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[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / equivalence / cpcs.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/conversion/cpc.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
-
-definition cpcs: lenv → relation term ≝
-                 λL. TC … (cpc L).
-
-interpretation "context-sensitive parallel equivalence (term)"
-   'PConvStar L T1 T2 = (cpcs L T1 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma cpcs_ind: ∀L,T1. ∀R:predicate term. R T1 →
-                (∀T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → R T → R T2) →
-                ∀T2. L ⊢ T1 ⬌* T2 → R T2.
-#L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
-qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: pc3_refl *)
-lemma cpcs_refl: ∀L,T. L ⊢ T ⬌* T.
-/2 width=1/ qed.
-
-lemma cpcs_strap1: ∀L,T1,T,T2.
-                   L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
-/2 width=3/ qed.
-
-lemma cpcs_strap2: ∀L,T1,T,T2.
-                   L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-/2 width=3/ qed.
-
-(* Basic_1: removed theorems 1: clear_pc3_trans *)