Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthannotequal.
Require Export GeoCoq.Elements.OriginalProofs.lemma_together.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ray5.
Require Export GeoCoq.Elements.OriginalProofs.lemma_subtractequals.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ondiameter.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_22 :
forall A B C E F a b c,
TG A a B b C c -> TG A a C c B b -> TG B b C c A a -> neq F E ->
exists X Y, Cong F X B b /\ Cong F Y A a /\ Cong X Y C c /\ Out F E X /\ Triangle F X Y.