∀ {n : ℕ} (c : OrderedFinpartition (n + 1)) (i : Fin (c.length - 1)) (j : Fin (c.partSize (Fin.cast ⋯ i.succ)))
  (this : c.length - 1 + 1 = c.length),
  c.emb (Fin.cast this i.succ) j ∈ (fun m => Set.range (c.emb m)) (Fin.cast this i.succ)