Require Export GeoCoq.Elements.OriginalProofs.lemma_TCreflexive.

Section Euclid.

Context `{Ax:area}.

Lemma lemma_ETreflexive : 
   forall A B C, 
   Triangle A B C ->
   ET A B C A B C.
Proof.
(* Goal: forall (A B C : @Point Ax0) (_ : @Triangle Ax0 A B C), @ET Ax0 Ax1 Ax2 Ax A B C A B C *)
intros.
(* Goal: @ET Ax0 Ax1 Ax2 Ax A B C A B C *)
assert (nCol A B C) by (conclude_def Triangle ).
(* Goal: @ET Ax0 Ax1 Ax2 Ax A B C A B C *)
assert (Cong_3 A B C A B C) by (conclude lemma_TCreflexive).
(* Goal: @ET Ax0 Ax1 Ax2 Ax A B C A B C *)
assert (ET A B C A B C) by (conclude axiom_congruentequal).
(* Goal: @ET Ax0 Ax1 Ax2 Ax A B C A B C *)
close.
Qed.

End Euclid.


