apply le_to_or_lt_eq.apply le_O_n.
qed.
-(* esempio di sfarfallalmento !!! *)
-(*
-theorem bad: \forall n,p,q:nat.prime n \to divides n (p*q) \to
-divides n p \lor divides n q.
-intros.
-cut divides n p \lor \not (divides n p).
-elim Hcut.left.assumption.
-right.
-cut \exists a,b. a*n - b*p = (S O) \lor b*p - a*n = (S O).
-elim Hcut1.elim H3.*)
-
theorem divides_times_to_divides: \forall n,p,q:nat.prime n \to divides n (p*q) \to
divides n p \lor divides n q.
intros.