Section Completeness.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** If there exists n such that (f A) X = n times (f A) (f B), then X belongs to the image of the line extension f *)
(** If there exists n such that (f A) X = (f A) (f B) divided by 2^n, then X belongs to the image of the line extension f *)

Lemma extension_gradexp : forall {Tm: Tarski_neutral_dimensionless}
{TmEQD : Tarski_neutral_dimensionless_with_decidable_point_equality Tm}
P Q (f : @Tpoint Tn -> @Tpoint Tm),
line_extension f P Q ->
forall A B X, Col P Q A -> Col P Q B -> GradExp (f A) X (f B) ->
exists C, Col P Q C /\ GradExp A C B /\ f C = X.