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_NCdistinct.
Require Export GeoCoq.Elements.OriginalProofs.lemma_planeseparation.
Require Export GeoCoq.Elements.OriginalProofs.lemma_parallelflip.
Require Export GeoCoq.Elements.OriginalProofs.lemma_collinearparallel.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_crisscross :
forall A B C D,
Par A C B D -> ~ CR A B C D ->
CR A D B C.