proposition: Lemma inv_f : forall A, Col O E A -> {B | inv O E E' A B}.
proof: Proof. intros; apply constructive_definite_description; rewrite <- unique_existence. split; [apply inv_exists_with_notation| unfold uniqueness; apply inv_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