intros a b c; elim c; simpl in |- *; auto.
intros H'; apply cong_ref.
intros n0 H' H'0.
apply cong_mult; auto.
Qed.

(* Specifications: *)
Theorem congruent' :
forall a b : nat, b <= a -> congruent a b -> exists k : nat, a = k * n + b.