Theorems · Theorem · special functions
Real.cos_arccos
∀ {x : ℝ}, -1 ≤ x → x ≤ 1 → Real.cos (Real.arccos x) = x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.cosstatement and proof · cited by 424
- Real.arcsinproof · cited by 125
- Real.arccosstatement · cited by 90
- Real.cos_pi_div_two_subproof · cited by 8
- Real.sin_arcsinproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- InnerProductGeometry.cos_angle_add_of_inner_eq_zeroproof · cited by 5
- InnerProductGeometry.cos_angleproof · cited by 4
- Polynomial.Chebyshev.integral_measureT_eq_integral_cosproof · cited by 3
- Polynomial.Chebyshev.abs_eval_T_real_eq_one_iffproof · cited by 3
- Polynomial.Chebyshev.eval_T_real_mem_Iccproof · cited by 1