From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 24 Apr 2008 13:00:21 +0000 (+0000)
Subject: added coinductive example
X-Git-Tag: make_still_working~5290
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=75f1cb233da81b8db172128c7e93493009c0754e;p=helm.git

added coinductive example
---

diff --git a/helm/software/matita/tests/formal_topology.ma b/helm/software/matita/tests/formal_topology.ma
new file mode 100755
index 000000000..54c6aa629
--- /dev/null
+++ b/helm/software/matita/tests/formal_topology.ma
@@ -0,0 +1,37 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "logic/connectives.ma".
+
+coinductive fish (A:Type) (i: A → Type) (C: ∀a:A.i a → A → Prop) (U: A → Prop)
+               : A → Prop
+≝
+ mk_foo: ∀a:A. (U a ∧ ∀j: i a. ∃y: A. C a j y ∧ fish A i C U y) → fish A i C U a.
+
+let corec fish_rec (A:Type) (i: A → Type) (C: ∀a:A.i a → A → Prop) (U: A → Prop)
+ (P: A → Prop) (H1: ∀a:A. P a → U a)
+  (H2: ∀a:A. P a → ∀j: i a. ∃y: A. C a j y ∧ P y) :
+   ∀a:A. ∀p: P a. fish A i C U a ≝
+ λa,p.
+  mk_foo A i C U a
+   (conj ? ? (H1 ? p)
+   (λj: i a.
+    match H2 a p j with
+     [ ex_intro (y: A) (Ha: C a j y ∧ P y) ⇒
+        match Ha with
+         [ conj (fHa: C a j y) (sHa: P y) ⇒
+            ex_intro A (λy.C a j y ∧ fish A i C U y) y
+             (conj ? ? fHa (fish_rec A i C U P H1 H2 y sHa))
+         ]
+     ])).
\ No newline at end of file