Section T10_1.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma hilbert_s_version_of_pasch_aux : forall A B C I P, Coplanar A B C P ->
~ Col A I P -> ~ Col B C P -> Bet B I C -> B <> I -> I <> C -> B <> C ->
exists X, Col I P X /\
((Bet A X B /\ A <> X /\ X <> B /\ A <> B) \/
(Bet A X C /\ A <> X /\ X <> C /\ A <> C)).