Theorems · Theorem · functional analysis
disjoint_ball_ball_iff
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] {x y : E} {δ ε : ℝ},
0 < δ → 0 < ε → (Disjoint (Metric.ball x δ) (Metric.ball y ε) ↔ δ + ε ≤ dist x y)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Disjointstatement and proof · cited by 2,201
- Dist.diststatement and proof · cited by 1,539
- add_commproof · cited by 1,535
- Metric.ballstatement and proof · cited by 735
- le_of_not_gtproof · cited by 430
- dist_commproof · cited by 188
- Disjoint.le_botproof · cited by 52
- exists_dist_lt_ltproof · cited by 3
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