Theorems · Theorem · complex analysis
Real.abs_cos_le_one
∀ (x : ℝ), |Real.cos x| ≤ 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- absstatement · cited by 1,814
- Real.cosstatement and proof · cited by 424
- abs_le_one_iff_mul_self_le_oneproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- Real.cos_le_oneproof · cited by 3
- Real.neg_one_le_cosproof · cited by 3
- Real.lipschitzWith_sinproof · cited by 1
- HurwitzZeta.isBigO_atTop_cosKernel_subproof · cited by 0