Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors
∀ {R : Type u_1} [inst : CommMonoidWithZero R] {f : ArithmeticFunction R},
f.IsMultiplicative → ∀ (l : ℕ), ∀ t ⊆ l.primeFactors, f (∏ a ∈ t, a) = ∏ a ∈ t, f a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 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.
Cites9
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
- Finset.prodstatement · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- ArithmeticFunctionstatement and proof · cited by 290
- Nat.primeFactorsstatement and proof · cited by 129
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- ArithmeticFunction.IsMultiplicative.map_prod_of_primeproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- BoundingSieve.prod_primeFactors_nuproof · cited by 2
- ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefreeproof · cited by 1
- ArithmeticFunction.IsMultiplicative.prod_primeFactorsproof · cited by 0