Theorems · Theorem · geometry

AffineIndependent.vectorSpan_image_eq_iff

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} [Nontrivial k] {p : ι → P},
  AffineIndependent k p →
    ∀ {s₁ s₂ : Set ι}, vectorSpan k (p '' s₁) = vectorSpan k (p '' s₂) ↔ s₁ = s₂ ∨ s₁.Subsingleton ∧ s₂.Subsingleton

Defined in

Mathlib.LinearAlgebra.AffineSpace.Independent

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorNontrivial