Theorems · Theorem · functional analysis
add_ball
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (s : Set E) (x : E),
s + Metric.ball x δ = x +ᵥ Metric.thickening δ s- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddstatement and proof · cited by 1,820
- Metric.ballstatement and proof · cited by 735
- Set.vaddSetstatement · cited by 403
- Set.addstatement · cited by 338
- Metric.thickeningstatement and proof · cited by 130
- add_vadd_commproof · cited by 6
- add_ball_zeroproof · cited by 4
- vadd_ball_zeroproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ball_addproof · cited by 3
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- sub_ballproof · cited by 0