Theorems · Theorem · geometry

EuclideanGeometry.right_ne_of_oangle_sign_ne_zero

∀ {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 : P}, (EuclideanGeometry.oangle p₁ p₂ p₃).sign ≠ 0 → p₃ ≠ p₂

If the sign of the angle between three points is nonzero, the last two points are not equal.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

2 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented