(* Julien Narboux *)
(* Formalization of *)
(* Tarski's axiomatic *)
Require Export Ch02_congruence_properties.
(** Axiom 12 of Givant. *)
Proof with eTarski.
intros.
assert (exists x : Point, Bet A B x /\ Cong B x B B)...
DecompExAnd H x.
assert (B = x).
assert (Cong B B B x)...
congruence.
Qed.
Hint Resolve beetween_trivial : Tarski.
(** Axiom 14 of Givant. *)

Lemma between_symmetry : forall A B C : Point,
Bet A B C -> Bet C B A.