Theorems · Theorem · functional analysis
dist_eq_norm
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), dist a b = ‖a - b‖Alias of dist_eq_norm_sub.
- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 182 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 111 definitions · uses propext
- Assumes
- SeminormedAddCommGroup
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
- SeminormedAddCommGroupstatement · cited by 2,671
- Dist.diststatement · cited by 1,539
- dist_eq_norm_subproof · cited by 29
Cited by182
Results whose statement or proof uses this declaration.
- closure_ballproof · cited by 20
- dist_smul₀proof · cited by 11
- Complex.dist_eqproof · cited by 11
- tendstoUniformlyOn_tsumproof · cited by 9
- Complex.continuous_expproof · cited by 8
- interior_closedBallproof · cited by 8
- ball_normSeminormproof · cited by 7
- tendstoUniformlyOn_tsum_of_cofinite_eventuallyproof · cited by 6
- ContinuousLinearMap.isOpenMapproof · cited by 6
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- NumberField.InfinitePlace.mk_eq_iffproof · cited by 5
- TotallyBounded.isVonNBoundedproof · cited by 4