UpperHalfPlane.dist_log_im_le
∀ (z w : UpperHalfPlane), dist (Real.log z.im) (Real.log w.im) ≤ dist z w
Hyperbolic distance between two points is greater than or equal to the distance between the logarithms of their imaginary parts.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- zero_addproof · cited by 2,366
- absproof · cited by 1,814
- Dist.diststatement and proof · cited by 1,539
- le_of_ltproof · cited by 1,175
- sub_selfproof · cited by 996
- Real.logstatement · cited by 939
- UpperHalfPlanestatement and proof · cited by 626
- Real.sqrtproof · cited by 545
- mul_posproof · cited by 374
- zero_powproof · cited by 361
- mul_le_mul_of_nonneg_leftproof · cited by 361
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.im_le_im_mul_exp_distproof · cited by 1