Require Export GeoCoq.Elements.OriginalProofs.lemma_parallelsymmetric.
Require Export GeoCoq.Elements.OriginalProofs.lemma_paralleldef2B.
Require Export GeoCoq.Elements.OriginalProofs.lemma_parallelNC.
Require Export GeoCoq.Elements.OriginalProofs.lemma_planeseparation.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_parallelPasch :
forall A B C D E,
PG A B C D -> BetS A D E ->
exists X, BetS B X E /\ BetS C X D.