Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.pmul
∀ {R : Type u_1} [inst : CommSemiring R] {f g : ArithmeticFunction R},
f.IsMultiplicative → g.IsMultiplicative → (f.pmul g).IsMultiplicative- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- mul_oneproof · cited by 3,885
- ArithmeticFunctionstatement and proof · cited by 290
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
- ArithmeticFunction.pmulstatement · cited by 9
- ArithmeticFunction.IsMultiplicative.map_mul_of_coprimeproof · cited by 9
- ArithmeticFunction.IsMultiplicative.map_oneproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- BoundingSieve.selbergTerms_isMultiplicativeproof · cited by 1
- ArithmeticFunction.IsMultiplicative.ppowproof · cited by 1