Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence2.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ray4.
Require Export GeoCoq.Elements.OriginalProofs.lemma_layoffunique.
Require Export GeoCoq.Elements.OriginalProofs.lemma_trichotomy2.
Require Export GeoCoq.Elements.OriginalProofs.lemma_outerconnectivity.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_lessthanadditive :
forall A B C D E F,
Lt A B C D -> BetS A B E -> BetS C D F -> Cong B E D F ->
Lt A E C F.