Theorems · Theorem · real analysis
Real.sin_nonpos_of_nonpos_of_neg_pi_le
∀ {x : ℝ}, x ≤ 0 → -Real.pi ≤ x → Real.sin x ≤ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Real.pistatement and proof · cited by 1,774
- Real.sinstatement · cited by 389
- neg_nonnegproof · cited by 60
- Real.sin_negproof · cited by 34
- neg_leproof · cited by 27
- Real.sin_nonneg_of_nonneg_of_le_piproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Real.abs_sin_eq_sin_abs_of_abs_le_piproof · cited by 1
- Real.sin_half_eq_neg_sqrtproof · cited by 1