Require Export GeoCoq.Elements.OriginalProofs.lemma_equalanglesNC.
Require Export GeoCoq.Elements.OriginalProofs.lemma_layoffunique.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ray5.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ray3.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_04 :
forall A B C a b c,
Cong A B a b -> Cong A C a c -> CongA B A C b a c ->
Cong B C b c /\ CongA A B C a b c /\ CongA A C B a c b.