Theorems · Definition · field theory
IsPowMul
{R : Type u_1} → [Pow R ℕ] → (R → ℝ) → PropA function f : R → ℝ is power-multiplicative if for all r ∈ R and all positive n ∈ ℕ,
f (r ^ n) = (f r) ^ n.
- Defined in
- Mathlib.Data.Real.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Pow
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
Cited by41
Results whose statement or proof uses this declaration.
- tendsto_seminormFromConst_seq_atTopstatement and proof · cited by 9
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalstatement · cited by 5
- spectralNorm_uniquestatement and proof · cited by 3
- spectralNorm_eq_invariantExtensionproof · cited by 3
- isPowMul_spectralNormstatement · cited by 3
- norm_root_le_spectralValuestatement and proof · cited by 3
- seminormFromConststatement and proof · cited by 2
- contraction_of_isPowMul_of_boundedWrtstatement and proof · cited by 2
- MulRingNorm.isPowMulstatement · cited by 2
- spectralNorm_eq_iSup_of_finiteDimensional_normalstatement and proof · cited by 2
- eq_of_powMul_faithfulstatement and proof · cited by 1
- seminormFromConst_apply_cstatement and proof · cited by 1