Theorems · Theorem · geometry

EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne

∀ {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] {s : Set P},
  EuclideanGeometry.Cospherical s →
    ∀ {p₁ p₂ p₃ : P}, p₁ ∈ s → p₂ ∈ s → p₃ ∈ s → p₁ ≠ p₂ → p₁ ≠ p₃ → p₂ ≠ p₃ → AffineIndependent ℝ ![p₁, p₂, p₃]

Any three points in a cospherical set are affinely independent.

Defined in

Mathlib.Geometry.Euclidean.Sphere.Basic

Cited by

1 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor