Orientation.oangle_smul_right_of_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) {r : ℝ}, r < 0 → o.oangle x (r • y) = o.oangle x (-y)Multiplying the second vector passed to oangle by a negative real produces the same angle
as negating that vector.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- neg_negproof · cited by 960
- Real.Anglestatement and proof · cited by 518
- Orientationstatement and proof · cited by 360
- neg_smulproof · cited by 306
- Orientation.oanglestatement and proof · cited by 205
- smul_negproof · cited by 181
- neg_pos_of_negproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_sign_smul_rightproof · cited by 2
- Orientation.angle_eq_iff_oangle_eq_or_sameRayproof · cited by 1
- Orientation.two_zsmul_oangle_smul_right_of_ne_zeroproof · cited by 1
- Orientation.two_zsmul_oangle_smul_right_selfproof · cited by 1
- EuclideanGeometry.oangle_homothetyproof · cited by 0
- EuclideanGeometry.oangle_eq_of_parallelproof · cited by 0