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Theorems · Theorem · number theory

ArithmeticFunction.ppow_apply

∀ {R : Type u_1} [inst : Semiring R] {f : ArithmeticFunction R} {k x : ℕ}, 0 < k → (f.ppow k) x = f x ^ k
Defined in
Mathlib.NumberTheory.ArithmeticFunction.Zeta
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ArithmeticFunction.pow_apply · cited by 3ArithmeticFunction.pow_ap…ArithmeticFunction.ppow_succ' · cited by 1ArithmeticFunction.ppow_s…ArithmeticFunction.ppow_succ · cited by 0ArithmeticFunction.ppow_s…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringArithmeticFunction · cited by 290ArithmeticFunctionArithmeticFunction.ppow · cited by 6ArithmeticFunction.ppowArithmeticFunction.coe_mk · cited by 2ArithmeticFunction.coe_mkArithmeticFunction.ppow_applyCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.