Theorems · Theorem · functional analysis
dist_zero
∀ {E : Type u_5} [inst : SeminormedAddGroup E], dist 0 = norm- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- 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
- dist_zero_leftproof · cited by 15
Cited by16
Results whose statement or proof uses this declaration.
- norm_sub_revproof · cited by 41
- norm_smul_leproof · cited by 24
- IsUltrametricDist.isNonarchimedean_normproof · cited by 8
- HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNEproof · cited by 4
- lipschitzWith_one_normproof · cited by 4
- IsUltrametricDist.norm_add_eq_max_of_norm_ne_normproof · cited by 3
- QuotientAddGroup.norm_lt_iffproof · cited by 3
- AddCircle.norm_eq_of_zeroproof · cited by 2
- BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding'proof · cited by 2
- Continuous.exists_contMDiff_approx_and_eqOnproof · cited by 2