Require Export GeoCoq.Elements.OriginalProofs.lemma_ABCequalsCBA.
Require Export GeoCoq.Elements.OriginalProofs.lemma_supplements.
Require Export GeoCoq.Elements.OriginalProofs.lemma_equalanglestransitive.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

(* Specifications: *)
Lemma proposition_15 :
forall A B C D E,
BetS A E B -> BetS C E D -> nCol A E C ->
CongA A E C D E B /\ CongA C E B A E D.
Lemma proposition_15a :
forall A B C D E : Point,
BetS A E B ->
BetS C E D -> nCol A E C -> CongA A E C D E B.
Lemma proposition_15b :
forall A B C D E : Point,
BetS A E B ->
BetS C E D -> nCol A E C ->
CongA C E B A E D.