Theorems · Theorem · special functions
Real.arcsin_of_le_neg_one
∀ {x : ℝ}, x ≤ -1 → Real.arcsin x = -(Real.pi / 2)- Cited by
- 7 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.
Cites12
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
- Set.Elemproof · cited by 7,166
- Real.pistatement and proof · cited by 1,774
- Set.Iccproof · cited by 1,702
- zero_le_oneproof · cited by 316
- Real.arcsinstatement and proof · cited by 125
- Subtype.coe_mkproof · cited by 81
- Set.left_mem_Iccproof · cited by 67
- neg_le_selfproof · cited by 8
- Set.projIcc_of_le_leftproof · cited by 5
- Real.arcsin_projIccproof · cited by 2
- Real.arcsin_neg_oneproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Real.arcsin_negproof · cited by 11
- Real.cos_arcsinproof · cited by 4
- Real.arcsin_le_iff_le_sin'proof · cited by 3
- Real.hasDerivWithinAt_arcsin_Iicproof · cited by 2
- Real.deriv_arcsin_auxproof · cited by 2
- Real.arcsin_eq_neg_pi_div_twoproof · cited by 2
- Real.arccos_of_le_neg_oneproof · cited by 1