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Theorems · Theorem · number theory

ArithmeticFunction.IsMultiplicative.map_one

∀ {R : Type u_1} [inst : MonoidWithZero R] {f : ArithmeticFunction R}, f.IsMultiplicative → f 1 = 1
Defined in
Mathlib.NumberTheory.ArithmeticFunction.Defs
Cited by
8 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext
Assumes
MonoidWithZero
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Around this declaration

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

ArithmeticFunction.moebius_mul_coe_zeta · cited by 4ArithmeticFunction.moebiu…ArithmeticFunction.IsMultiplicative.natCast · cited by 4IsMultiplicative.natCastArithmeticFunction.IsMultiplicative.pmul · cited by 3IsMultiplicative.pmulArithmeticFunction.IsMultiplicative.intCast · cited by 1IsMultiplicative.intCastArithmeticFunction.IsMultiplicative.map_prod · cited by 1IsMultiplicative.map_prodArithmeticFunction.IsMultiplicative.pdiv · cited by 0IsMultiplicative.pdivArithmeticFunction.sum_moebius_mul_log_eq · cited by 0ArithmeticFunction.sum_mo…ArithmeticFunction.tendsTo_eulerProduct_ofPowerSeries · cited by 0ArithmeticFunction.tendsT…DFunLike.coe · cited by 62936DFunLike.coeMonoidWithZero · cited by 456MonoidWithZeroArithmeticFunction · cited by 290ArithmeticFunctionArithmeticFunction.IsMultiplicative · cited by 45ArithmeticFunction.IsMult…IsMultiplicative.map_oneCITED BYCITES

Cites4

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Cited by8

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