Theorems · Theorem · commutative algebra
multiplicity_le_emultiplicity
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, ↑(multiplicity a b) ≤ emultiplicity a b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 25 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.
Cites9
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
- Nat.cast_oneproof · cited by 2,501
- emultiplicitystatement · cited by 156
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicityproof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- emultiplicity_eq_topproof · cited by 9
- multiplicity_eq_one_of_not_finiteMultiplicityproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- lt_emultiplicity_of_lt_multiplicityproof · cited by 2
- FiniteMultiplicity.multiplicity_add_of_gtproof · cited by 2
- multiplicity_le_of_emultiplicity_leproof · cited by 1
- le_emultiplicity_of_le_multiplicityproof · cited by 1
- multiplicity_lt_of_emultiplicity_ltproof · cited by 0