Section weak_tarski_s_parallel_postulate_weak_inverse_projection_postulate.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** Formalization of a proof from Bachmann's article "Zur Parallelenfrage" *)

Lemma  weak_tarski_s_parallel_postulate__weak_inverse_projection_postulate_aux :
weak_tarski_s_parallel_postulate ->
forall A B C P T,
Per A B C -> InAngle T A B C ->
P <> T -> CongA P B A P B C -> Per B P T -> Coplanar A B C P ->
(exists X, Out B A X /\ Col T P X) \/ (exists Y, Out B C Y /\ Col T P Y).