Theorems · Theorem · linear algebra

LinearIndepOn.span_image_extend_eq_span_image

∀ {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} (hs : LinearIndepOn K v s) (hst : s ⊆ t),
  Submodule.span K (v '' hs.extend hst) = Submodule.span K (v '' t)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule