InnerProductGeometry.angle_neg_right
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x y : V),
InnerProductGeometry.angle x (-y) = Real.pi - InnerProductGeometry.angle x yThe angle between a vector and the negation of another vector.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 193 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
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Real.pistatement · cited by 1,774
- Inner.innerproof · cited by 1,089
- norm_negproof · cited by 190
- InnerProductGeometry.anglestatement · cited by 170
- neg_divproof · cited by 161
- Real.arccosproof · cited by 90
- inner_neg_rightproof · cited by 41
- Real.arccos_negproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_normproof · cited by 2
- InnerProductGeometry.angle_smul_right_of_negproof · cited by 2
- InnerProductGeometry.angle_add_angle_sub_add_angle_sub_eq_piproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_twoproof · cited by 1
- InnerProductGeometry.angle_self_neg_of_nonzeroproof · cited by 1
- EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_distproof · cited by 1
- InnerProductGeometry.angle_neg_leftproof · cited by 1