- intermediate commit to allow debugging of auto tactic in xprs.ma

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / xpr.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/xpr.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/xpr.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/static/ssta.ma".
+include "basic_2/reducibility/cpr.ma".
+
+(* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
+
+definition xpr: ∀h. sd h → lenv → relation term ≝
+   λh,g,L,T1,T2. L ⊢ T1 ➡ T2 ∨ ∃l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2.
+
+interpretation
+   "extended parallel reduction (term)"
+   'XPRed h g L T1 T2 = (xpr h g L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma cpr_xpr: ∀h,g,L,T1,T2. L ⊢ T1 ➡ T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
+/2 width=1/ qed.
+
+lemma ssta_xpr: ∀h,g,L,T1,T2,l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
+/3 width=2/ qed.
+
+lemma xpr_refl: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ➸[g] T.
+/2 width=1/ qed.