Orientation.right_ne_zero_of_oangle_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 ≠ 0 → y ≠ 0If the angle between two vectors is nonzero, the second vector is nonzero.
- Cited by
- 6 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.
Cites9
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
- Real.Anglestatement · cited by 518
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement and proof · cited by 205
- Orientation.oangle_zero_rightproof · cited by 22
Cited by6
Results whose statement or proof uses this declaration.
- Orientation.right_ne_zero_of_oangle_eq_pi_div_twoproof · cited by 7
- EuclideanGeometry.right_ne_of_oangle_ne_zeroproof · cited by 4
- Orientation.right_ne_zero_of_oangle_sign_ne_zeroproof · cited by 2
- Orientation.norm_eq_of_two_zsmul_oangle_sub_eqproof · cited by 1
- Orientation.right_ne_zero_of_oangle_eq_neg_pi_div_twoproof · cited by 0
- Orientation.right_ne_zero_of_oangle_eq_piproof · cited by 0