Theorems · Theorem · geometry

Orientation.oangle_sign_smul_sub_right

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) (x y : V) (r : ℝ), (o.oangle x (r • x - y)).sign = -(o.oangle x y).sign

Subtracting the second vector passed to oangle from a multiple of the first vector negates the sign of the angle.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

1 results in Mathlib

Foundations

Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact