Theorems · Theorem · geometry

finrank_vectorSpan_image_finset_le

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} {ι : Type u_4} [inst : DivisionRing k] [inst_1 : AddCommGroup V]
  [inst_2 : Module k V] [inst_3 : AddTorsor V P] [inst_4 : DecidableEq P] (p : ι → P) (s : Finset ι) {n : ℕ},
  s.card = n + 1 → Module.finrank k ↥(vectorSpan k ↑(Finset.image p s)) ≤ n

The vectorSpan of n + 1 points in an indexed family has dimension at most n.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

1 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorDecidableEq