struct P3; auto.
Qed.

Inductive return_inner_gen (S: list mpred): option val -> (environ -> mpred) -> (environ -> mpred) -> Prop :=
| return_inner_gen_main: forall ov_gen P ts u,
    return_inner_gen S ov_gen (main_post P ts u) (PROPx nil (LOCALx nil (SEPx (TT :: S))))
| return_inner_gen_canon_nil':
    forall ov_gen P R,
      return_inner_gen S ov_gen
        (PROPx P (LOCALx nil (SEPx R)))
        (PROPx P (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_canon_Some':
    forall P v R v_gen,
      return_inner_gen S (Some v_gen)
        (PROPx P (LOCALx (temp ret_temp v :: nil) (SEPx R)))
        (PROPx (P ++ (v_gen = v) :: nil) (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_EX':
    forall ov_gen (A: Type) (post1 post2: A -> environ -> mpred),
      (forall a: A, return_inner_gen S ov_gen (post1 a)struct P3; auto.
Qed.

Inductive return_inner_gen (S: list mpred): option val -> (environ -> mpred) -> (environ -> mpred) -> Prop :=
| return_inner_gen_main: forall ov_gen P ts u,
    return_inner_gen S ov_gen (main_post P ts u) (PROPx nil (LOCALx nil (SEPx (TT :: S))))
| return_inner_gen_canon_nil':
    forall ov_gen P R,
      return_inner_gen S ov_gen
        (PROPx P (LOCALx nil (SEPx R)))
        (PROPx P (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_canon_Some':
    forall P v R v_gen,
      return_inner_gen S (Some v_gen)
        (PROPx P (LOCALx (temp ret_temp v :: nil) (SEPx R)))
        (PROPx (P ++ (v_gen = v) :: nil) (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_EX':
    forall ov_gen (A: Type) (post1 post2: A -> environ -> mpred),
      (forall a: A, return_inner_gen S ov_gen (post1 a)struct P3; auto.
Qed.

Inductive return_inner_gen (S: list mpred): option val -> (environ -> mpred) -> (environ -> mpred) -> Prop :=
| return_inner_gen_main: forall ov_gen P ts u,
    return_inner_gen S ov_gen (main_post P ts u) (PROPx nil (LOCALx nil (SEPx (TT :: S))))
| return_inner_gen_canon_nil':
    forall ov_gen P R,
      return_inner_gen S ov_gen
        (PROPx P (LOCALx nil (SEPx R)))
        (PROPx P (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_canon_Some':
    forall P v R v_gen,
      return_inner_gen S (Some v_gen)
        (PROPx P (LOCALx (temp ret_temp v :: nil) (SEPx R)))
        (PROPx (P ++ (v_gen = v) :: nil) (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_EX':
    forall ov_gen (A: Type) (post1 post2: A -> environ -> mpred),
      (forall a: A, return_inner_gen S ov_gen (post1 a)struct P3; auto.
Qed.

Inductive return_inner_gen (S: list mpred): option val -> (environ -> mpred) -> (environ -> mpred) -> Prop :=
| return_inner_gen_main: forall ov_gen P ts u,
    return_inner_gen S ov_gen (main_post P ts u) (PROPx nil (LOCALx nil (SEPx (TT :: S))))
| return_inner_gen_canon_nil':
    forall ov_gen P R,
      return_inner_gen S ov_gen
        (PROPx P (LOCALx nil (SEPx R)))
        (PROPx P (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_canon_Some':
    forall P v R v_gen,
      return_inner_gen S (Some v_gen)
        (PROPx P (LOCALx (temp ret_temp v :: nil) (SEPx R)))
        (PROPx (P ++ (v_gen = v) :: nil) (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_EX':
    forall ov_gen (A: Type) (post1 post2: A -> environ -> mpred),
      (forall a: A, return_inner_gen S ov_gen (post1 a)struct P3; auto.
Qed.

Inductive return_inner_gen (S: list mpred): option val -> (environ -> mpred) -> (environ -> mpred) -> Prop :=
| return_inner_gen_main: forall ov_gen P ts u,
    return_inner_gen S ov_gen (main_post P ts u) (PROPx nil (LOCALx nil (SEPx (TT :: S))))
| return_inner_gen_canon_nil':
    forall ov_gen P R,
      return_inner_gen S ov_gen
        (PROPx P (LOCALx nil (SEPx R)))
        (PROPx P (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_canon_Some':
    forall P v R v_gen,
      return_inner_gen S (Some v_gen)
        (PROPx P (LOCALx (temp ret_temp v :: nil) (SEPx R)))
        (PROPx (P ++ (v_gen = v) :: nil) (LOCALx nil (SEPx (R ++ S))))
| return_inner_gen_EX':
    forall ov_gen (A: Type) (post1 post2: A -> environ -> mpred),
      (forall a: A, return_inner_gen S ov_gen (post1 a)

Lemma SEP_nth_isolate: forall n R Rn, nth_error R n = Some Rn ->