Theorems · Theorem · special functions
Real.arcsin_neg
∀ (x : ℝ), Real.arcsin (-x) = -Real.arcsin x
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.piproof · cited by 1,774
- neg_negproof · cited by 960
- le_totalproof · cited by 294
- Real.arcsinstatement and proof · cited by 125
- Real.sin_negproof · cited by 34
- neg_le_negproof · cited by 34
- neg_leproof · cited by 27
- le_negproof · cited by 16
- Real.arcsin_le_pi_div_twoproof · cited by 7
- Real.arcsin_of_le_neg_oneproof · cited by 7
- Real.arcsin_of_one_leproof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- Real.arctan_negproof · cited by 6
- Complex.sin_argproof · cited by 4
- Real.le_arcsin_iff_sin_le'proof · cited by 4
- Real.arccos_negproof · cited by 3
- Complex.arg_conjproof · cited by 3
- Real.arccos_neg_oneproof · cited by 2
- Complex.arg_neg_Iproof · cited by 2
- Real.differentiableWithinAt_arcsin_Iciproof · cited by 2
- Real.differentiableWithinAt_arcsin_Iicproof · cited by 2
- Real.arcsin_nonposproof · cited by 1
- Real.le_arcsin_iff_sin_leproof · cited by 1