Theorems · Theorem · complex analysis
Real.cos_bound
∀ {x : ℝ}, |x| ≤ 1 → |Real.cos x - (1 - x ^ 2 / 2)| ≤ |x| ^ 4 * (5 / 96)- 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.
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
- Norm.normproof · cited by 5,413
- absstatement and proof · cited by 1,814
- Complex.ofRealproof · cited by 1,654
- Real.cosstatement and proof · cited by 424
- Complex.norm_realproof · cited by 105
- Complex.ofReal_divproof · cited by 83
- Complex.ofReal_powproof · cited by 81
- Complex.ofReal_subproof · cited by 63
- Complex.cos_boundproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.cos_pos_of_le_oneproof · cited by 2
- Real.cos_one_leproof · cited by 1