Section alternate_interior_angles_playfair_bis.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma alternate_interior__playfair_aux : alternate_interior_angles_postulate ->
forall A1 A2 B1 B2 C1 C2 P,
Perp2 A1 A2 B1 B2 P -> ~ Col A1 A2 P -> Col P B1 B2 -> Coplanar A1 A2 B1 B2 ->
Par A1 A2 C1 C2 -> Col P C1 C2 ->
Col C1 B1 B2. (** "half" of playfair_bis *)