Theorems · Theorem · functional analysis
NormedSpace.normalize_smul
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] (r : ℝ) (x : V),
NormedSpace.normalize (r • x) = ↑(SignType.sign r) • NormedSpace.normalize x- Defined in
- Mathlib.Analysis.Normed.Module.Normalize
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- one_smulproof · cited by 1,374
- OrderHomstatement · cited by 934
- zero_smulproof · cited by 716
- SignTypestatement · cited by 318
- neg_smulproof · cited by 306
- lt_trichotomyproof · cited by 178
- SignType.signstatement · cited by 128
- SignType.caststatement and proof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- signedDist_smulproof · cited by 5