Orientation.oangle_neg_orientation_eq_neg
∀ {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 = -o.oangle x yNegating the orientation negates the value of oangle.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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 · cited by 518
- Real.Angle.coeproof · cited by 360
- Orientationstatement and proof · cited by 360
- AlternatingMapstatement · cited by 329
- Complex.argproof · cited by 220
- Orientation.oanglestatement · cited by 205
Cited by26
Results whose statement or proof uses this declaration.
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_add_left_smul_rotation_pi_div_twoproof · cited by 2
- Orientation.oangle_sub_left_eq_arccos_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.oangle_sub_left_eq_arcsin_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.oangle_sub_left_eq_arctan_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.tan_oangle_add_left_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.tan_oangle_add_left_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.tan_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.tan_oangle_sub_left_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.norm_div_cos_oangle_add_left_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.norm_div_cos_oangle_sub_left_of_oangle_eq_pi_div_twoproof · cited by 0
- Orientation.norm_div_sin_oangle_add_left_of_oangle_eq_pi_div_twoproof · cited by 0