Theorems · Theorem · commutative algebra
emultiplicity_eq_coe
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {n : ℕ}, emultiplicity a b = ↑n ↔ a ^ n ∣ b ∧ ¬a ^ (n + 1) ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 69 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement and proof · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- emultiplicitystatement and proof · cited by 156
- pow_dvd_of_le_emultiplicityproof · cited by 8
- emultiplicity_eq_of_dvd_of_not_dvdproof · cited by 5
- not_pow_dvd_of_emultiplicity_ltproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- emultiplicity_eq_zeroproof · cited by 8
- padicValNat_eq_emultiplicity_of_ne_oneproof · cited by 3
- Nat.Prime.dvd_choose_powproof · cited by 3
- UniqueFactorizationMonoid.count_normalizedFactors_eqproof · cited by 2
- Int.emultiplicity_pow_sub_powproof · cited by 2
- emultiplicity_geom_sum₂_eq_oneproof · cited by 1
- Int.two_pow_sub_pow'proof · cited by 1
- Int.two_pow_two_pow_add_two_pow_two_powproof · cited by 1
- emultiplicity_eq_ofNatproof · cited by 0