Orientation.oangle_rev
∀ {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 y x = -o.oangle x ySwapping the two vectors passed to oangle negates the angle.
- Cited by
- 42 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.
Cites14
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
- Complex.argproof · cited by 220
- Orientation.oanglestatement · cited by 205
- Orientation.kahlerproof · cited by 39
Cited by42
Results whose statement or proof uses this declaration.
- Orientation.oangle_sign_sub_right_swapproof · cited by 13
- EuclideanGeometry.oangle_revproof · cited by 8
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_sign_add_smul_leftproof · cited by 3
- Orientation.angle_eq_iff_oangle_eq_neg_of_sign_eq_negproof · cited by 2
- Orientation.oangle_add_left_smul_rotation_pi_div_twoproof · cited by 2
- Orientation.oangle_add_oangle_revproof · cited by 2
- Orientation.oangle_eq_pi_iff_oangle_rev_eq_piproof · cited by 2
- Orientation.oangle_sign_sub_left_swapproof · cited by 2
- Orientation.norm_eq_of_two_zsmul_oangle_sub_eqproof · cited by 1
- Orientation.oangle_eq_neg_of_angle_eq_of_sign_eq_negproof · cited by 1
- Orientation.oangle_eq_zero_iff_oangle_rev_eq_zeroproof · cited by 1