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[helm.git] / matita / contribs / LOGIC / Weight / defs.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+(* PROOF WEIGHT
+   For cut elimination and confluence
+*)
+
+include "datatypes_defs/Context.ma".
+
+
+inductive Weight: Nat \to Context \to Proof \to Nat \to Prop \def
+   | weight_prin: \forall Q,n,m. Weight m Q (prin n) m
+   | weight_impw: \forall p,Q,m0,m1. Weight m0 Q p m1 \to
+                  \forall m. (m1 + m0 == m) \to
+                  Weight m0 Q (impw p) m
+   | weight_impr: \forall p,Q,m0,m1. Weight m0 Q p m1 \to
+                  \forall m. (m1 + m0 == m) \to
+                  Weight m0 Q (impr p) m
+   | weight_scut: \forall p1,Q,m0,m1. Weight (succ m0) Q p1 m1 \to
+                  \forall p2,m2. Weight (succ m0) Q p2 m2 \to
+                  \forall m. (m1 + m2 == m) \to
+                  Weight m0 Q (scut p1 p2) m
+.