Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.map_prod_of_prime
∀ {R : Type u_1} [inst : CommMonoidWithZero R] {f : ArithmeticFunction R},
f.IsMultiplicative → ∀ (t : Finset ℕ), (∀ p ∈ t, Nat.Prime p) → f (∏ a ∈ t, a) = ∏ a ∈ t, f a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Finset.prodstatement · cited by 2,356
- Nat.Primestatement and proof · cited by 2,059
- CommMonoidWithZerostatement and proof · cited by 913
- ArithmeticFunctionstatement and proof · cited by 290
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
- Nat.coprime_primesproof · cited by 9
- ArithmeticFunction.IsMultiplicative.map_prodproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactorsproof · cited by 3