Theorems · Theorem · functional analysis
NormedSpace.norm_normalize_eq_one_iff
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] {x : V}, ‖NormedSpace.normalize x‖ = 1 ↔ x ≠ 0- Defined in
- Mathlib.Analysis.Normed.Module.Normalize
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- smul_zeroproof · cited by 665
- norm_zeroproof · cited by 366
- inv_mul_cancel₀proof · cited by 267
- norm_smulproof · cited by 242
- inv_zeroproof · cited by 184
- norm_invproof · cited by 126
- norm_normproof · cited by 113
- NormedSpace.normalizestatement · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- NormedSpace.norm_normalizeproof · cited by 1
- InnerProductGeometry.angle_le_angle_add_angleproof · cited by 1
- InnerProductGeometry.angle_eq_angle_add_angle_iffproof · cited by 0