Theorems · Theorem · functional analysis
dist_zero_left
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), dist 0 a = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SeminormedAddGroup
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
- Dist.diststatement · cited by 1,539
- SeminormedAddGroupstatement and proof · cited by 331
- dist_commproof · cited by 188
- dist_zero_rightproof · cited by 172
Cited by15
Results whose statement or proof uses this declaration.
- dist_zeroproof · cited by 16
- IsUltrametricDist.norm_add_eq_max_of_norm_ne_normproof · cited by 3
- QuotientAddGroup.norm_mk_le_normproof · cited by 2
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
- dist_self_add_rightproof · cited by 2
- BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding'proof · cited by 2
- Real.dist_mulExpNegMulSq_le_two_mul_sqrtproof · cited by 1
- tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_auxproof · cited by 1
- dist_add_self_rightproof · cited by 1
- difference_quotients_converge_uniformlyproof · cited by 1