Theorems · Theorem · commutative algebra
FiniteMultiplicity.pow_dvd_iff_le_multiplicity
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, FiniteMultiplicity a b → ∀ {k : ℕ}, a ^ k ∣ b ↔ k ≤ multiplicity a b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- multiplicitystatement · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- pow_dvd_iff_le_emultiplicityproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- padicNorm.dvd_iff_norm_leproof · cited by 5
- Choose.eq_pow_multiplicity_of_choose_modEq_zeroproof · cited by 1
- Nat.emultiplicity_eq_card_pow_dvdproof · cited by 1
- FiniteMultiplicity.multiplicity_lt_iff_not_dvdproof · cited by 0