Definition var_env_or (ve1 ve2 : var_env) (x : ad) := ve1 x || ve2 x.
Definition var_env'_or (ve1 ve2 : var_env') (x : nat) := ve1 x || ve2 x.

Lemma replacel_lemma :
forall (n : nat) (be : bool_expr),
n <= N -> replacel be (lx_1 n) (lx'_1 N n) = renamef (renfnad n) be.