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Theorems · Theorem · order theory

IncidenceAlgebra.mu_mul_zeta

∀ (𝕜 : Type u_2) (α : Type u_5) [inst : AddCommGroup 𝕜] [inst_1 : MulOneClass 𝕜] [inst_2 : PartialOrder α]
  [inst_3 : LocallyFiniteOrder α] [inst_4 : DecidableEq α] [inst_5 : DecidableLE α],
  IncidenceAlgebra.mu 𝕜 * IncidenceAlgebra.zeta 𝕜 = 1
Defined in
Mathlib.Combinatorics.Enumerative.IncidenceAlgebra
Cited by
3 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupMulOneClassPartialOrderLocallyFiniteOrderDecidableEqDecidableLE
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IncidenceAlgebra.mu_toDual · cited by 3IncidenceAlgebra.mu_toDualIncidenceAlgebra.moebius_inversion_top · cited by 1IncidenceAlgebra.moebius_…IncidenceAlgebra.mu_prod_mu · cited by 0IncidenceAlgebra.mu_prod_…DFunLike.coe · cited by 62936DFunLike.coeAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderFinset.sum · cited by 5195Finset.summul_one · cited by 3885mul_oneFinset.sum_congr · cited by 2323Finset.sum_congrMulOneClass · cited by 1018MulOneClassLocallyFiniteOrder · cited by 658LocallyFiniteOrderFinset.Icc · cited by 348Finset.IccIncidenceAlgebra · cited by 51IncidenceAlgebraFinset.mem_Icc · cited by 39Finset.mem_IccIncidenceAlgebra.mu · cited by 15IncidenceAlgebra.muIncidenceAlgebra.zeta · cited by 11IncidenceAlgebra.zetaIncidenceAlgebra.ext · cited by 6IncidenceAlgebra.extIncidenceAlgebra.mul_apply · cited by 2IncidenceAlgebra.mul_applyIncidenceAlgebra.mu_mul_zetaCITED BYCITES

Cites16

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Cited by3

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