InnerProductGeometry.angle_self_neg_of_nonzero
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x : V},
x ≠ 0 → InnerProductGeometry.angle x (-x) = Real.piThe angle between a nonzero vector and its negation.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Real.pistatement and proof · cited by 1,774
- sub_zeroproof · cited by 938
- InnerProductGeometry.anglestatement · cited by 170
- InnerProductGeometry.angle_neg_rightproof · cited by 7
- InnerProductGeometry.angle_selfproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductGeometry.angle_neg_self_of_nonzeroproof · cited by 0