Theorems · Theorem · linear algebra

exists_linearIndepOn_id_extension

∀ {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s t : Set V},
  LinearIndepOn K id s → s ⊆ t → ∃ b ⊆ t, s ⊆ b ∧ t ⊆ ↑(Submodule.span K b) ∧ LinearIndepOn K id b

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

1 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModule