intros.
assert {Y : Point | Col Y P Q}.
apply on_lineex...
DecompEx H0 Y.
exists Y.
unfold on_line...
Qed.

(* Specifications: *)
Theorem on_line_dex :
forall (P Q : Point) (lambda : F),
P <> Q -> {Y : Point | Col Y P Q /\ P ** Y = lambda * P ** Q}.