Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence2.
Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence.
Section Euclid.
Context `{Ax1:euclidean_neutral_ruler_compass}.

Lemma lemma_together :
forall A B C D F G P Q a b c,
TG A a B b C c -> Cong D F A a -> Cong F G B b -> BetS D F G -> Cong P Q C c ->
Lt P Q D G /\ neq A a /\ neq B b /\ neq C c.