intros...
assert (a + - a = 0)...
apply Fplus_Fopp_r...
intuition...
rewrite H1 in H0...
assert (a = 0)...
assert (a + 0 = 0 + a)...
apply Fplus_sym...
rewrite H2 in H0...
assert (0 + a = a)...
apply Fplus_Ol...
Qed.

Theorem divnonzero: forall a b: F, a / b <> 0 -> a<>0.
intros a b H1 H2; case H1; unfold Fdiv; rewrite H2; ring.