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.

(* Specifications: *)
Theorem O3_i : forall (l : Line) (a : Point), Ort (ort l a) l.
Theorem O3_ii : forall (l : Line) (a : Point), Incident a (ort l a).
Theorem O4' : forall (l m n : Line) (a : Point), (Incident a l /\ Incident a m) /\ Ort l n /\ Ort m n -> EqLn l m.
Theorem Uniqueness_of_orthogonality : forall (l m : Line) (a : Point), Incident a l /\ Ort l m -> EqLn l (ort m a).
Theorem Unort_reflexive : Reflexive Line Unort.
Theorem cmp_unort_con : forall l m n : Line, Unort l m -> ConLn l n \/ Unort m n.
Theorem cmp_unort_diln : forall l m n : Line, Unort l m -> DiLn l n \/ Unort m n.
Theorem Unort_symmetric : Symmetric Line Unort.
Theorem thm8_6 : forall l m n : Line, ConLn l m -> Unort l n \/ Unort m n.