(** This file contains the proof that Dedekind completeness implies Hilbert's line completeness. *)
Section Line_extension.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma pres_bet_line__col : forall {Tm: Tarski_neutral_dimensionless}
f (P Q : @Tpoint Tn), P <> Q -> pres_bet_line f P Q ->
forall A B C, Col P Q A -> Col P Q B -> Col P Q C -> Col (f A) (f B) (f C).