Orientation.left_ne_zero_of_oangle_sign_ne_zero
∀ {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).sign ≠ 0 → x ≠ 0If the sign of the angle between two vectors is nonzero, the first vector is nonzero.
- Cited by
- 2 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.
Cites11
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
- Orientationstatement and proof · cited by 360
- SignTypestatement · cited by 318
- Orientation.oanglestatement and proof · cited by 205
- Real.Angle.signstatement and proof · cited by 158
- Real.Angle.sign_ne_zero_iffproof · cited by 6
- Orientation.left_ne_zero_of_oangle_ne_zeroproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Orientation.left_ne_zero_of_oangle_sign_eq_neg_oneproof · cited by 0
- Orientation.left_ne_zero_of_oangle_sign_eq_oneproof · cited by 0