Section union_refl_proof.
Variable A : Ens.
Let U := union A A.
Let step1 : SUB A U.
Proof union_pr1 A A.
Let step2 : SUB A A. Proof SUB_refl A.
Let step3 : SUB U A. Proof union_pr3 A A A step2 step2.
Proof Build_EQ A U step1 step3.
End union_refl_proof.

Theorem union_refl : forall A : Ens, EQ A (union A A).