Theorems · Theorem · Lie groups
Real.Angle.cos_coe
∀ (x : ℝ), (↑x).cos = Real.cos x
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.cosstatement · cited by 424
- Real.Angle.coestatement · cited by 360
- Real.Angle.cosstatement · cited by 77
Cited by20
Results whose statement or proof uses this declaration.
- Real.Angle.tan_coeproof · cited by 19
- Real.Angle.cos_zeroproof · cited by 2
- Real.Angle.arg_toCircleproof · cited by 2
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- Real.Angle.cos_toRealproof · cited by 1
- Orientation.inner_eq_norm_mul_norm_mul_cos_oangleproof · cited by 1
- Orientation.norm_div_cos_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.norm_div_cos_oangle_sub_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_sub_right_of_oangle_eq_pi_div_twoproof · cited by 1