branch for universe

[helm.git] / matita / tests / coercions_contravariant.ma

diff --git a/matita/tests/coercions_contravariant.ma b/matita/tests/coercions_contravariant.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 "logic/equality.ma".
+include "nat/nat.ma".
+
+axiom A : nat -> Type.
+axiom B : nat -> Type.
+axiom A1: nat -> Type.
+axiom B1: nat -> Type.
+axiom c : ∀n,m. A1 n -> A m.
+axiom d : ∀n,m. B n -> B1 m.
+axiom f : ∀n,m. A n -> B m.
+axiom g : ∀n.B n.
+
+coercion cic:/matita/tests/coercions_contravariant/c.con.
+coercion cic:/matita/tests/coercions_contravariant/d.con.
+
+definition foo :=  λn,n1,m,m1.(λx.d m m1 (f n m (c n1 n x)) : A1 n1 -> B1 m1).
+definition foo1_1 := λn,n1,m,m1.(f n m : A1 n1 -> B1 m1).
+
+definition h := λn,m.λx:A n.g m.
+definition foo2 := λn,n1,m,m1.(h n m : A1 n1 -> B1 m1).
+definition foo3 := λn1,n,m,m1.(h n m : A1 n1 -> B1 m1).
+definition foo4 := λn1,n,m1,m.(h n m : A1 n1 -> B1 m1).