Proof with Midpoint.
intros.
assert (Cong P Q P' Q').
eapply l7_13...
assert (Cong R S R' S').
eapply l7_13...
eapply cong_transitivity with (C:=P) (D:=Q);sTarski.
eapply cong_transitivity with (C:=R) (D:=S);sTarski.
Qed.
(** Symmetry preserves midpoint *)

(* Specifications: *)
Lemma symmetry_preserves_midpoint :
forall A B C D E F Z,
is_midpoint Z A D -> is_midpoint Z B E -> is_midpoint Z C F ->
is_midpoint B A C -> is_midpoint E D F.