Section alternate_interior_angles_proclus.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma alternate_interior__proclus_aux :
greenberg_s_axiom ->
alternate_interior_angles_postulate -> forall A C D P Q,
Par_strict P A C D -> Perp C D P C -> OS P A C Q -> OS P C Q A -> OS P C Q D ->
exists Y, Col P Q Y /\ Col C D Y.