Theorems · Theorem · functional analysis
norm_zpow_le_mul_norm
∀ {α : Type u_1} [inst : SeminormedCommGroup α] (n : ℤ) (a : α), ‖a ^ n‖ ≤ ‖n‖ * ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Int
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- SeminormedCommGroupstatement and proof · cited by 191
- norm_negproof · cited by 190
- norm_inv'proof · cited by 23
- norm_pow_le_mul_normproof · cited by 4
- Int.norm_natCastproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_zpow_le_mul_normproof · cited by 0