Theorems · Theorem · special functions
Real.cos_arcsin
∀ (x : ℝ), Real.cos (Real.arcsin x) = √(1 - x ^ 2)
- Cited by
- 4 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.
Cites29
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
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- Real.piproof · cited by 1,774
- le_of_ltproof · cited by 1,175
- Real.sqrtstatement and proof · cited by 545
- le_of_not_gtproof · cited by 430
- Real.cosstatement and proof · cited by 424
- Real.sinproof · cited by 389
- not_leproof · cited by 328
- sqproof · cited by 280
Cited by4
Results whose statement or proof uses this declaration.
- Complex.cos_argproof · cited by 7
- Real.tan_arcsinproof · cited by 2
- Real.sin_arccosproof · cited by 2
- Real.arcsin_eq_arccosproof · cited by 0