Orientation.oangle_rotation_self_right
∀ {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 : V}, x ≠ 0 → ∀ (θ : Real.Angle), o.oangle x ((o.rotation θ) x) = θA vector has an angle of θ from the rotation of that vector by θ.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 278 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.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- zero_addproof · cited by 2,366
- Module.finrankstatement and proof · cited by 1,770
- LinearIsometryEquivstatement · cited by 748
- Real.Anglestatement and proof · cited by 518
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement · cited by 205
Cited by3
Results whose statement or proof uses this declaration.
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- 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