Theorems · Theorem · complex analysis
Real.cos_pos_of_le_one
∀ {x : ℝ}, |x| ≤ 1 → 0 < Real.cos x- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Nat.cast_oneproof · cited by 2,501
- absstatement and proof · cited by 1,814
- le_of_ltproof · cited by 1,175
- add_le_addproof · cited by 666
- Real.cosstatement · cited by 424
- div_posproof · cited by 337
- mul_le_mul_of_nonneg_rightproof · cited by 301
- sqproof · cited by 280
- abs_nonnegproof · cited by 168
- sub_posproof · cited by 147
- abs_mulproof · cited by 98
Cited by2
Results whose statement or proof uses this declaration.
- Real.cos_one_posproof · cited by 2
- Real.sin_pos_of_pos_of_le_twoproof · cited by 1