UpperHalfPlane.dist_le_iff_dist_coe_center_le
∀ {z w : UpperHalfPlane} {r : ℝ}, dist z w ≤ r ↔ dist ↑z ↑(w.center r) ≤ w.im * Real.sinh r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 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.
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Dist.diststatement · cited by 1,539
- UpperHalfPlanestatement and proof · cited by 626
- UpperHalfPlane.coestatement · cited by 288
- Real.sinhstatement · cited by 142
- UpperHalfPlane.imstatement · cited by 128
- UpperHalfPlane.centerstatement · cited by 20
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- le_iff_le_of_cmp_eq_cmpproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.image_coe_closedBallproof · cited by 0