Orientation.oangle_eq_angle_of_sign_eq_one
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
(o : Orientation ℝ V (Fin 2)) {x y : V}, (o.oangle x y).sign = 1 → o.oangle x y = ↑(InnerProductGeometry.angle x y)The oriented angle between two vectors equals the unoriented angle if the sign is positive.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- Real.Anglestatement and proof · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Orientationstatement and proof · cited by 360
- not_leproof · cited by 328
- SignTypestatement and proof · cited by 318
- Orientation.oanglestatement and proof · cited by 205
- InnerProductGeometry.anglestatement and proof · cited by 170
Cited by25
Results whose statement or proof uses this declaration.
- EuclideanGeometry.oangle_eq_angle_of_sign_eq_oneproof · cited by 24
- Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_twoproof · cited by 2
- Orientation.oangle_sub_right_eq_arccos_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.oangle_sub_right_eq_arcsin_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.oangle_sub_right_eq_arctan_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_sub_right_of_oangle_eq_pi_div_twoproof · 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.norm_div_sin_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1