branch for universe

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

diff --git a/matita/tests/match_inference.ma b/matita/tests/match_inference.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+inductive pos: Set \def
+| one : pos
+| next : pos \to pos.
+
+inductive nat:Set \def
+| O : nat
+| S : nat \to nat.
+
+definition pos2nat : pos \to nat  \def 
+     \lambda x:pos . match x with  
+      [ one \Rightarrow O 
+      | (next z) \Rightarrow O]. 
+
+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].