∀ {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},
  a ≠ b → (IncidenceAlgebra.mu 𝕜) a b = -∑ x ∈ Finset.Ico a b, (IncidenceAlgebra.mu 𝕜) a x