Lemma extension_grad : forall {Tm: Tarski_neutral_dimensionless} {Tm2 : 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 -> Grad (f A) (f B) X -> exists C, Col P Q C /\ Grad A B C /\ f C = X.