Theorems · Theorem · special functions
Real.neg_pi_div_two_lt_arcsin
∀ {x : ℝ}, -(Real.pi / 2) < Real.arcsin x ↔ -1 < x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.pistatement and proof · cited by 1,774
- Real.arcsinstatement · cited by 125
- Real.sin_negproof · cited by 34
- Real.sin_pi_div_twoproof · cited by 29
- Real.pi_div_two_posproof · cited by 22
- Set.left_mem_Icoproof · cited by 18
- neg_lt_selfproof · cited by 7
- Real.lt_arcsin_iff_sin_lt'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.arg_le_pi_div_two_iffproof · cited by 4
- Real.arcsin_eq_neg_pi_div_twoproof · cited by 2