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

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