- lambda_delta: programmed renaming to lambdadelta

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/fpcs.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/fpcs.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/fpc.ma".
-
-(* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
-
-definition fpcs: bi_relation lenv term ≝ bi_TC … fpc.
-
-interpretation "context-free parallel equivalence (closure)"
-   'FocalizedPConvStar L1 T1 L2 T2 = (fpcs L1 T1 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma fpcs_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
-                (∀L,L2,T,T2. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ → ⦃L, T⦄ ⬌ ⦃L2, T2⦄ → R L T → R L2 T2) →
-                ∀L2,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → R L2 T2.
-/3 width=7 by bi_TC_star_ind/ qed-.
-
-lemma fpcs_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
-                   (∀L1,L,T1,T. ⦃L1, T1⦄ ⬌ ⦃L, T⦄ → ⦃L, T⦄ ⬌* ⦃L2, T2⦄ → R L T → R L1 T1) →
-                   ∀L1,T1. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → R L1 T1.
-/3 width=7 by bi_TC_star_ind_dx/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma fpcs_refl: bi_reflexive … fpcs.
-/2 width=1/ qed.
-
-lemma fpcs_sym: bi_symmetric … fpcs.
-/3 width=1/ qed.
-
-lemma fpcs_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ → ⦃L, T⦄ ⬌ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma fpcs_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⬌ ⦃L, T⦄ → ⦃L, T⦄ ⬌* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma fpcs_fpr_dx: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=1/ qed.
-
-lemma fpcs_fpr_sn: ∀L1,L2,T1,T2. ⦃L2, T2⦄ ➡ ⦃L1, T1⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=1/ qed.
-
-lemma fpcs_fpr_strap1: ∀L1,L,T1,T. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ →
-                       ∀L2,T2. ⦃L, T⦄ ➡ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=4/ qed.
-
-lemma fpcs_fpr_strap2: ∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ →
-                       ∀L2,T2. ⦃L, T⦄ ⬌* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=4/ qed.
-
-lemma fpcs_fpr_div: ∀L1,L,T1,T. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ →
-                    ∀L2,T2. ⦃L2, T2⦄ ➡ ⦃L, T⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=4/ qed.
-
-lemma fpr_div: ∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ∀L2,T2. ⦃L2, T2⦄ ➡ ⦃L, T⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=4/ qed-.
-
-lemma fpcs_fpr_conf: ∀L1,L,T1,T. ⦃L, T⦄ ➡ ⦃L1, T1⦄ →
-                     ∀L2,T2. ⦃L, T⦄ ⬌* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
-/3 width=4/ qed.