Theorems · Theorem · functional analysis
mul_ball_one
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (s : Set E), s * Metric.ball 1 δ = Metric.thickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- mul_oneproof · cited by 3,885
- Set.iUnionproof · cited by 2,483
- Set.extproof · cited by 2,266
- Metric.ballstatement and proof · cited by 735
- Set.iUnion_congr_Propproof · cited by 374
- Set.mulstatement · cited by 297
- SeminormedCommGroupstatement and proof · cited by 191
- Metric.thickeningstatement · cited by 130
- Set.biUnion_of_singletonproof · cited by 43
- Metric.thickening_eq_biUnion_ballproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- ball_mul_oneproof · cited by 3
- mul_ballproof · cited by 2
- div_ball_oneproof · cited by 0