Theorems · Theorem · functional analysis
norm_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 norm_pow_le'.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingNormOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- pow_zeroproof · cited by 1,094
- SeminormedRingstatement and proof · cited by 446
- NormOneClass.norm_oneproof · cited by 148
- NormOneClassstatement and proof · cited by 136
- norm_pow_le'proof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.house_pow_leproof · cited by 0