Theorems · Theorem · functional analysis
norm_isUnit_zsmul
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E) {n : ℤ}, IsUnit n → ‖n • a‖ = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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
- SeminormedAddGroupstatement and proof · cited by 331
- one_nsmulproof · cited by 63
- Int.isUnit_iff_natAbs_eqproof · cited by 6
- norm_natAbs_smulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- nnnorm_units_zsmulproof · cited by 0
- nnnorm_isUnit_zsmulproof · cited by 0
- norm_units_zsmulproof · cited by 0