Section Hilbert_2D_to_Tarski_2D.
Context `{Hi:Hilbert_neutral_dimensionless}.
(** Tarski's betweenness is not strict: *)
Definition Bet A B C := BetH A B C \/ A = B \/ B = C.

Lemma betH_distincts : forall A B C, BetH A B C -> A <> B /\ B <> C /\ A <> C.