Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthantransitive.
Require Export GeoCoq.Elements.OriginalProofs.lemma_trichotomy2.
Section Euclid.
Context `{Ax1:euclidean_neutral_ruler_compass}.

Lemma lemma_subtractequals :
forall A B C D E,
BetS A B C -> BetS A D E -> Cong B C D E -> BetS A C E ->
BetS A B D.