Parameter Unort : Line -> Line -> Prop.Axiom O1 : forall l m : Line, ConLn l m \/ Unort l m.Axiom O2 : Separating Line (fun l m : Line => ConLn l m /\ Unort l m).Definition Ort := Negation Line Unort.Axiom
  constructed_orthogonal :
    forall (l : Line) (a : Point), {l' : Line | Ort l' l /\ Incident a l'}.Definition ort : Line -> Point -> Line.Axiom
  constructive_uniqueness_for_orthogonals :
    forall (l m n : Line) (a : Point),
    DiLn l m -> (Apart a l \/ Apart a m) \/ Unort l n \/ Unort m n.

Theorem O3_i : forall (l : Line) (a : Point), Ort (ort l a) l.