proposition: Lemma opp_f : forall A, Col O E A -> {B | Opp O E E' A B}.
proof: Proof. intros; apply constructive_definite_description; rewrite <- unique_existence. split; [apply opp_exists|unfold uniqueness; apply opp_uniqueness]; auto. apply ncolOEE'. 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