Section nsatz1.
Context {R:Type}`{Rid:Integral_domain R}.
intros x y H; setoid_replace x with ((x - y) + y); simpl;
[setoid_rewrite H | idtac]; simpl. cring. cring.
Qed.
intros x y H; simpl; setoid_rewrite H; simpl; cring.
Qed.

Lemma nsatzR_diff: forall x y:R, not (x == y) -> not (x - y == 0).