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 enc_equiv_injective n m:
enc n ≡ enc m -> n = m.