branch for universe

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

diff --git a/matita/tests/letrecand.ma b/matita/tests/letrecand.ma
new file mode 100644 (file)
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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 "nat/nat.ma".
+
+let rec pari n : Prop :=
+ match n with
+  [ O ⇒ True
+  | S n ⇒ dispari n
+  ]
+and dispari n : Prop :=
+ match n with
+  [ O => False
+  | S n => pari n
+  ].
+  
+definition pari2 ≝
+let rec pari n : Prop :=
+ match n with
+  [ O ⇒ True
+  | S n ⇒ dispari n
+  ]
+and dispari n : Prop :=
+ match n with
+  [ O => False
+  | S n => pari n
+  ]
+in pari.
+
+definition dispari2 ≝
+let rec pari n : Prop :=
+ match n with
+  [ O ⇒ True
+  | S n ⇒ dispari n
+  ]
+and dispari n : Prop :=
+ match n with
+  [ O => False
+  | S n => pari n
+  ]
+in dispari.
+
+lemma test_pari: pari (S (S O)).
+simplify.
+constructor 1.
+qed.
+
+lemma test_pari2: pari2 (S (S O)).
+simplify.
+constructor 1.
+qed.
+
+lemma test_dispari: dispari (S O).
+simplify.
+constructor 1.
+qed.
+
+lemma test_dispari2: dispari2 (S O).
+simplify.
+constructor 1.
+qed.