EuclideanGeometry.Cospherical.affineIndependent_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] {p₁ p₂ p₃ : P},
EuclideanGeometry.Cospherical {p₁, p₂, p₃} → p₁ ≠ p₂ → p₁ ≠ p₃ → p₂ ≠ p₃ → AffineIndependent ℝ ![p₁, p₂, p₃]The three points of a cospherical set are affinely independent.
- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Matrix.vecConsstatement · cited by 852
- Matrix.vecEmptystatement · cited by 832
- Set.mem_singletonproof · cited by 183
- AffineIndependentstatement · cited by 144
- Set.mem_insertproof · cited by 109
- Set.mem_insert_of_memproof · cited by 50
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