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.

Lemma enc_mul' n m s f:
enc (n * m) s f ≡ (enc n) s (lambda (enc m (var 0) (ren shift f))).