Proof with Midpoint.
intros.
eapply l4_6.
apply H2.
unfold Cong_3.
repeat split;eapply l7_13...
Qed.
(** Symmetry preserves Cong. *)

Lemma l7_16 : forall P Q R S P' Q' R' S' A,
is_midpoint A P P' -> is_midpoint A Q Q' ->
is_midpoint A R R' -> is_midpoint A S S' ->
Cong P Q R S  -> Cong P' Q' R' S'.