Orientation.oangle_zero_left
∀ {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), o.oangle 0 x = 0If the first vector passed to oangle is 0, the result is 0.
- Cited by
- 25 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.
Cites14
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
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- map_zeroproof · cited by 1,614
- Real.Anglestatement · cited by 518
- Real.Angle.coeproof · cited by 360
- Orientationstatement and proof · cited by 360
- Complex.argproof · cited by 220
- Orientation.oanglestatement · cited by 205
Cited by25
Results whose statement or proof uses this declaration.
- Orientation.oangle_eq_angle_of_sign_eq_oneproof · cited by 25
- Orientation.oangle_sign_smul_add_rightproof · cited by 6
- Orientation.left_ne_zero_of_oangle_ne_zeroproof · cited by 6
- EuclideanGeometry.oangle_self_leftproof · cited by 5
- Orientation.oangle_eq_of_angle_eq_of_sign_eqproof · cited by 3
- Orientation.oangle_eq_pi_iff_sameRay_negproof · cited by 3
- Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zeroproof · cited by 3
- Orientation.oangle_eq_pi_iff_angle_eq_piproof · cited by 2
- Orientation.two_zsmul_oangle_neg_leftproof · cited by 2
- Orientation.two_zsmul_oangle_neg_rightproof · cited by 2
- Orientation.oangle_rotation_oangle_leftproof · cited by 2
- Orientation.oangle_sign_neg_leftproof · cited by 2