Theorems · Theorem · functional analysis
dist_mulIndicator
∀ {α : Type u_2} {E : Type u_5} [inst : SeminormedGroup E] (s t : Set α) (f : α → E) (x : α),
dist (s.mulIndicator f x) (t.mulIndicator f x) = ‖(symmDiff s t).mulIndicator f x‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Dist.diststatement · cited by 1,539
- div_oneproof · cited by 629
- one_divproof · cited by 624
- inv_oneproof · cited by 301
- SeminormedGroupstatement and proof · cited by 250
- symmDiffstatement and proof · cited by 236
- Set.mulIndicatorstatement and proof · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- nndist_mulIndicatorproof · cited by 1