Software Foundations: weak_pumping lemma proof

Continuing my work on Software Foundations, I've reached the weak_pumping lemma. I managed to get through almost everything, but I can't find a solution for MStarApp case.

Here's the Lemma:

  s =~ re ->
  pumping_constant re <= length s ->
  exists s1 s2 s3,
    s = s1 ++ s2 ++ s3 /\
    s2 <> [] /\
    forall m, s1 ++ napp m s2 ++ s3 =~ re.

(** You are to fill in the proof. Several of the lemmas about
    [le] that were in an optional exercise earlier in this chapter
    may be useful. *)
Proof.
  intros T re s Hmatch.
  induction Hmatch
    as [ | x | s1 re1 s2 re2 Hmatch1 IH1 Hmatch2 IH2
       | s1 re1 re2 Hmatch IH | re1 s2 re2 Hmatch IH
       | re | s1 s2 re Hmatch1 IH1 Hmatch2 IH2 ].

I've managed to solve every case, except for the last one. Here's the current state:

1 subgoal (ID 918)
  
  T : Type
  s1, s2 : list T
  re : reg_exp T
  Hmatch1 : s1 =~ re
  Hmatch2 : s2 =~ Star re
  IH1 : pumping_constant re <= length s1 ->
        exists s2 s3 s4 : list T,
          s1 = s2 ++ s3 ++ s4 /\
          s3 <> [ ] /\ (forall m : nat, s2 ++ napp m s3 ++ s4 =~ re)
  IH2 : pumping_constant (Star re) <= length s2 ->
        exists s1 s3 s4 : list T,
          s2 = s1 ++ s3 ++ s4 /\
          s3 <> [ ] /\ (forall m : nat, s1 ++ napp m s3 ++ s4 =~ Star re)
  H : pumping_constant (Star re) <= length s1 + length s2
  ============================
  exists s0 s4 s5 : list T,
    s1 ++ s2 = s0 ++ s4 ++ s5 /\
    s4 <> [ ] /\ (forall m : nat, s0 ++ napp m s4 ++ s5 =~ Star re)

It looks to me that if I can find a way to split H into pumping_constant re <= length s1 \/ pumping_constant (Star re) <= length s2 then I have a way forward (by splitting H into H1 and H2 and applying the relevant IHk to the matching Hk then proceeding with a destruct, three exists, and so on).

But I can't find a lemma that allows me to split H as suggested.

Is there anything else I can do here?

Thanks

Try to destruct s1 and look again on lemma napp_star in one of cases.