Section equality_symmetric.
Variable A : Ens.
Variable B : Ens.
Hypothesis h : EQ A B.
Let stepfor : SUB A B.
Proof EQ_forwards A B h.
Let stepback : SUB B A.
Proof EQ_backwards A B h.

Lemma equality_symmetric_Out : EQ B A.
Proof Build_EQ B A stepback stepfor.