X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fnat.ma;h=b098279e62e9ed3ecf1cf99a04e564faaf3bbf2c;hb=eac90238cf23594c64e305d2945fd29ed075df0a;hp=b600072c61ba97cfa9e862251d04c566b3a0e765;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git diff --git a/helm/software/matita/library/nat/nat.ma b/helm/software/matita/library/nat/nat.ma index b600072c6..b098279e6 100644 --- a/helm/software/matita/library/nat/nat.ma +++ b/helm/software/matita/library/nat/nat.ma @@ -12,21 +12,22 @@ (* *) (**************************************************************************) -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. +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.