Orientation.oangle_sign_sub_left_swap
∀ {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) x).sign = (o.oangle x y).signSubtracting the second vector passed to oangle from the first vector then swapping the
vectors does not change the sign of the angle.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Angleproof · cited by 518
- Orientationstatement and proof · cited by 360
- SignTypestatement and proof · cited by 318
- Orientation.oanglestatement and proof · cited by 205
- Real.Angle.signstatement and proof · cited by 158
- Orientation.oangle_revproof · cited by 42
- Real.Angle.sign_negproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Orientation.norm_eq_of_two_zsmul_oangle_sub_eqproof · cited by 1
- Orientation.abs_oangle_sub_left_toReal_lt_pi_div_twoproof · cited by 1