Theorems · Theorem · real analysis
Real.sinh_le_sinh
∀ {x y : ℝ}, Real.sinh x ≤ Real.sinh y ↔ x ≤ y- Cited by
- 5 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Real.sinhstatement · cited by 142
- StrictMono.le_iff_leproof · cited by 104
- Real.sinh_strictMonoproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Real.sinhOrderIsoproof · cited by 6
- Real.sinh_nonneg_iffproof · cited by 2
- UpperHalfPlane.dist_le_iff_le_sinhproof · cited by 2
- Real.arsinh_nonneg_iffproof · cited by 1
- Real.arsinh_nonpos_iffproof · cited by 1
- Real.sinh_nonpos_iffproof · cited by 0