Theorems · Theorem · commutative algebra
FiniteMultiplicity.emultiplicity_eq_multiplicity
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, FiniteMultiplicity a b → emultiplicity a b = ↑(multiplicity a b)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- ENatstatement · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- emultiplicitystatement and proof · cited by 156
- multiplicitystatement · cited by 117
- ENat.recTopCoeproof · cited by 75
- FiniteMultiplicitystatement and proof · cited by 73
- multiplicity_eq_of_emultiplicity_eq_someproof · cited by 11
Cited by31
Results whose statement or proof uses this declaration.
- emultiplicity_mulproof · cited by 10
- FiniteMultiplicity.not_pow_dvd_of_multiplicity_ltproof · cited by 5
- multiplicity_le_emultiplicityproof · cited by 5
- FiniteMultiplicity.multiplicity_eq_iffproof · cited by 4
- FiniteMultiplicity.pow_dvd_iff_le_multiplicityproof · cited by 4
- Ideal.emultiplicity_eq_emultiplicity_spanproof · cited by 3
- emultiplicity_add_of_gtproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- FiniteMultiplicity.multiplicity_add_of_gtproof · cited by 2
- Nat.Prime.emultiplicity_choose_prime_powproof · cited by 2
- Ideal.irreducible_pow_sup_of_geproof · cited by 2