Theorems · Theorem · real analysis
Real.cos_half
∀ {x : ℝ}, -Real.pi ≤ x → x ≤ Real.pi → Real.cos (x / 2) = √((1 + Real.cos x) / 2)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Real.sqrtstatement and proof · cited by 545
- le_of_not_gtproof · cited by 430
- Real.cosstatement and proof · cited by 424
- two_mulproof · cited by 232
- add_divproof · cited by 89
- add_halvesproof · cited by 78
- Real.sqrt_sqproof · cited by 36
- Real.cos_nonneg_of_mem_Iccproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Complex.cpow_inv_two_reproof · cited by 6
- Real.cos_pi_div_sixproof · cited by 3