Theorems · Theorem · linear algebra

LinearIndepOn.union

∀ {ι : Type u'} {R : Type u_2} {s : Set ι} {M : Type u_4} {v : ι → M} [inst : Ring R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] {t : Set ι},
  LinearIndepOn R v s →
    LinearIndepOn R v t → Disjoint (Submodule.span R (v '' s)) (Submodule.span R (v '' t)) → LinearIndepOn R v (s ∪ t)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Basic

Cited by

5 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule