Theorems · Theorem · commutative algebra
emultiplicity_ne_zero
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, emultiplicity a b ≠ 0 ↔ a ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites3
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
- emultiplicitystatement · cited by 156
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.dvd_choose_powproof · cited by 3