Require Export GeoCoq.Elements.OriginalProofs.lemma_NCorder.
Require Export GeoCoq.Elements.OriginalProofs.lemma_oppositesidesymmetric.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_crossimpliesopposite :
forall A B C D,
CR A B C D -> nCol A C D ->
TS A C D B /\ TS A D C B /\ TS B C D A /\ TS B D C A.