Global Instance Euclid_neutral_ruler_compass_follows_from_Tarski_ruler_and_compass :
  euclidean_neutral_ruler_compass Euclid_neutral_follows_from_Tarski_neutral.

Lemma Euclid5 : forall a p q r s t, BetS r t s -> BetS p t q -> BetS r a q -> Cong p t q t -> Cong t r t s -> nCol p q s -> exists X, BetS p a X /\ BetS s q X.