∀ (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 b a = if a = b then 1 else -∑ x ∈ (Finset.Ioc a b).attach, IncidenceAlgebra.muFun'✝¹ 𝕜 b ↑x