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