∀ (𝕜 : Type u_2) {α : Type u_5} [inst : AddCommGroup 𝕜] [inst_1 : One 𝕜] [inst_2 : Preorder α]
  [inst_3 : LocallyFiniteOrder α] [inst_4 : DecidableEq α] (a b : α),
  IncidenceAlgebra.muFun✝ 𝕜 a b = if a = b then 1 else -∑ x ∈ (Finset.Ico a b).attach, IncidenceAlgebra.muFun✝¹ 𝕜 a ↑x