Theorems · Theorem · functional analysis
closedBall_add_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
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- HVAdd.hVAddproof · cited by 1,820
- add_commproof · cited by 1,535
- Metric.closedBallstatement and proof · cited by 704
- Set.addstatement · cited by 338
- ProperSpacestatement and proof · cited by 190
- ProperSpace.isCompact_closedBallproof · cited by 40
- vadd_eq_addproof · cited by 39
- Metric.vadd_closedBallproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- closedBall_sub_closedBallproof · cited by 0