∀ {α : Type u_1} {le : α → α → Bool} {n : ℕ}
  {k : Batteries.BinomialHeap.Imp.Heap α → Batteries.BinomialHeap.Imp.Heap α},
  (∀ {s : Batteries.BinomialHeap.Imp.Heap α},
      Batteries.BinomialHeap.Imp.Heap.WF le n s → Batteries.BinomialHeap.Imp.Heap.WF le 0 (k s)) →
    ∀ (r : ℕ),
      n ≤ r →
        ∀ {s : Batteries.BinomialHeap.Imp.Heap α},
          Batteries.BinomialHeap.Imp.Heap.WF le r s → Batteries.BinomialHeap.Imp.Heap.WF le 0 (k s)