Theorems · Theorem · functional analysis
dist_zero_right
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), dist a 0 = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 172 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 67 definitions · uses propext
- Assumes
- SeminormedAddGroup
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
- zero_addproof · cited by 2,366
- Dist.diststatement · cited by 1,539
- neg_zeroproof · cited by 542
- SeminormedAddGroupstatement and proof · cited by 331
- dist_eq_norm_neg_add'proof · cited by 3
Cited by172
Results whose statement or proof uses this declaration.
- norm_nonnegproof · cited by 725
- norm_zeroproof · cited by 366
- continuous_normproof · cited by 36
- BoundedContinuousFunction.norm_coe_le_normproof · cited by 25
- norm_smul_leproof · cited by 24
- norm_le_zero_iffproof · cited by 23
- mem_ball_zero_iffproof · cited by 22
- Asymptotics.isLittleO_one_iffproof · cited by 20
- pi_norm_le_iff_of_nonnegproof · cited by 18
- mem_closedBall_zero_iffproof · cited by 16
- dist_zero_leftproof · cited by 15
- mem_sphere_zero_iff_normproof · cited by 13