UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center
∀ (z w : UpperHalfPlane) (r : ℝ), cmp (dist z w) r = cmp (dist ↑z ↑(w.center r)) (w.im * Real.sinh r)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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 and proof · cited by 5,565
- zero_addproof · cited by 2,366
- MetricSpaceproof · cited by 1,684
- PseudoMetricSpaceproof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- le_of_ltproof · cited by 1,175
- LT.lt.trans_leproof · cited by 678
- UpperHalfPlanestatement and proof · cited by 626
- mul_nonnegproof · cited by 397
- mul_posproof · cited by 374
- UpperHalfPlane.coestatement and proof · cited by 288
Cited by5
Results whose statement or proof uses this declaration.
- UpperHalfPlane.dist_eq_iff_dist_coe_center_eqproof · cited by 3
- UpperHalfPlane.dist_le_iff_dist_coe_center_leproof · cited by 1
- UpperHalfPlane.dist_lt_iff_dist_coe_center_ltproof · cited by 1
- UpperHalfPlane.le_dist_iff_le_dist_coe_centerproof · cited by 0
- UpperHalfPlane.lt_dist_iff_lt_dist_coe_centerproof · cited by 0