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