Theorems · Theorem · Lie groups
Real.Angle.sign_eq_zero_iff
∀ {θ : Real.Angle}, θ.sign = 0 ↔ θ = 0 ∨ θ = ↑Real.pi- Cited by
- 7 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Real.pistatement and proof · cited by 1,774
- Real.Anglestatement and proof · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- SignTypestatement and proof · cited by 318
- Real.Angle.signstatement · cited by 158
- sign_eq_zero_iffproof · cited by 3
- Real.Angle.sin_eq_zero_iffproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Real.Angle.sign_ne_zero_iffproof · cited by 6
- Orientation.oangle_sign_smul_add_rightproof · cited by 6
- Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zeroproof · cited by 3
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- Orientation.norm_eq_of_two_zsmul_oangle_sub_eqproof · cited by 1
- Real.Angle.neg_coe_abs_toReal_of_sign_nonposproof · cited by 0
- EuclideanGeometry.oangle_sign_eq_zero_iff_collinearproof · cited by 0