some renaming to free the baseuri cic:/matita/lambda

[helm.git] / matita / matita / lib / pts_dummy_new / convertibility.ma

diff --git a/matita/matita/lib/pts_dummy_new/convertibility.ma b/matita/matita/lib/pts_dummy_new/convertibility.ma
new file mode 100644 (file)
index 0000000..377d3c8
--- /dev/null
+++ b/matita/matita/lib/pts_dummy_new/convertibility.ma
@@ -0,0 +1,73 @@
+(*
+    ||M||  This file is part of HELM, an Hypertextual, Electronic        
+    ||A||  Library of Mathematics, developed at the Computer Science     
+    ||T||  Department of the University of Bologna, Italy.                     
+    ||I||                                                                 
+    ||T||  
+    ||A||  This file is distributed under the terms of the 
+    \   /  GNU General Public License Version 2        
+     \ /      
+      V_______________________________________________________________ *)
+
+include "lambda/reduction.ma".
+
+(*
+inductive T : Type[0] ≝
+  | Sort: nat → T
+  | Rel: nat → T 
+  | App: T → T → T 
+  | Lambda: T → T → T (* type, body *)
+  | Prod: T → T → T (* type, body *)
+  | D: T →T
+.
+*)
+
+inductive conv : T →T → Prop ≝
+  | cbeta: ∀P,M,N. conv (App (Lambda P M) N) (M[0 ≝ N])
+  | cappl: ∀M,M1,N. conv M M1 → conv (App M N) (App M1 N)
+  | cappr: ∀M,N,N1. conv N N1 → conv (App M N) (App M N1)
+  | claml: ∀M,M1,N. conv M M1 → conv (Lambda M N) (Lambda M1 N)
+  | clamr: ∀M,N,N1. conv N N1 → conv (Lambda M N) (Lambda M N1)
+  | cprodl: ∀M,M1,N. conv M M1 → conv (Prod M N) (Prod M1 N)
+  | cprodr: ∀M,N,N1. conv N N1 → conv (Prod M N) (Prod M N1)
+  | cd: ∀M,M1. conv (D M) (D M1). 
+
+definition CO ≝ star … conv.
+
+lemma red_to_conv: ∀M,N. red M N → conv M N.
+#M #N #redMN (elim redMN) /2/
+qed.
+
+inductive d_eq : T →T → Prop ≝
+  | same: ∀M. d_eq M M
+  | ed: ∀M,M1. d_eq (D M) (D M1)
+  | eapp: ∀M1,M2,N1,N2. d_eq M1 M2 → d_eq N1 N2 → 
+      d_eq (App M1 N1) (App M2 N2)
+  | elam: ∀M1,M2,N1,N2. d_eq M1 M2 → d_eq N1 N2 → 
+      d_eq (Lambda M1 N1) (Lambda M2 N2)
+  | eprod: ∀M1,M2,N1,N2. d_eq M1 M2 → d_eq N1 N2 → 
+      d_eq (Prod M1 N1) (Prod M2 N2).
+      
+lemma conv_to_deq: ∀M,N. conv M N → red M N ∨ d_eq M N.
+#M #N #coMN (elim coMN)
+  [#P #B #C %1 //
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 #N1 #coPM1 * [#redP %1 /2/ | #eqPM1 %2 /3/]
+  |#P #M1 %2 //
+  ]
+qed.
+
+(* FG: THIS IN NOT COMPLETE
+theorem main1: ∀M,N. CO M N → 
+  ∃P,Q. star … red M P ∧ star … red N Q ∧ d_eq P Q.
+#M #N #coMN (elim coMN)
+  [#B #C #rMB #convBC * #P1 * #Q1 * * #redMP1 #redBQ1 
+   #deqP1Q1 (cases (conv_to_deq … convBC))
+    [
+  |@(ex_intro … M) @(ex_intro … M) % // % //
+  ]
+*)