(* Julien Narboux *)
(* Formalization of *)
(* Tarski's axiomatic *)
Require Export Ch06_out_lines.
Unset Regular Subst Tactic.
Definition is_midpoint := fun M A B => Bet A M B /\ Cong A M M B.
Proof with Tarski.
unfold is_midpoint.
intros.
intuition.
Qed.
Proof with Tarski.
unfold is_midpoint.
intros.
intuition.
eTarski.
Qed.
Proof with Tarski.
unfold is_midpoint.
intros.
intuition.
Qed.
Hint Resolve l7_2 l7_3 l7_3_2 : Midpoint.
Ltac Midpoint := eauto with Midpoint.

Lemma symmetric_point_construction : forall A P,
exists P', is_midpoint P A P'.