Theorems · Theorem · linear algebra

LinearIndepOn.span_extend_eq_span

∀ {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s t : Set V}
  (hs : LinearIndepOn K id s) (hst : s ⊆ t), Submodule.span K (hs.extend hst) = Submodule.span K t

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule