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 cong_sum : forall A B C,
O <> C \/ B <> A -> Ar2 O E E' A B C ->
Cong O A B C -> Cong O B A C ->
Sum O E E' A B C.