intros...
assert (a + a = - a + a)...
assert (- a + a = 0)...
rewrite H1 in H0...
assert (a + a = 2 * a)...
rewrite H2 in H0...
assert (2 * a / 2 = a)...
field...
auto with Geom...
assert (2 * a / 2 = 0 / 2)...
rewrite H3 in H4...
assert (0 / 2 = 0)...
field...
auto with Geom...
Qed.
Hint Resolve field_prop_2: Geom.

Lemma trivial_col1 : forall A B : Point, 0 = S A A B.
intros.