Axiom
  constructed_parallel :
    forall (l : Line) (a : Point), {l' : Line | Par l' l /\ Incident a l'}.Definition par : Line -> Point -> Line.Axiom
  constructive_uniqueness_for_parallels :
    forall (l m : Line) (a : Point),
    DiLn l m -> (Apart a l \/ Apart a m) \/ ConLn l m.

Theorem DiLn_qimp_con : forall l m : Line, DiLn l m -> ex (fun b : Point => Incident b l /\ Incident b m) -> ConLn l m.