+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/tests/coercions/".
+include "legacy/coq.ma".
+
inductive pos: Set \def
| one : pos
| next : pos \to pos.
inductive empty : Set \def .
-let rec pos2nat (x:pos) : nat \def
+let rec pos2nat x \def
match x with
[ one \Rightarrow (S O)
| (next z) \Rightarrow S (pos2nat z)].
-let rec nat2int (x:nat) :int \def
- match x with
- [ O \Rightarrow positive O
- | (S z) \Rightarrow positive (S z)].
-
-coercion pos2nat.
-
-coercion nat2int.
-
-let rec plus x y : int \def
- match x with
- [ (positive n) \Rightarrow x
- | (negative z) \Rightarrow y].
-
-theorem a: plus O one.
-
-
-
-
+definition nat2int \def \lambda x. positive x.
+coercion cic:/matita/tests/coercions/pos2nat.con.
+coercion cic:/matita/tests/coercions/nat2int.con.
+definition fst \def \lambda x,y:int.x.
+theorem a: fst O one = fst (positive O) (next one).
+reflexivity.
+qed.
+definition double:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (nat2int x).
+
+definition double1:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (pos2nat x).
+definition double2:
+ \forall f:int \to int. pos \to int
+\def
+ \lambda f:int \to int. \lambda x : pos .f (nat2int (pos2nat x)).
+
+