Theorems · Theorem · real analysis
Real.sin_pos_of_pos_of_lt_pi
∀ {x : ℝ}, 0 < x → x < Real.pi → 0 < Real.sin x- Cited by
- 11 results in Mathlib
- Foundations
- Depth 176 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
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- le_of_not_gtproof · cited by 430
- Real.sinstatement · cited by 389
- lt_of_not_geproof · cited by 374
- sub_posproof · cited by 147
- Real.sin_pi_subproof · cited by 4
- Real.pi_le_fourproof · cited by 3
- Real.sin_pos_of_pos_of_le_twoproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- Real.sin_pi_div_twoproof · cited by 29
- Real.sin_eq_zero_iffproof · cited by 5
- Real.sin_pos_of_mem_Iooproof · cited by 5
- Real.sin_lt_sin_of_lt_of_le_pi_div_twoproof · cited by 3
- Real.sin_neg_of_neg_of_neg_pi_ltproof · cited by 3
- EuclideanGeometry.sin_pos_of_not_collinearproof · cited by 2
- Polynomial.Chebyshev.roots_U_realproof · cited by 2
- Real.tan_pos_of_pos_of_lt_pi_div_twoproof · cited by 2
- Real.strictMonoOn_tanproof · cited by 2
- Real.Angle.sign_toRealproof · cited by 1
- Real.sin_eq_zero_iff_of_lt_of_ltproof · cited by 0