Definition be_le2 (be1 be2 : bool_expr) :=
  forall ve : var_env,
  bool_fun_of_bool_expr be1 ve = true -> bool_fun_of_bool_expr be2 ve = true.

Lemma replacel_le2 : forall (lz ly : list ad) (be1 be2 : bool_expr), be_le2 be1 be2 -> be_le2 (replacel be1 lz ly) (replacel be2 lz ly).