Theorems · Theorem · general topology
dist_self_add_left
∀ {E : Type u_2} [inst : SeminormedAddGroup E] (a b : E), dist (b + a) b = ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- 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_self_add_rightproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.isOpenMapproof · cited by 6
- Complex.mem_slitPlane_of_norm_lt_oneproof · cited by 5
- IsOpen.analyticOn_iff_analyticOnNhdproof · cited by 5
- IsUpperSet.exists_subset_ballproof · cited by 2
- AnalyticAt.eventually_constant_or_nhds_le_map_nhdsproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- analyticWithinAt_of_singleton_memproof · cited by 0
- EuclideanGeometry.hasFDerivAt_inversionproof · cited by 0
- analyticOn_of_locally_analyticOnproof · cited by 0