Theorems · Theorem · order theory

IncidenceAlgebra.mu_apply

∀ {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.Ico a b, (IncidenceAlgebra.mu 𝕜) a x

Defined in

Mathlib.Combinatorics.Enumerative.IncidenceAlgebra

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupOnePreorderLocallyFiniteOrderDecidableEq