Section universal_posidonius_postulate_perpendicular_transversal_postulate.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma universal_posidonius_postulate__perpendicular_transversal_postulate_aux :
universal_posidonius_postulate -> forall E F G H R P,
Perp E G R P -> Coplanar F H P R -> Col E G R -> Saccheri E F H G ->
Perp F H P R.