(** 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_cong2 : forall A B C,
Sum O E E' A B C ->
(A <> O \/ B <> O) ->
(Cong O A B C /\ Cong O B A C).