Theorems · Theorem · geometry

EuclideanGeometry.oangle_eq_zero_iff_angle_eq_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)]
  {p p₁ p₂ : P}, p₁ ≠ p → p₂ ≠ p → (EuclideanGeometry.oangle p₁ p p₂ = 0 ↔ EuclideanGeometry.angle p₁ p p₂ = 0)

The unoriented angle at p between two points not equal to p is zero if and only if the unoriented angle is zero.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented