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 sum_plg : forall A B C, Sum O E E' A B C -> (A <> O ) \/ ( B <> O) -> exists A', exists C', Plg O B C' A' /\ Plg C' A' A C.