Theorems · Theorem · real analysis
Real.sin_nonneg_of_mem_Icc
∀ {x : ℝ}, x ∈ Set.Icc 0 Real.pi → 0 ≤ Real.sin x- Cited by
- 6 results in Mathlib
- Foundations
- Depth 178 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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- Set.Iccstatement and proof · cited by 1,702
- Real.sinstatement · cited by 389
- continuous_constproof · cited by 278
- closure_monoproof · cited by 133
- Real.pi_ne_zeroproof · cited by 24
- closure_Iooproof · cited by 20
- Real.continuous_sinproof · cited by 16
- closure_lt_subset_leproof · cited by 6
- Real.sin_pos_of_mem_Iooproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Real.cos_nonneg_of_mem_Iccproof · cited by 10
- Real.sin_nonneg_of_nonneg_of_le_piproof · cited by 9
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5
- Complex.arg_nonneg_iffproof · cited by 4
- integral_sin_pow_succ_leproof · cited by 3
- EuclideanGeometry.dist_lt_of_angle_ltproof · cited by 1