- lambdadelta: third recursive part of preservation finally proved!

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / ypr.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/reducibility/ltpr.ma".
+include "basic_2/dynamic/lsubsv.ma".
+
+(* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
+
+inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝
+| ypr_fw    : ∀L2,T2. ♯{L2, T2} < ♯{L1, T1} → ypr h g L1 T1 L2 T2
+| ypr_ltpr  : ∀L2. L1 ➡ L2 → ypr h g L1 T1 L2 T1
+| ypr_cpr   : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2
+| ypr_ssta  : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] T2 → ypr h g L1 T1 L1 T2
+| ypr_lsubsv: ∀L2. h ⊢ L2 ⊩:⊑[g] L1 → ypr h g L1 T1 L2 T1
+.
+
+interpretation
+   "'big tree' parallel reduction (closure)"
+   'BTPRed h g L1 T1 L2 T2 = (ypr h g L1 T1 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma ypr_refl: ∀h,g. bi_reflexive … (ypr h g).
+/2 width=1/ qed.