Library GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence2

Require Export GeoCoq.Elements.OriginalProofs.lemma_congruencetransitive.

Section Euclid.

Context `{Ax1:euclidean_neutral}.

Lemma lemma_lessthancongruence2 :
   ∀ A B C D E F,
   Lt A B C D → Cong A B E F →
   Lt E F C D.
Proof.
intros.
let Tf:=fresh in
assert (Tf:∃ G, (BetS C G D ∧ Cong C G A B)) by (conclude_def Lt );destruct Tf as [G];spliter.
assert (Cong C G E F) by (conclude lemma_congruencetransitive).
assert (Lt E F C D) by (conclude_def Lt ).
close.
Qed.

End Euclid.