intros...
assert (- - a = - - b)...
assert (- - a = a)...
assert (- - b = b)...
Qed.

(* Specifications: *)
Lemma nonzeromult : forall a b : F, a <> 0 -> b <> 0 -> a * b <> 0.
Proof with try solve [ auto with field_hints | congruence ].