-theorem aaa_lcpcs_mono: ∀L1,L2. L1 ⊢ ⬌* L2 →
-                        ∀T,A1. L1 ⊢ T ⁝ A1 → ∀A2. L2 ⊢ T ⁝ A2 →
-                        A1 = A2.
-#L1 #L2 #HL12 #T #A1 #HT1 #A2 #HT2
-elim (lcpcs_inv_lcprs … HL12) -HL12 #L #HL1 #HL2
-lapply (aaa_lcprs_conf … HT1 … HL1) -L1 #HT1
-lapply (aaa_lcprs_conf … HT2 … HL2) -L2 #HT2
-lapply (aaa_mono … HT1 … HT2) -L -T //
-qed-.
-
-theorem aaa_cpcs_mono: ∀L,T1,T2. L ⊢ T1 ⬌* T2 →
-                       ∀A1. L ⊢ T1 ⁝ A1 → ∀A2. L ⊢ T2 ⁝ A2 →
-                       A1 = A2.
-#L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
-elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
-lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1
-lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2
-lapply (aaa_mono … HA1 … HA2) -L -T //
-qed-.