Proof with Geometry.
intros.
unfold not;intro;subst C...
Qed.
Hint Resolve not_parallel_not_eq_1 not_parallel_not_eq_2 : Geom.

(* Specifications: *)
Lemma mid_point_degenerated_1 : forall A B, mid_point A A B -> A=B.
Lemma mid_point_degenerated_2 : forall A B, mid_point A B B -> A=B.
Proof with Geometry.