Section neq_symm_proof.
Variable A : Ens.
Variable B : Ens.
Hypothesis k : NEQ A B.
Hypothesis m : EQ B A.
Let step1 : EQ A B.
Proof EQ_symm B A m.
Proof k step1.
End neq_symm_proof.

Theorem NEQ_symm : forall (A B : Ens) (k : NEQ A B), NEQ B A.