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_id : forall A A', Proj A A' O E' E E' -> Col O E A -> Col O E A' -> A = O.