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.
(** Hilbert's congruence is 'defined' only for non degenerated segments, while Tarski's segment congruence allows the null segment. *)
Global Instance IncidL_morphism' : Proper(eq ==> EqL ==> iff) IncidL.

Lemma colH_trivial112 : forall A B, ColH A A B.