Theorems · Theorem · functional analysis
nnnorm_pow_le
∀ {α : Type u_2} [inst : SeminormedRing α] [NormOneClass α] (a : α) (n : ℕ), ‖a ^ n‖₊ ≤ ‖a‖₊ ^ nIf α is a seminormed ring with ‖1‖₊ = 1, then ‖a ^ n‖₊ ≤ ‖a‖₊ ^ n.
See also nnnorm_pow_le'.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingNormOneClass
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- pow_zeroproof · cited by 1,094
- NNNorm.nnnormstatement and proof · cited by 952
- SeminormedRingstatement and proof · cited by 446
- NormOneClassstatement and proof · cited by 136
- nnnorm_oneproof · cited by 11
- nnnorm_pow_le'proof · cited by 3
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