∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : IsCancelMulZero M] {N : Type u_2}
  [inst_2 : CommMonoidWithZero N] [inst_3 : Subsingleton Mˣ] [inst_4 : Subsingleton Nˣ] [inst_5 : IsCancelMulZero N]
  {m : M} {n : N} {d : { l // l ∣ m } ≃ { l // l ∣ n }} (l : Associates M) (hl : l ∈ Set.Iic (Associates.mk m)),
  (fun l => ⟨Associates.mk ↑(d.symm ⟨associatesEquivOfUniqueUnits ↑l, ⋯⟩), ⋯⟩)
      ((fun l => ⟨Associates.mk ↑(d ⟨associatesEquivOfUniqueUnits ↑l, ⋯⟩), ⋯⟩) ⟨l, hl⟩) =
    ⟨l, hl⟩