Theorems · Theorem · functional analysis
dist_eq_norm_sub
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), dist a b = ‖a - b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement · cited by 1,539
- sub_eq_neg_addproof · cited by 51
- dist_eq_norm_neg_add'proof · cited by 3
Cited by29
Results whose statement or proof uses this declaration.
- dist_eq_normproof · cited by 182
- edist_eq_enorm_subproof · cited by 37
- mem_ball_iff_normproof · cited by 20
- tendsto_iff_norm_sub_tendsto_zeroproof · cited by 17
- norm_neg_addproof · cited by 12
- mem_closedBall_iff_normproof · cited by 12
- mem_sphere_iff_normproof · cited by 9
- IsCompact.add_closedBall_zeroproof · cited by 5
- multipliable_one_add_of_summableproof · cited by 4
- mem_ball_iff_norm'proof · cited by 4
- mem_closedBall_iff_norm'proof · cited by 4
- TendstoLocallyUniformlyOn.inv₀_of_disjointproof · cited by 3