intros...
unfold not in |- *; intro...
assert (a * / a = 1)...
field...
assert (a * / a = a * 0)...
rewrite H1 in H2...
assert (a * 0 = 0)...
ring...
rewrite H3 in H2...
Qed.

Lemma opzero : forall a : F, a <> 0 -> - a <> 0.
Proof with try solve [ congruence ].