Section Substitution.
End Substitution.
Hint Rewrite add_ren add_subst mul_ren mul_subst
enc_ren enc_subst : asimpl.
Hint Rewrite enc_zero enc_succ : simplify.
Hint Resolve normal_enc : core.

Lemma dec_enc s:
{ n | s = enc n} + forall n, s <> enc n.