Section Nsec.
Variable N : nat.
Definition ap (n : nat) := N_of_nat n.
Definition ap' (n : nat) := N_of_nat (N + n).
Fixpoint lx_1 (n : nat) : list ad :=
match n with
| O => nil
| S m => ap m :: lx_1 m
end.
Fixpoint lx'_1 (n : nat) : list ad :=
match n with
| O => nil (A:=ad)
| S m => ap' m :: lx'_1 m
end.
Definition lx := lx_1 N.
Definition lx' := lx'_1 N.

Lemma lt_O_n_lx'_1 : forall n : nat, 0 < n -> In (ap' 0) (lx'_1 n).
Definition bool_fun_mu_all (bft bfg : bool_fun) : bool_fun :=
bool_fun_univl (bool_fun_impl bft (bool_fun_replacel bfg lx lx')) lx'.