Theorems · Theorem · complex analysis
Complex.cos_sub
∀ (x y : ℂ), Complex.cos (x - y) = Complex.cos x * Complex.cos y + Complex.sin x * Complex.sin y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 148 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.
- Complexstatement and proof · cited by 5,565
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.cos_negproof · cited by 17
- Complex.sin_negproof · cited by 17
- Complex.cos_addproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Complex.cos_sub_cosproof · cited by 3
- Complex.cos_add_cosproof · cited by 2