Require Export GeoCoq.Elements.OriginalProofs.lemma_betweennotequal.
Require Export GeoCoq.Elements.OriginalProofs.lemma_localextension.
Require Export GeoCoq.Elements.OriginalProofs.lemma_congruencesymmetric.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_betweennesspreserved :
forall A B C a b c,
Cong A B a b -> Cong A C a c -> Cong B C b c -> BetS A B C ->
BetS a b c.