Section Grid.
Variable O E E' : Tpoint.
Variable grid_ok : ~ Col O E E'.
(** We are not faithful to Tarski's def because for uniqueness we do not need the assumption that A and B are on line OE as it is implied by the definition of sum. *)

Lemma proj_col : forall A A' C' , A = O -> Col O E A -> Par O E A' C' -> Proj A A' O E' E E' -> A' = O.