Require Export GeoCoq.Elements.OriginalProofs.proposition_31short.
Require Export GeoCoq.Elements.OriginalProofs.lemma_triangletoparallelogram.
Require Export GeoCoq.Elements.OriginalProofs.lemma_equaltorightisright.
Require Export GeoCoq.Elements.OriginalProofs.lemma_samenotopposite.
Require Export GeoCoq.Elements.OriginalProofs.proposition_34.
Require Export GeoCoq.Elements.OriginalProofs.lemma_PGsymmetric.
Require Export GeoCoq.Elements.OriginalProofs.lemma_PGflip.
Section Euclid.
Context `{Ax:euclidean_euclidean}.

Lemma proposition_46 :
forall A B R,
neq A B -> nCol A B R ->
exists X Y, SQ A B X Y /\ TS Y A B R /\ PG A B X Y.