Theorems · Theorem · functional analysis
norm_zpow_abs
∀ {E : Type u_5} [inst : SeminormedGroup E] (a : E) (n : ℤ), ‖a ^ |n|‖ = ‖a ^ n‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- absstatement · cited by 1,814
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- SeminormedGroupstatement and proof · cited by 250
- zpow_negproof · cited by 198
- abs_of_nonposproof · cited by 53
- norm_inv'proof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- norm_pow_natAbsproof · cited by 2
- nnnorm_zpow_absproof · cited by 0