proposition: Lemma sum_f : forall A B, Col O E A -> Col O E B -> {C | Sum O E E' A B C}.
proof: Proof. intros; apply constructive_definite_description; rewrite <- unique_existence. split; [apply sum_exists; auto|unfold uniqueness; apply sum_uniqueness]. apply ncolOEE'. Qed.
imports: Description Ring Field Nsatz Rtauto GeoCoq.Tarski_dev.Ch16_coordinates GeoCoq.Tarski_dev.Ch15_pyth_rel GeoCoq.Tarski_dev.Annexes.midpoint_theorems