Theorems · Theorem · commutative algebra
FiniteMultiplicity.not_iff_forall
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, ¬FiniteMultiplicity a b ↔ ∀ (n : ℕ), a ^ n ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 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.
Cites4
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
- pow_zeroproof · cited by 1,094
- FiniteMultiplicitystatement and proof · cited by 73
- one_dvdproof · cited by 37
Cited by4
Results whose statement or proof uses this declaration.
- Nat.finiteMultiplicity_iffproof · cited by 13
- emultiplicity_eq_zeroproof · cited by 8
- pow_dvd_of_le_emultiplicityproof · cited by 8
- Ideal.emultiplicity_eq_emultiplicity_spanproof · cited by 3