Theorems · Theorem · commutative algebra
emultiplicity_eq_iff_multiplicity_eq_of_ne_one
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {n : ℕ}, n ≠ 1 → (emultiplicity a b = ↑n ↔ multiplicity a b = n)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 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.
Cites6
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
- emultiplicitystatement and proof · cited by 156
- multiplicitystatement and proof · cited by 117
- multiplicity_eq_of_emultiplicity_eq_someproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- multiplicity_eq_zeroproof · cited by 3
- emultiplicity_eq_zero_iff_multiplicity_eq_zeroproof · cited by 0