Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.prodPrimeFactors
∀ {R : Type u_1} [inst : CommMonoidWithZero R] (f : ℕ → R), (ArithmeticFunction.prodPrimeFactors f).IsMultiplicative- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Finset.prodproof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.prod_congrproof · cited by 646
- mul_ne_zeroproof · cited by 178
- Nat.primeFactorsproof · cited by 129
- ArithmeticFunction.IsMultiplicativestatement · cited by 45
- Finset.prod_unionproof · cited by 31
- Nat.primeFactors_mulproof · cited by 6
- Nat.primeFactors_oneproof · cited by 6
- ArithmeticFunction.IsMultiplicative.iff_ne_zeroproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- BoundingSieve.selbergTerms_isMultiplicativeproof · cited by 1