Orientation.inner_eq_zero_of_oangle_eq_pi_div_two
∀ {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 = ↑(Real.pi / 2) → inner ℝ x y = 0If the oriented angle between two vectors is π / 2, the inner product of those vectors
is zero.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Real.pistatement and proof · cited by 1,774
- Module.finrankstatement and proof · cited by 1,770
- Inner.innerstatement · cited by 1,089
- Real.Anglestatement · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement and proof · cited by 205
- Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zeroproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_twoproof · cited by 13
- Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_twoproof · cited by 12
- Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_twoproof · cited by 2
- Orientation.norm_div_sin_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.norm_div_tan_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.cos_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.oangle_add_right_eq_arcsin_of_oangle_eq_pi_div_twoproof · cited by 1
- Orientation.sin_oangle_add_right_mul_norm_of_oangle_eq_pi_div_twoproof · cited by 1