UpperHalfPlane.dist_le_iff_le_sinh
∀ {z w : UpperHalfPlane} {r : ℝ}, dist z w ≤ r ↔ dist ↑z ↑w / (2 * √(z.im * w.im)) ≤ Real.sinh (r / 2)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 1,539
- UpperHalfPlanestatement and proof · cited by 626
- Real.sqrtstatement and proof · cited by 545
- UpperHalfPlane.coestatement and proof · cited by 288
- Real.sinhstatement and proof · cited by 142
- UpperHalfPlane.imstatement and proof · cited by 128
- div_le_div_iff_of_pos_rightproof · cited by 20
- zero_lt_two'proof · cited by 16
- UpperHalfPlane.sinh_half_distproof · cited by 6
- Real.sinh_le_sinhproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.dist_triangleproof · cited by 0
- UpperHalfPlane.dist_le_dist_coe_div_sqrtproof · cited by 0