proposition: Lemma orthogonales_toute_droite_orthogonaux : forall A B C D E : PO, ~ alignes A B C -> D <> E -> (forall F G : PO, F <> G -> coplanaires A B C F -> coplanaires A B C G -> orthogonales (droite F G) (droite D E)) -> orthogonaux (droite D E) (plan A B C).
proof: Proof. intros. assert (A <> B); auto with geo. apply def_orthogonaux; auto with geo. apply H1; auto with geo. apply non_alignes_distincts with B; auto with geo. Qed.