Theorems · Theorem · linear algebra

Module.Basis.range_extendLe

∀ {K : Type u_3} {V : Type u_4} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s t : Set V}
  (hs : LinearIndepOn K id s) (hst : s ⊆ t) (ht : ⊤ ≤ Submodule.span K t),
  Set.range ⇑(Module.Basis.extendLe hs hst ht) = hs.extend hst

Defined in

Mathlib.LinearAlgebra.Basis.VectorSpace

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule