Theorems · Theorem · geometry

Orientation.oangle_smul_left_of_neg

∀ {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}, r < 0 → o.oangle (r • x) y = o.oangle (-x) y

Multiplying the first vector passed to oangle by a negative real produces the same angle as negating that vector.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

5 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact