Theorems · Theorem · geometry

InnerProductGeometry.angle_neg_left

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x y : V),
  InnerProductGeometry.angle (-x) y = Real.pi - InnerProductGeometry.angle x y

The angle between the negation of a vector and another vector.

Defined in: Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace

Mathlib docs Source Loogle LeanSearch

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
neg_negproof · cited by 960
InnerProductGeometry.anglestatement and proof · cited by 170
InnerProductGeometry.angle_neg_rightproof · cited by 7
InnerProductGeometry.angle_neg_negproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_piproof · cited by 1