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

(* Specifications: *)
Theorem O3_ii : forall (l : Line) (a : Point), Incident a (ort l a).
Hint Resolve O3_i O3_ii.
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.
Definition Oblique : Relation Line :=
fun l m : Line => ConLn l m /\ Unort l m.
Theorem apart_obl : Apartness Line Oblique.
Theorem ort_ort_like_par_i :
forall (l : Line) (a : Point), Incident a (ort (ort l a) a).
Theorem thm8_8 :
forall (l : Line) (a b : Point),
Incident b (ort l a) -> EqLn (ort l a) (ort l b).