Theorems · Theorem · commutative algebra
multiplicity_eq_one_of_not_finiteMultiplicity
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, ¬FiniteMultiplicity a b → multiplicity a b = 1- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 4 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.
- ENatproof · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- multiplicitystatement · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- WithTop.untopDproof · cited by 33
- emultiplicity_eq_topproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- multiplicity_le_emultiplicityproof · cited by 5
- multiplicity_selfproof · cited by 2
- multiplicity_pos_of_dvdproof · cited by 2
- multiplicity_zeroproof · cited by 0