milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / fpa / fpas.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpa/fpas.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpa/fpas.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/rajuststar_5.ma".
+include "basic_2/substitution/fpa.ma".
+
+(* MULTIPLE AJUSTMENT *******************************************************)
+
+definition fpas: bool → bi_relation lenv term ≝ λs. bi_TC … (fpa s).
+
+interpretation
+   "multiple ajustment (restricted closure)"
+   'RAjustStar L1 T1 s L2 T2 = (fpas s L1 T1 L2 T2).
+
+(* Basic eliminators ********************************************************)
+
+lemma fpas_ind: ∀L1,T1,s. ∀R:relation2 …. R L1 T1 →
+                (∀L,L2,T,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳[s] ⦃L2, T2⦄ → R L T → R L2 T2) →
+                ∀L2,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ → R L2 T2.
+#L1 #T1 #s #R #IH1 #IH2 #L2 #T2 #H
+@(bi_TC_star_ind … IH1 IH2 L2 T2 H) //
+qed-.
+
+lemma fpas_ind_dx: ∀L2,T2,s. ∀R:relation2 …. R L2 T2 →
+                   (∀L1,L,T1,T. ⦃L1, T1⦄ ⇳[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ → R L T → R L1 T1) →
+                   ∀L1,T1. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ → R L1 T1.
+#L2 #T2 #s #R #IH1 #IH2 #L1 #T1 #H
+@(bi_TC_star_ind_dx … IH1 IH2 L1 T1 H) //
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma fpas_refl: ∀s. bi_reflexive … (fpas s).
+/2 width=1 by bi_inj/ qed.
+
+lemma fpas_sym: ∀s. bi_symmetric … (fpas s).
+/3 width=1 by fpa_sym, bi_TC_symmetric/ qed-.
+
+lemma fpa_fpas: ∀L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L2, T2⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
+/2 width=1 by bi_inj/ qed.
+
+lemma fpas_strap1: ∀L1,L,L2,T1,T,T2,s. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳[s] ⦃L2, T2⦄ →
+                   ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
+/2 width=4 by bi_step/ qed-.
+
+lemma fpas_strap2: ∀L1,L,L2,T1,T,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L, T⦄ → ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ →
+                   ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
+/2 width=4 by bi_TC_strap/ qed-.