Theorems · Theorem · geometry

EuclideanGeometry.oangle_sub_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)]
  {p p₁ p₂ p₃ : P},
  p₁ ≠ p →
    p₂ ≠ p →
      p₃ ≠ p → EuclideanGeometry.oangle p₁ p p₃ - EuclideanGeometry.oangle p₂ p p₃ = EuclideanGeometry.oangle p₁ p p₂

Given three points not equal to p, the angle between the first and the third at p minus the angle between the second and the third equals the angle between the first and the second.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

0 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented