Theorems · Theorem · linear algebra

exists_linearIndepOn_extension

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

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

5 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModule