(* Julien Narboux *)
(* Formalization of *)
(* Tarski's axiomatic *)
Require Export Ch07_midpoint.
Unset Regular Subst Tactic.
Definition Per := fun A B C =>
exists C', is_midpoint B C C' /\ Cong A C A C'.
Hint Resolve l8_2 : Perp.
Ltac Perp := eauto with Perp.
intros.
unfold Per.
exists B;intuition.
Qed.
Hint Resolve l8_5 : Perp.

Lemma l8_6 : forall A B C A',
Per A B C -> Per A' B C -> Bet A C A' -> B=C.