Theorems · Theorem · commutative algebra
emultiplicity_eq_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
- 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- le_antisymmproof · cited by 2,068
- Eq.leproof · cited by 605
- Eq.geproof · cited by 375
- emultiplicitystatement and proof · cited by 156
- emultiplicity_le_emultiplicity_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- emultiplicity_negproof · cited by 3