Theorems · Theorem · geometry

Collinear.two_zsmul_oangle_eq_right

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₂ p₃ p₃' : P},
  Collinear ℝ {p₃, p₂, p₃'} →
    p₃ ≠ p₂ → p₃' ≠ p₂ → 2 • EuclideanGeometry.oangle p₁ p₂ p₃ = 2 • EuclideanGeometry.oangle p₁ p₂ p₃'

Replacing the third point by one on the same line does not change twice the oriented angle.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

2 results in Mathlib

Foundations

Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented