Theorems · Theorem · functional analysis
closedBall_sub_closedBall
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] {δ ε : ℝ} [ProperSpace E],
0 ≤ ε → 0 ≤ δ → ∀ (a b : E), Metric.closedBall a ε - Metric.closedBall b δ = Metric.closedBall (a - b) (ε + δ)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- sub_eq_add_negproof · cited by 1,023
- Metric.closedBallstatement and proof · cited by 704
- ProperSpacestatement and proof · cited by 190
- Set.substatement · cited by 136
- neg_closedBallproof · cited by 5
- closedBall_add_closedBallproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.