Theorems · Theorem · functional analysis
vadd_ball_zero
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x : E), x +ᵥ Metric.ball 0 δ = Metric.ball x δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 2 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.
Cites9
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
- add_zeroproof · cited by 2,707
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddstatement · cited by 1,820
- Metric.ballstatement and proof · cited by 735
- Set.vaddSetstatement · cited by 403
- vadd_eq_addproof · cited by 39
- Metric.vadd_ballproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- add_ballproof · cited by 4
- affinity_unitBallproof · cited by 0