Theorems · Definition · Lie groups
Real.Angle.sign
Real.Angle → SignType
The sign of a Real.Angle is 0 if the angle is 0 or π, 1 if the angle is strictly
between 0 and π and -1 is the angle is strictly between -π and 0. It is defined as the
sign of the sine of the angle.
- Cited by
- 158 results in Mathlib
- Foundations
- Depth 177 from the axioms, rests on 4,758 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Real.Anglestatement and proof · cited by 518
- SignTypestatement · cited by 318
- SignType.signproof · cited by 128
- Real.Angle.sinproof · cited by 75
Cited by158
Results whose statement or proof uses this declaration.
- Real.Angle.sign_coe_pi_div_twostatement · cited by 48
- EuclideanGeometry.oangle_rotate_signstatement and proof · cited by 27
- Orientation.oangle_eq_angle_of_sign_eq_onestatement and proof · cited by 25
- EuclideanGeometry.oangle_eq_angle_of_sign_eq_onestatement and proof · cited by 24
- Real.Angle.sign_negstatement · cited by 15
- Orientation.oangle_sign_sub_right_swapstatement and proof · cited by 13
- Orientation.oangle_sign_add_rightstatement and proof · cited by 12
- Real.Angle.sign_zerostatement · cited by 9
- Real.Angle.sign_add_pistatement · cited by 7
- Real.Angle.sign_eq_zero_iffstatement · cited by 7
- Real.Angle.sign_ne_zero_iffstatement and proof · cited by 6
- Orientation.oangle_sign_smul_add_rightstatement and proof · cited by 6