Theorems · Theorem · special functions
Real.arcsin_le_iff_le_sin
∀ {x y : ℝ}, x ∈ Set.Icc (-1) 1 → y ∈ Set.Icc (-(Real.pi / 2)) (Real.pi / 2) → (Real.arcsin x ≤ y ↔ x ≤ Real.sin y)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- Set.Iccstatement and proof · cited by 1,702
- Real.sinstatement and proof · cited by 389
- Real.arcsinstatement and proof · cited by 125
- StrictMonoOn.le_iff_leproof · cited by 17
- Real.sin_mem_Iccproof · cited by 5
- Real.strictMonoOn_arcsinproof · cited by 4
- Real.arcsin_sin'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Real.arcsin_le_iff_le_sin'proof · cited by 3
- Real.le_arcsin_iff_sin_leproof · cited by 1
- Real.lt_arcsin_iff_sin_ltproof · cited by 0