intros.
unfold mid_point in H.
DecompAndAll.
replace (A**B) with (- B**A) in H1.
2:symmetry...
assert (B**A = 0)...
symmetry;Geometry.
Qed.

(* Specifications: *)
Lemma mid_point_degenerated_3 : forall A B, mid_point A B A -> A=B.
Hint Resolve mid_point_degenerated_1 mid_point_degenerated_2 mid_point_degenerated_3:Geom.
Lemma eq_diff_diff : forall A B C D, A<>B -> A**B=C**D -> C<>D.
Proof with Geometry.