Axiom
constructed_orthogonal :
forall (l : Line) (a : Point), {l' : Line | Ort l' l /\ Incident a l'}.
Definition ort : Line -> Point -> Line.

Theorem O4' :
forall (l m n : Line) (a : Point),
(Incident a l /\ Incident a m) /\ Ort l n /\ Ort m n -> EqLn l m.