Theorems · Theorem · linear algebra

Module.Basis.extend_apply_self

∀ {K : Type u_3} {V : Type u_4} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s : Set V}
  (hs : LinearIndepOn K id s) (x : ↑(hs.extend ⋯)), (Module.Basis.extend hs) x = ↑x

Defined in

Mathlib.LinearAlgebra.Basis.VectorSpace

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule