Theorems · Theorem · geometry

Collinear.affineSpan_eq_of_ne

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {s : Set P},
  Collinear k s → ∀ {p₁ p₂ : P}, p₁ ∈ s → p₂ ∈ s → p₁ ≠ p₂ → line[k, p₁, p₂] = affineSpan k s

The affine span of any two distinct points of a collinear set of points equals the affine span of the whole set.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

1 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsor