From ed89b51673624e80ae63c3086245cd8deb86c110 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 26 Sep 2007 17:35:28 +0000
Subject: [PATCH] started the Proof Weight predicate for cut elimination and
 confluence

---
 matita/contribs/LOGIC/PRed/defs.ma   |  2 ++
 matita/contribs/LOGIC/Track/pred.ma  |  3 +++
 matita/contribs/LOGIC/Weight/defs.ma | 36 ++++++++++++++++++++++++++++
 3 files changed, 41 insertions(+)
 create mode 100644 matita/contribs/LOGIC/Weight/defs.ma

diff --git a/matita/contribs/LOGIC/PRed/defs.ma b/matita/contribs/LOGIC/PRed/defs.ma
index ef0f86194..51aaa94b2 100644
--- a/matita/contribs/LOGIC/PRed/defs.ma
+++ b/matita/contribs/LOGIC/PRed/defs.ma
@@ -47,6 +47,8 @@ inductive PRed: Context \to Proof \to Sequent \to
                 \forall h. PRed P1 (scut (prin h) q1) S P2 q2 S
    | pred_b_dx: \forall p1,p2,Q1,Q2,S. PRed Q1 p1 S Q2 p2 S \to
                 \forall h. PRed Q1 (scut p1 (prin h)) S Q2 p2 S
+   | pred_c   : \forall p1,p2,Q1,Q2,S. PRed Q1 p1 S Q2 p2 S \to 
+                \forall p. PRed Q1 (scut (impr p) (impw p1)) S Q2 p2 S    
 .
 
 (*CSC: the URI must disappear: there is a bug now *)
diff --git a/matita/contribs/LOGIC/Track/pred.ma b/matita/contribs/LOGIC/Track/pred.ma
index 3b640b97c..c7f6198f9 100644
--- a/matita/contribs/LOGIC/Track/pred.ma
+++ b/matita/contribs/LOGIC/Track/pred.ma
@@ -36,5 +36,8 @@ theorem track_pred: \forall Q1,Q2,p1,p2,S1,S2. PRed Q1 p1 S1 Q2 p2 S2 \to
    lapply linear track_inv_prin to H5; subst; autobatch
  | lapply linear track_inv_scut to H3; decompose; subst;
    lapply linear track_inv_prin to H4; subst; autobatch
+ | lapply linear track_inv_scut to H3; decompose; subst;
+   lapply linear track_inv_impw to H4; decompose; subst;
+   lapply linear track_inv_impr to H5; decompose; subst; autobatch
  ].
 qed.
diff --git a/matita/contribs/LOGIC/Weight/defs.ma b/matita/contribs/LOGIC/Weight/defs.ma
new file mode 100644
index 000000000..73c935913
--- /dev/null
+++ b/matita/contribs/LOGIC/Weight/defs.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/LOGIC/Weight/defs".
+
+(* PROOF WEIGHT
+   For cut elimination and confluence
+*)
+
+include "datatypes/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
+.
-- 
2.39.2