Theorems · Theorem · complex analysis
Real.cos_sub
∀ (x y : ℝ), Real.cos (x - y) = Real.cos x * Real.cos y + Real.sin x * Real.sin y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- Real.sin_negproof · cited by 34
- Real.cos_negproof · cited by 27
- Real.cos_addproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Real.two_mul_cos_mul_cosproof · cited by 0
- Real.two_mul_sin_mul_sinproof · cited by 0