Theorems · Theorem · commutative algebra
Finset.emultiplicity_prod
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {β : Type u_3} {p : α},
Prime p → ∀ (s : Finset β) (f : β → α), emultiplicity p (∏ x ∈ s, f x) = ∑ x ∈ s, emultiplicity p (f x)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 2 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- ENatstatement · cited by 4,985
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- Finset.sum_insertproof · cited by 196
- IsCancelMulZerostatement and proof · cited by 177
- emultiplicitystatement and proof · cited by 156
- Finset.prod_insertproof · cited by 109
- Finset.inductionproof · cited by 108
- Prime.not_isUnitproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Int.two_pow_two_pow_sub_pow_two_powproof · cited by 1
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1