Hint Resolve para_not_eq_1 para_not_eq_2 para_not_eq_3
para_not_eq_4 para_not_eq_5 para_not_eq_6 : Geom.

(* Specifications: *)
Theorem mid_point_equation :
forall A C O P Q : Point,
Col O A C -> A <> C -> A ** O = O ** C ->
S A P Q + S C P Q = 2 * S O P Q.
Theorem col_par_par :  forall A B C D D',
~C=D ->
parallel A B C D ->
Col C D D' ->
parallel A B C D'.