(** 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_stability : forall {Tm: Tarski_neutral_dimensionless}
(f : @Tpoint Tn -> @Tpoint Tm) P Q R,
Col P Q R -> P <> R -> line_extension f P Q -> line_extension f P R.