∀ (𝕜 : Type u_2) {α : Type u_5} {β : Type u_6} [inst : Ring 𝕜] [inst_1 : PartialOrder α] [inst_2 : PartialOrder β]
  [inst_3 : LocallyFiniteOrder α] [inst_4 : LocallyFiniteOrder β] [inst_5 : DecidableEq α] [inst_6 : DecidableEq β]
  [inst_7 : DecidableLE α] [inst_8 : DecidableLE β],
  (IncidenceAlgebra.mu 𝕜).prod (IncidenceAlgebra.mu 𝕜) = IncidenceAlgebra.mu 𝕜