(** * Group IV Congruence *)
(** The cong predicate of Hilbert is the same as the one of Tarski: *)
Definition outH := fun P A B => Between_H P A B \/ Between_H P B A \/ (P <> A /\ A = B).

Lemma out_outH : forall P A B, Out P A B -> outH P A B.
unfold Out.