Theorems · Theorem · functional analysis
dist_eq_norm_neg_add
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b : E), dist a b = ‖-a + b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 5,413
- Dist.diststatement · cited by 1,539
- SeminormedAddGroupstatement and proof · cited by 331
- SeminormedAddGroup.dist_eqproof · cited by 3
Cited by46
Results whose statement or proof uses this declaration.
- norm_add_leproof · cited by 68
- norm_sub_revproof · cited by 41
- norm_neg_addproof · cited by 12
- IsUltrametricDist.norm_add_le_maxproof · cited by 7
- AddMonoidHomClass.antilipschitz_of_boundproof · cited by 7
- AddMonoidHomClass.lipschitz_of_boundproof · cited by 6
- AddMonoidHomClass.isometry_iff_normproof · cited by 5
- dist_sum_sum_le_of_leproof · cited by 4
- dist_eq_norm_sub'proof · cited by 4
- nndist_eq_nnnorm_neg_addproof · cited by 3
- IsUltrametricDist.norm_add_eq_max_of_norm_ne_normproof · cited by 3