X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Ftotient.ma;h=9933490a2dda03f20da09be3124dee5919ec3d8e;hb=947ee89dec9e60561dfac3ce7e1842f35f178cb8;hp=a86986a81f743efd78b0dd004e38653c0788d601;hpb=d5afc8f8891d0020f5804eb2322fc0d1c8c60702;p=helm.git diff --git a/helm/software/matita/library/nat/totient.ma b/helm/software/matita/library/nat/totient.ma index a86986a81..9933490a2 100644 --- a/helm/software/matita/library/nat/totient.ma +++ b/helm/software/matita/library/nat/totient.ma @@ -33,7 +33,9 @@ include "nat/iteration2.ma". definition totient : nat \to nat \def \lambda n.sigma_p n (\lambda m. eqb (gcd m n) (S O)) (\lambda m.S O). - +lemma totient1: totient (S(S(S(S(S(S O)))))) = ?. +[|simplify. + theorem totient_times: \forall n,m:nat. (gcd m n) = (S O) \to totient (n*m) = (totient n)*(totient m). intros.