Theorems · Theorem · commutative algebra
emultiplicity_eq_zero
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, emultiplicity a b = 0 ↔ ¬a ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 70 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.
Cites11
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
- zero_addproof · cited by 2,366
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- emultiplicitystatement and proof · cited by 156
- FiniteMultiplicityproof · cited by 73
- emultiplicity_eq_topproof · cited by 9
- emultiplicity_eq_coeproof · cited by 9
- ENat.natCast_zeroproof · cited by 7
- FiniteMultiplicity.not_iff_forallproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- multiplicity_eq_zeroproof · cited by 3
- emultiplicity_of_isUnit_rightproof · cited by 2
- emultiplicity_pow_sub_pow_of_primeproof · cited by 2
- emultiplicity_zero_eq_zero_of_ne_zeroproof · cited by 1
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1
- emultiplicity_eq_zero_of_irreducible_neproof · cited by 0
- Nat.emultiplicity_two_factorial_ltproof · cited by 0
- Ideal.IsDedekindDomain.emultiplicity_map_eq_zero_of_neproof · cited by 0