Require Export GeoCoq.Elements.OriginalProofs.lemma_NChelper.
Require Export GeoCoq.Elements.OriginalProofs.proposition_20.
Require Export GeoCoq.Elements.OriginalProofs.lemma_21helper.
Require Export GeoCoq.Elements.OriginalProofs.lemma_TTorder.
Require Export GeoCoq.Elements.OriginalProofs.lemma_TTflip.
Require Export GeoCoq.Elements.OriginalProofs.lemma_TTtransitive.
Require Export GeoCoq.Elements.OriginalProofs.lemma_TTflip2.
Require Export GeoCoq.Elements.OriginalProofs.lemma_NCdistinct.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_21 :
forall A B C D E,
Triangle A B C -> BetS A E C -> BetS B D E ->
TT B A A C B D D C /\ LtA B A C B D C.