update in groud_2 and models

[helm.git] / helm / software / matita / library / nat / nat.ma

diff --git a/helm/software/matita/library/nat/nat.ma b/helm/software/matita/library/nat/nat.ma
index b600072c61ba97cfa9e862251d04c566b3a0e765..83b489f06eb08a6772e0d7abb00e315032604ad0 100644 (file)
--- a/helm/software/matita/library/nat/nat.ma
+++ b/helm/software/matita/library/nat/nat.ma
@@ -1,5 +1,5 @@
 (**************************************************************************)
-(*       ___                                                                 *)
+(*       ___                                                             *)
 (*      ||M||                                                             *)
 (*      ||A||       A project by Andrea Asperti                           *)
 (*      ||T||                                                             *)
@@ -12,21 +12,25 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/nat".
-
 include "higher_order_defs/functions.ma".
 
 inductive nat : Set \def
   | O : nat
   | S : nat \to nat.
 
+interpretation "Natural numbers" 'N = nat.
+
+default "natural numbers" cic:/matita/nat/nat/nat.ind.
+
+alias num (instance 0) = "natural number".
+
 definition pred: nat \to nat \def
  \lambda n:nat. match n with
  [ O \Rightarrow  O
  | (S p) \Rightarrow p ].
 
 theorem pred_Sn : \forall n:nat.n=(pred (S n)).
- intros. reflexivity.
+ intros. simplify. reflexivity.
 qed.
 
 theorem injective_S : injective nat nat S.