Theorems · Theorem · number theory
threeAPFree_sphere
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [StrictConvexSpace ℝ E] (x : E) (r : ℝ),
ThreeAPFree (Metric.sphere x r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddMonoidproof · cited by 2,864
- eq_or_neproof · cited by 1,117
- Metric.closedBallproof · cited by 704
- Metric.spherestatement and proof · cited by 371
- frontierproof · cited by 214
- StrictConvexSpacestatement and proof · cited by 57
- ThreeAPFreestatement and proof · cited by 38
- Metric.isClosed_closedBallproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Behrend.threeAPFree_sphereproof · cited by 1