Theorems · Theorem · functional analysis
neg_closedBall
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (δ : ℝ) (x : E), -Metric.closedBall x δ = Metric.closedBall (-x) δ- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 160 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.
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Metric.closedBallstatement · cited by 704
- Set.negstatement · cited by 168
- IsometryEquiv.negproof · cited by 8
- IsometryEquiv.preimage_closedBallproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- singleton_sub_closedBallproof · cited by 1
- ball_sub_closedBallproof · cited by 0
- IsCompact.sub_closedBallproof · cited by 0
- IsCompact.sub_closedBall_zeroproof · cited by 0
- closedBall_sub_closedBallproof · cited by 0