Instance Hilbert_3D_follows_from_Tarski_3D : Hilbert_neutral_3D Hilbert_neutral_follows_from_Tarski_neutral.(** * Group Parallels *)

Definition Para := fun l m =>
  (~ exists X, IncidentL X l /\ IncidentL X m) /\ exists p, IncidentLP l p /\ IncidentLP m p.

Lemma axiom_euclid_uniqueness : forall l P m1 m2, ~ IncidentL P l -> Para l m1 -> IncidentL P m1 -> Para l m2 -> IncidentL P m2 -> EqL m1 m2.