Theorems · Theorem · commutative algebra
FiniteMultiplicity.multiplicity_lt_iff_not_dvd
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {k : ℕ}, FiniteMultiplicity a b → (multiplicity a b < k ↔ ¬a ^ k ∣ b)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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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
- not_leproof · cited by 328
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.pow_dvd_iff_le_multiplicityproof · cited by 4
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