+(**************************************************************************)
+(* ___ *)
+(* ||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/match_inference/".
+
inductive pos: Set \def
| one : pos
| next : pos \to pos.
| O : nat
| S : nat \to nat.
-inductive empty : Set \def .
-
definition pos2nat : pos \to nat \def
\lambda x:pos . match x with
[ one \Rightarrow O
| (next z) \Rightarrow O].
-definition empty2nat : empty \to nat \def
- \lambda x : empty . S (match x in empty with []).
\ No newline at end of file
+inductive empty (x:nat) : nat \to Set \def .
+
+definition empty2nat : (empty O O) \to nat \def
+ \lambda x : (empty O O). S (match x in empty with []).
+
+inductive le (n:nat) : nat \to Prop \def
+ | le_n : le n n
+ | le_S : \forall m:nat. le n m \to le n (S m).
+
+inductive True : Prop \def
+ I : True.
+
+definition r : True \def
+ match (le_n O) with
+ [ le_n \Rightarrow I
+ | (le_S y p') \Rightarrow I ].
+
+inductive Prod (A,B:Set): Set \def
+pair : A \to B \to Prod A B.
+
+definition fst : \forall A,B:Set. (Prod A B) \to A \def
+\lambda A,B:Set. \lambda p:(Prod A B). match p with
+[(pair a b) \Rightarrow a].