Theorems · Theorem · linear algebra

exists_of_linearIndepOn_of_finite_span

∀ {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s : Set V}
  {t : Finset V}, LinearIndepOn K id s → s ⊆ ↑(Submodule.span K ↑t) → ∃ t', ↑t' ⊆ s ∪ ↑t ∧ s ⊆ ↑t' ∧ t'.card = t.card

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule