Theorems · Theorem · functional analysis
norm_pow_le_mul_norm
∀ {E : Type u_5} [inst : SeminormedGroup E] {a : E} {n : ℕ}, ‖a ^ n‖ ≤ ↑n * ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 5,413
- SeminormedGroupstatement and proof · cited by 250
Cited by4
Results whose statement or proof uses this declaration.
- pow_mem_ballproof · cited by 2
- norm_zpow_le_mul_normproof · cited by 1
- pow_mem_closedBallproof · cited by 0
- nnnorm_pow_le_mul_normproof · cited by 0