Library GeoCoq.Elements.OriginalProofs.proposition_03

Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence.

Section Euclid.

Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_03 :
   ∀ A B C D E F,
   neq A B → neq C D → Lt C D A B → Cong E F A B →
   ∃ X, BetS E X F ∧ Cong E X C D.
Proof.
intros.
assert (Cong A B E F) by (conclude lemma_congruencesymmetric).
assert (Lt C D E F) by (conclude lemma_lessthancongruence).
let Tf:=fresh in
assert (Tf:∃ G, (BetS E G F ∧ Cong E G C D)) by (conclude_def Lt );destruct Tf as [G];spliter.
close.
Qed.

End Euclid.