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