X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Fnat%2Ftotient.ma;h=24c3920ed82571324c2977a7be798b492fbf43e7;hb=97c2d258a5c524eb5c4b85208899d80751a2c82f;hp=df863fa04f7746f86104ecaea9a9f223ae0d41d4;hpb=b3f74fab711510628cff64aff3e48e73cc9f6e09;p=helm.git

diff --git a/helm/matita/library/nat/totient.ma b/helm/matita/library/nat/totient.ma
index df863fa04..24c3920ed 100644
--- a/helm/matita/library/nat/totient.ma
+++ b/helm/matita/library/nat/totient.ma
@@ -64,4 +64,39 @@ intro.
 rewrite > eq_to_eqb_true.
 rewrite > eq_to_eqb_true.
 reflexivity.
-rewrite < H4.
\ No newline at end of file
+rewrite < H4.
+rewrite > sym_gcd.
+rewrite > gcd_mod.
+apply (gcd_times_SO_to_gcd_SO ? ? (S m2)).
+unfold lt.apply le_S_S.apply le_O_n.
+unfold lt.apply le_S_S.apply le_O_n.
+assumption.
+unfold lt.apply le_S_S.apply le_O_n.
+rewrite < H5.
+rewrite > sym_gcd.
+rewrite > gcd_mod.
+apply (gcd_times_SO_to_gcd_SO ? ? (S m)).
+unfold lt.apply le_S_S.apply le_O_n.
+unfold lt.apply le_S_S.apply le_O_n.
+rewrite > sym_times.
+assumption.
+unfold lt.apply le_S_S.apply le_O_n.
+intro.
+apply eqb_elim.
+intro.apply eqb_elim.
+intro.apply False_ind.
+apply H6.
+apply eq_gcd_times_SO.
+unfold lt.apply le_S_S.apply le_O_n.
+unfold lt.apply le_S_S.apply le_O_n.
+rewrite < gcd_mod.
+rewrite > H4.
+rewrite > sym_gcd.assumption.
+unfold lt.apply le_S_S.apply le_O_n.
+rewrite < gcd_mod.
+rewrite > H5.
+rewrite > sym_gcd.assumption.
+unfold lt.apply le_S_S.apply le_O_n.
+intro.reflexivity.
+intro.reflexivity.
+qed.
\ No newline at end of file