Theorems · Theorem · commutative algebra
FiniteMultiplicity.multiplicity_le_multiplicity_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Monoid α] [inst_1 : Monoid β] {a b : α} {c d : β},
FiniteMultiplicity a b →
FiniteMultiplicity c d → (multiplicity a b ≤ multiplicity c d ↔ ∀ (n : ℕ), a ^ n ∣ b → c ^ n ∣ d)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatproof · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- emultiplicityproof · cited by 156
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- ENat.natCast_le_natCastproof · cited by 19
- emultiplicity_le_emultiplicity_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- padicValRat.padicValRat_le_padicValRat_iffproof · cited by 1