Theorems · Theorem · commutative algebra
emultiplicity_le_emultiplicity_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Monoid α] [inst_1 : Monoid β] {a b : α} {c d : β},
emultiplicity a b ≤ emultiplicity c d ↔ ∀ (n : ℕ), a ^ n ∣ b → c ^ n ∣ d- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- ENatstatement · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- le_transproof · cited by 985
- emultiplicitystatement and proof · cited by 156
- Nat.findproof · cited by 139
- FiniteMultiplicityproof · cited by 73
- Nat.find.congr_simpproof · cited by 11
- pow_dvd_of_le_emultiplicityproof · cited by 8
- le_emultiplicity_of_pow_dvdproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- emultiplicity_le_emultiplicity_of_dvd_rightproof · cited by 4
- emultiplicity_le_emultiplicity_of_dvd_leftproof · cited by 2
- padicValRat.le_padicValRat_add_of_leproof · cited by 1
- IsDiscreteValuationRing.addVal_le_iff_dvdproof · cited by 1
- emultiplicity_eq_emultiplicity_iffproof · cited by 1
- FiniteMultiplicity.multiplicity_le_multiplicity_iffproof · cited by 1
- le_emultiplicity_mapproof · cited by 0