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_uniqueness : forall A B C1 C2,
Sum O E E' A B C1 ->
Sum O E E' A B C2 ->
C1 = C2.