Theorems · Theorem · real analysis
Real.sin_lt_sin_of_lt_of_le_pi_div_two
∀ {x y : ℝ}, -(Real.pi / 2) ≤ x → y ≤ Real.pi / 2 → x < y → Real.sin x < Real.sin y- Cited by
- 3 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.
Cites12
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
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Real.cosproof · cited by 424
- Real.sinstatement and proof · cited by 389
- lt_of_not_geproof · cited by 374
- mul_posproof · cited by 374
- sub_posproof · cited by 147
- Real.cos_pos_of_mem_Iooproof · cited by 14
- Real.sin_pos_of_pos_of_lt_piproof · cited by 11
- Real.sin_sub_sinproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Real.cos_lt_cos_of_nonneg_of_le_piproof · cited by 6
- Real.strictMonoOn_sinproof · cited by 4
- EuclideanGeometry.dist_lt_of_angle_ltproof · cited by 1