Theorems · Theorem · functional analysis
norm_pow
∀ {α : Type u_2} [inst : SeminormedRing α] [NormOneClass α] [NormMulClass α] (a : α) (n : ℕ), ‖a ^ n‖ = ‖a‖ ^ n- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 106 results in Mathlib
- Foundations
- Depth 99 from the axioms, rests on 2,138 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SeminormedRingstatement and proof · cited by 446
- NormOneClassstatement and proof · cited by 136
- NormMulClassstatement and proof · cited by 66
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- MonoidHom.map_powproof · cited by 30
- normHomproof · cited by 8
Cited by106
Results whose statement or proof uses this declaration.
- NormedField.exists_lt_normproof · cited by 14
- Complex.hasDerivAt_expproof · cited by 10
- ProperSpace.of_locallyCompactSpaceproof · cited by 6
- innerSL_apply_normproof · cited by 5
- HurwitzKernelBounds.summable_f_natproof · cited by 5
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- hasSum_choose_mul_geometric_of_norm_lt_one'proof · cited by 4
- hasSum_geometric_of_norm_lt_oneproof · cited by 4
- MvPowerSeries.isRestricted_abs_iffproof · cited by 4
- summable_geometric_iff_norm_lt_oneproof · cited by 4
- PeriodPair.hasFPowerSeriesOnBall_weierstrassPExceptproof · cited by 3