Theorems · Theorem · commutative algebra
emultiplicity_pow
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {p a : α},
Prime p → ∀ {k : ℕ}, emultiplicity p (a ^ k) = ↑k * emultiplicity p a- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- Nat.cast_addproof · cited by 586
- pow_succproof · cited by 374
- add_mulproof · cited by 363
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
Cited by3
Results whose statement or proof uses this declaration.
- FiniteMultiplicity.multiplicity_powproof · cited by 1
- Nat.Prime.emultiplicity_powproof · cited by 0
- UniqueFactorizationMonoid.pow_dvd_pow_iff_dvdproof · cited by 0