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[helm.git] / matita / tests / coercions_dependent.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+include "nat/nat.ma".
+include "list/list.ma".
+include "decidable_kit/list_aux.ma".
+(* tests from "Dependent Coersion" by Luo and Soloviev *)
+
+inductive vec (A : Type) : nat -> Type :=
+ | vnil : vec A O
+ | vcons : ∀a:A.∀n:nat.vec A n -> vec A (S n).
+ 
+axiom c : ∀A,B.∀l:list A.vec B (length A l).
+
+axiom veclen : ∀A,n.vec A n -> nat.
+
+coercion cic:/matita/tests/coercions_dependent/c.con.
+
+alias num (instance 0) = "natural number".
+definition xxx := veclen nat ? [3; 4; 7].