(** 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 line_extension_reverse_bet : forall {Tm: Tarski_neutral_dimensionless}
{Tm2: Tarski_neutral_dimensionless_with_decidable_point_equality Tm}
(f : @Tpoint Tn -> @Tpoint Tm) P Q, line_extension f P Q ->
forall A B C, Col P Q A -> Col P Q B -> Col P Q C -> Bet (f A) (f B) (f C) -> Bet A B C.