Proof with Tarski.
unfold is_midpoint.
intros;intuition.
cases_equality A X.
treat_equalities...
eapply (construction_unicity X A X A P Q);Between;sTarski.
Qed.

(* Specifications: *)
Lemma l7_13 : forall A P Q P' Q',
is_midpoint A P' P -> is_midpoint A Q' Q ->
Cong P Q P' Q'.