UpperHalfPlane.le_dist_iff_le_dist_coe_center
∀ {z w : UpperHalfPlane} {r : ℝ}, r < dist z w ↔ w.im * Real.sinh r < dist ↑z ↑(w.center r)- Cited by
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- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- lt_iff_lt_of_cmp_eq_cmpproof · cited by 6
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- cmp_eq_cmp_symmproof · cited by 4
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