+(**************************************************************************)
+(* ___ *)
+(* ||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/plus.ma".
+
+definition hole : ∀A:Type.A → A ≝ λA.λx.x.
+
+inductive pippo (T:Type) (x:T) : Prop ≝ .
+
+axiom A: Type.
+axiom B:A.
+
+axiom foo : \forall x: (hole ? A).pippo (hole ? A) x.
+
+axiom foo: (λx,y:A. pippo (hole ? A) x y)
+ (hole ? B) (hole ? B).
+
+axiom foo: λx:(hole ? Type).λy:(hole ? Type). pippo (hole ? Type) x y.
+
+axiom foo: (λx,y.(λz. z x + z (x+y)) (λw:nat.hole ? w)) = λx,y.x. (* KO, delift rels only *)
+axiom foo: (λx,y.(λz. z (x+y) + z x) (λw:nat.hole ? w)) = λx,y.x. (* OK *)
+
+
+axiom foo: (λx,y.(λz. z x + z y) (λw:nat.hole ? w)) = λx,y.x. (* OK *)
+