InnerProductGeometry.angle_self
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x : V},
x ≠ 0 → InnerProductGeometry.angle x x = 0The angle between a nonzero vector and itself.
- Cited by
- 5 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
- InnerProductSpacestatement and proof · cited by 3,523
- Inner.innerproof · cited by 1,089
- div_selfproof · cited by 237
- InnerProductGeometry.anglestatement · cited by 170
- Real.arccosproof · cited by 90
- real_inner_self_eq_norm_mul_normproof · cited by 17
- inner_self_ne_zeroproof · cited by 7
- Real.arccos_oneproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_self_of_neproof · cited by 6
- InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_normproof · cited by 2
- InnerProductGeometry.angle_eq_angle_add_add_angle_addproof · cited by 2
- InnerProductGeometry.angle_self_neg_of_nonzeroproof · cited by 1
- InnerProductGeometry.angle_eq_angle_add_add_angle_add_of_mem_spanproof · cited by 1