Theorems · Theorem · real analysis
Real.cos_pos_of_mem_Ioo
∀ {x : ℝ}, x ∈ Set.Ioo (-(Real.pi / 2)) (Real.pi / 2) → 0 < Real.cos x- Cited by
- 14 results in Mathlib
- Foundations
- Depth 179 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.
- Setstatement · cited by 53,352
- 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
- Set.Ioostatement and proof · cited by 1,214
- Real.cosstatement · cited by 424
- lt_of_not_geproof · cited by 374
- Real.sin_pos_of_mem_Iooproof · cited by 5
- Real.sin_add_pi_div_twoproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- Real.cos_arctan_posproof · cited by 6
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5
- PhragmenLindelof.quadrant_Iproof · cited by 4
- Real.sin_lt_sin_of_lt_of_le_pi_div_twoproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Real.lt_tanproof · cited by 2
- Real.tan_pos_of_pos_of_lt_pi_div_twoproof · cited by 2
- Real.strictMonoOn_tanproof · cited by 2
- Real.tendsto_cos_pi_div_twoproof · cited by 1
- Real.cos_lt_one_div_sqrt_sq_add_oneproof · cited by 1
- Real.hasDerivAt_tan_of_mem_Iooproof · cited by 1
- Real.cos_neg_of_pi_div_two_lt_of_ltproof · cited by 1