Library GeoCoq.Elements.OriginalProofs.lemma_RTcongruence

Require Export GeoCoq.Elements.OriginalProofs.lemma_equalanglestransitive.

Section Euclid.

Context `{Ax:euclidean_neutral}.

Lemma lemma_RTcongruence :
   ∀ A B C D E F P Q R,
   RT A B C D E F → CongA A B C P Q R →
   RT P Q R D E F.
Proof.
intros.
let Tf:=fresh in
assert (Tf:∃ a b c d e, (Supp a b c d e ∧ CongA A B C a b c ∧ CongA D E F d b e)) by (conclude_def RT );destruct Tf as [a[b[c[d[e]]]]];spliter.
assert (CongA P Q R A B C) by (conclude lemma_equalanglessymmetric).
assert (CongA P Q R a b c) by (conclude lemma_equalanglestransitive).
assert (RT P Q R D E F) by (conclude_def RT ).
close.
Qed.

End Euclid.