Theorems · Theorem · special functions
Real.lt_arcsin_iff_sin_lt
∀ {x y : ℝ}, x ∈ Set.Icc (-(Real.pi / 2)) (Real.pi / 2) → y ∈ Set.Icc (-1) 1 → (x < Real.arcsin y ↔ Real.sin x < y)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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 · cited by 389
- not_leproof · cited by 328
- Real.arcsinstatement · cited by 125
- Real.arcsin_le_iff_le_sinproof · cited by 3
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