InnerProductGeometry.angle_zero_right
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x : V),
InnerProductGeometry.angle x 0 = Real.pi / 2The angle between a vector and the zero vector.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 1,774
- zero_divproof · cited by 222
- InnerProductGeometry.anglestatement · cited by 170
- Real.arccosproof · cited by 90
- inner_zero_rightproof · cited by 40
- Real.arccos_zeroproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Orientation.oangle_eq_of_angle_eq_of_sign_eqproof · cited by 3
- Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zeroproof · cited by 3
- InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_normproof · cited by 2
- Orientation.oangle_eq_pi_iff_angle_eq_piproof · cited by 2
- Complex.angle_div_left_eq_angle_mul_rightproof · cited by 2
- Orientation.angle_eq_iff_oangle_eq_or_sameRayproof · cited by 1
- Complex.angle_mul_leftproof · cited by 1
- InnerProductGeometry.angle_le_angle_add_angleproof · cited by 1
- InnerProductGeometry.angle_eq_angle_add_angle_iffproof · cited by 0