Theorems · Theorem · functional analysis
inv_closedBall
∀ {E : Type u_1} [inst : SeminormedCommGroup E] (δ : ℝ) (x : E), (Metric.closedBall x δ)⁻¹ = Metric.closedBall x⁻¹ δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 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.
Cites7
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
- Metric.closedBallstatement · cited by 704
- SeminormedCommGroupstatement and proof · cited by 191
- Set.invstatement · cited by 132
- IsometryEquiv.invproof · cited by 8
- IsometryEquiv.preimage_closedBallproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- singleton_div_closedBallproof · cited by 1
- IsCompact.div_closedBallproof · cited by 0
- IsCompact.div_closedBall_oneproof · cited by 0