Theorems · Theorem · functional analysis
norm_zpow_isUnit
∀ {E : Type u_5} [inst : SeminormedGroup E] (a : E) {n : ℤ}, IsUnit n → ‖a ^ n‖ = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 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.
Cites7
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
- Norm.normstatement and proof · cited by 5,413
- IsUnitstatement and proof · cited by 1,602
- pow_oneproof · cited by 894
- SeminormedGroupstatement and proof · cited by 250
- Int.isUnit_iff_natAbs_eqproof · cited by 6
- norm_pow_natAbsproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_zpow_isUnitproof · cited by 0