Theorems · Theorem · linear algebra

linearIndepOn_insert

∀ {ι : Type u'} {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  {s : Set ι} {a : ι} {f : ι → V},
  a ∉ s → (LinearIndepOn K f (insert a s) ↔ LinearIndepOn K f s ∧ f a ∉ Submodule.span K (f '' s))

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule