milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / lpc / lfpcs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs.etc
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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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+notation "hvbox( ⦃ term 46 L1 ⦄ ⬌ ⬌ * break ⦃ term 46 L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvStarAlt $L1 $L2 }.
+
+include "basic_2/conversion/lfpc.ma".
+
+(* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
+
+definition lfpcs: relation lenv ≝ TC … lfpc.
+
+interpretation "focalized parallel equivalence (local environment)"
+   'FocalizedPConvStar L1 L2 = (lfpcs L1 L2).
+
+(* Basic eliminators ********************************************************)
+
+lemma lfpcs_ind: ∀L1. ∀R:predicate lenv. R L1 →
+                 (∀L,L2. ⦃L1⦄ ⬌* ⦃L⦄ → ⦃L⦄ ⬌ ⦃L2⦄ → R L → R L2) →
+                 ∀L2. ⦃L1⦄ ⬌* ⦃L2⦄ → R L2.
+#L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
+qed-.
+
+lemma lfpcs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
+                    (∀L1,L. ⦃L1⦄ ⬌ ⦃L⦄ → ⦃L⦄ ⬌* ⦃L2⦄ → R L → R L1) →
+                    ∀L1. ⦃L1⦄ ⬌* ⦃L2⦄ → R L1.
+#L2 #R #HL2 #IHL2 #L1 #HL12
+@(TC_star_ind_dx … HL2 IHL2 … HL12) //
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma lfpcs_refl: reflexive … lfpcs.
+/2 width=1/ qed.
+
+lemma lfpcs_sym: symmetric … lfpcs.
+/3 width=1/ qed.
+
+lemma lfpc_lfpcs: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/2 width=1/ qed.
+
+lemma lfpcs_strap1: ∀L1,L,L2. ⦃L1⦄ ⬌* ⦃L⦄ → ⦃L⦄ ⬌ ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/2 width=3/ qed.
+
+lemma lfpcs_strap2: ∀L1,L,L2. ⦃L1⦄ ⬌ ⦃L⦄ → ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/2 width=3/ qed.
+
+lemma lfpcs_lfpr_dx: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=1/ qed.
+
+lemma lfpcs_lfpr_sn: ∀L1,L2. ⦃L2⦄ ➡ ⦃L1⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=1/ qed.
+
+lemma lfpcs_lfpr_strap1: ∀L1,L. ⦃L1⦄ ⬌* ⦃L⦄ → ∀L2. ⦃L⦄ ➡ ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3/ qed.
+
+lemma lfpcs_lfpr_strap2: ∀L1,L. ⦃L1⦄ ➡ ⦃L⦄ → ∀L2. ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3/ qed.
+
+lemma lfpcs_lfpr_div: ∀L1,L. ⦃L1⦄ ⬌* ⦃L⦄ → ∀L2. ⦃L2⦄ ➡ ⦃L⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3/ qed.
+
+lemma lfpcs_lfpr_conf: ∀L1,L. ⦃L⦄ ➡ ⦃L1⦄ → ∀L2. ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3/ qed.