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

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