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[helm.git] / matita / tests / first.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+inductive nat : Set \def
+  | O : nat
+  | S : nat \to nat.
+
+inductive eq (A:Set): A \to A \to Prop \def
+  refl: \forall x:A.eq A x x. 
+
+inductive list (A:Set) : Set \def
+  | nil : list A
+  | cons : A \to list A \to list A.
+
+let rec list_len (A:Set) (l:list A) on l \def
+  match l with 
+  [ nil \Rightarrow O
+  | (cons a tl) \Rightarrow S (list_len A tl)].
+  
+theorem stupid: \forall A:Set.eq ? (list_len A (nil ?)) O.
+intros.
+normalize.
+apply refl.
+qed.