Theorems · Theorem · complex analysis
Real.cos_two_mul
∀ (x : ℝ), Real.cos (2 * x) = 2 * Real.cos x ^ 2 - 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Complex.ofRealproof · cited by 1,654
- Real.cosstatement and proof · cited by 424
- Complex.cosproof · cited by 279
- Complex.ofReal_mulproof · cited by 180
- Complex.ofReal_powproof · cited by 81
- Complex.ofReal_subproof · cited by 63
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_injectiveproof · cited by 23
- Complex.cos_two_mulproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Real.cos_piproof · cited by 20
- Real.quadratic_root_cos_pi_div_fiveproof · cited by 2
- Real.cos_two_negproof · cited by 1
- circleAverage_log_norm_sub_const₁proof · cited by 1