Orientation.oangle_smul_right_of_pos
∀ {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}, 0 < r → o.oangle x (r • y) = o.oangle x yMultiplying the second vector passed to oangle by a positive real does not change the
angle.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 252 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
- Complexproof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- map_smulproof · cited by 566
- Real.Anglestatement · cited by 518
- Real.Angle.coeproof · cited by 360
- Orientationstatement and proof · cited by 360
- Complex.argproof · cited by 220
Cited by10
Results whose statement or proof uses this declaration.
- Orientation.oangle_smul_right_of_negproof · cited by 7
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_smul_right_self_of_nonnegproof · cited by 2
- Orientation.oangle_sign_smul_rightproof · cited by 2
- Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zeroproof · cited by 2
- Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zeroproof · cited by 2
- Orientation.two_zsmul_oangle_smul_right_of_ne_zeroproof · cited by 1
- Orientation.angle_eq_iff_oangle_eq_or_sameRayproof · cited by 1
- EuclideanGeometry.oangle_homothetyproof · cited by 0
- EuclideanGeometry.oangle_eq_of_parallelproof · cited by 0