Library GeoCoq.Elements.OriginalProofs.lemma_congruenceflip

Require Export GeoCoq.Elements.OriginalProofs.lemma_congruencetransitive.

Section Euclid.

Context `{Ax:euclidean_neutral}.

Lemma lemma_congruenceflip :
   ∀ A B C D,
   Cong A B C D →
   Cong B A D C ∧ Cong B A C D ∧ Cong A B D C.
Proof.
intros.
assert (Cong B A A B) by (conclude cn_equalityreverse).
assert (Cong C D D C) by (conclude cn_equalityreverse).
assert (Cong B A C D) by (conclude lemma_congruencetransitive).
assert (Cong A B D C) by (conclude lemma_congruencetransitive).
assert (Cong B A D C) by (conclude lemma_congruencetransitive).
close.
Qed.

End Euclid.