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

Lemma weak_inverse_projection_postulate__bachmann_s_lotschnittaxiom_aux :
weak_inverse_projection_postulate -> forall A1 A2 B1 B2 C1 C2 Q P R M,
Perp A1 A2 B1 B2 -> Perp A1 A2 C1 C2 -> Col A1 A2 Q -> Col B1 B2 Q ->
Col A1 A2 P -> Col C1 C2 P -> Col B1 B2 R ->
Coplanar Q P R C1 -> Coplanar Q P R C2 -> ~ Col Q P R ->
InAngle M P Q R -> CongA M Q P M Q R ->
Par_strict B1 B2 C1 C2 /\ exists S, Out Q M S /\ Col C1 C2 S.