Theorems · Theorem · commutative algebra
le_emultiplicity_of_le_multiplicity
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {n : ℕ}, n ≤ multiplicity a b → ↑n ≤ emultiplicity a b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 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.
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.le.transproof · cited by 3,151
- emultiplicitystatement and proof · cited by 156
- multiplicitystatement and proof · cited by 117
- WithTop.coe_monoproof · cited by 6
- multiplicity_le_emultiplicityproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- pow_dvd_of_le_multiplicityproof · cited by 1