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).