Orientation.oangle_self
∀ {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 x x = 0If the two vectors passed to oangle are the same, the result is 0.
- Cited by
- 17 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.
Cites23
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
- Complexproof · cited by 5,565
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- HasQuotient.Quotientproof · cited by 2,301
- Real.piproof · cited by 1,774
- Module.finrankstatement and proof · cited by 1,770
- Complex.ofRealproof · cited by 1,654
- Real.Anglestatement and proof · cited by 518
- AddSubgroup.zmultiplesproof · cited by 493
Cited by17
Results whose statement or proof uses this declaration.
- Orientation.ne_of_oangle_ne_zeroproof · cited by 6
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_rotation_self_rightproof · cited by 3
- Orientation.oangle_neg_self_rightproof · cited by 2
- Orientation.oangle_smul_right_self_of_nonnegproof · cited by 2
- Orientation.oangle_neg_self_leftproof · cited by 1
- Orientation.two_zsmul_oangle_smul_right_selfproof · cited by 1
- EuclideanGeometry.oangle_self_left_rightproof · cited by 1
- Orientation.angle_eq_iff_oangle_eq_or_sameRayproof · cited by 1
- Orientation.rotation_eq_self_iff_angle_eq_zeroproof · cited by 1
- Orientation.oangle_smul_left_self_of_nonnegproof · cited by 1
- Orientation.oangle_sub_left_smul_rotation_pi_div_twoproof · cited by 0