Theorems · Theorem · functional analysis
norm_pow_natAbs
∀ {E : Type u_5} [inst : SeminormedGroup E] (a : E) (n : ℤ), ‖a ^ n.natAbs‖ = ‖a ^ n‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- zpow_natCastproof · cited by 271
- SeminormedGroupstatement and proof · cited by 250
- Int.abs_eq_natAbsproof · cited by 26
- norm_zpow_absproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- norm_zpow_isUnitproof · cited by 1
- nnnorm_pow_natAbsproof · cited by 0