Theorems · Theorem · commutative algebra
multiplicity_self
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {a : α}, multiplicity a a = 1- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- pow_oneproof · cited by 894
- sqproof · cited by 280
- IsCancelMulZerostatement and proof · cited by 177
- multiplicitystatement · cited by 117
- FiniteMultiplicityproof · cited by 73
- IsUnit.of_mul_eq_oneproof · cited by 43
- FiniteMultiplicity.multiplicity_eq_iffproof · cited by 4
- multiplicity_eq_one_of_not_finiteMultiplicityproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- padicValNat_selfproof · cited by 11
- FiniteMultiplicity.emultiplicity_selfproof · cited by 2