little change to theorem eq_gcd_times_times_eqv_times_gcd

diff --git a/matita/library/nat/gcd_properties1.ma b/matita/library/nat/gcd_properties1.ma
index aa9783a9638067f41a2b800a039b4730696ae2ee..637c20f4a375be17e11094e547cfa7c7783aec5b 100644 (file)
--- a/matita/library/nat/gcd_properties1.ma
+++ b/matita/library/nat/gcd_properties1.ma
@@ -203,7 +203,29 @@ apply (nat_case1 c)
   simplify.
   reflexivity
 | intros.
-  rewrite < H. 
+  rewrite < H.
+  apply gcd1
+  [ apply divides_times
+    [ apply divides_n_n
+    | apply divides_gcd_n.
+    ]
+  | apply divides_times
+    [ apply divides_n_n
+    | rewrite > sym_gcd.  
+      apply divides_gcd_n
+    ]
+  | intros.
+    apply (divides_d_times_gcd)
+    [ rewrite > H.
+      apply lt_O_S  
+    | assumption
+    | assumption
+    ]
+  ]
+]
+qed.
+  
+  (* 
   apply (nat_case1 a)
   [ intros.
     rewrite > (sym_times c O).
@@ -241,7 +263,7 @@ apply (nat_case1 c)
     ]
   ]
 ]
-qed.
+qed.*)
 
 
 theorem associative_nat_gcd: associative nat gcd.