Section enc_equations.
Hint Rewrite enc_ren enc_subst : asimpl.
Hint Resolve enc_normal : core.
Global Instance enc_equiv: Proper (Logic.eq ++> equiv step ++> equiv step) enc.

Lemma dec_enc:
forall s, normal s -> { n | s a ≡ enc n a } + ({ n | s a ≡ enc n a  } -> False).