Orientation.oangle_eq_zero_iff_sameRay
∀ {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 = 0 ↔ SameRay ℝ x yThe oriented angle between two vectors is zero if and only if they are on the same ray.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Module.finrankstatement and proof · cited by 1,770
- Complex.ofRealproof · cited by 1,654
Cited by5
Results whose statement or proof uses this declaration.
- Orientation.oangle_eq_pi_iff_sameRay_negproof · cited by 3
- Orientation.eq_iff_norm_eq_and_oangle_eq_zeroproof · cited by 2
- Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependentproof · cited by 1
- Orientation.angle_eq_iff_oangle_eq_or_sameRayproof · cited by 1
- Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smulproof · cited by 0