Require Export GeoCoq.Elements.OriginalProofs.lemma_congruencetransitive.
Require Export GeoCoq.Elements.OriginalProofs.lemma_betweennesspreserved.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_collinearitypreserved :
forall A B C a b c,
Col A B C -> Cong A B a b -> Cong A C a c -> Cong B C b c ->
Col a b c.