Theorems · Theorem · functional analysis
dist_one_right
∀ {E : Type u_5} [inst : SeminormedGroup E] (a : E), dist a 1 = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- SeminormedGroup
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
- one_mulproof · cited by 2,841
- Dist.diststatement · cited by 1,539
- inv_oneproof · cited by 301
- SeminormedGroupstatement and proof · cited by 250
- dist_eq_norm_inv_mul'proof · cited by 3
Cited by20
Results whose statement or proof uses this declaration.
- norm_nonneg'proof · cited by 21
- norm_one'proof · cited by 10
- dist_one_leftproof · cited by 6
- continuous_norm'proof · cited by 4
- norm_le_zero_iff'proof · cited by 3
- IsUltrametricDist.norm_mul_eq_max_of_norm_ne_normproof · cited by 3
- AntilipschitzWith.le_mul_norm'proof · cited by 2
- Isometry.norm_map_of_map_oneproof · cited by 2
- comap_norm_atTop'proof · cited by 2
- NormedGroup.tendsto_nhds_oneproof · cited by 2
- tendsto_norm'proof · cited by 1
- LipschitzWith.norm_le_mul'proof · cited by 1