Theorems · Theorem · functional analysis
vadd_closedBall_zero
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x : E), x +ᵥ Metric.closedBall 0 δ = Metric.closedBall x δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 162 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- add_zeroproof · cited by 2,707
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddstatement · cited by 1,820
- Metric.closedBallstatement and proof · cited by 704
- Set.vaddSetstatement · cited by 403
- Metric.vadd_closedBallproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- strictConvex_closedBallproof · cited by 8
- IsCompact.add_closedBallproof · cited by 3
- affinity_unitClosedBallproof · cited by 1
- convexHull_sphere_eq_closedBallproof · cited by 1