Theorems · Theorem · functional analysis
norm_abs_zsmul
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E) (n : ℤ), ‖|n| • a‖ = ‖n • a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
- Assumes
- SeminormedAddGroup
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
- SeminormedAddGroupstatement and proof · cited by 331
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- norm_negproof · cited by 190
- abs_of_nonposproof · cited by 53
- neg_zsmulproof · cited by 41
Cited by2
Results whose statement or proof uses this declaration.
- norm_natAbs_smulproof · cited by 2
- nnnorm_abs_zsmulproof · cited by 0