Theorems · Theorem · linear algebra

linearIndepOn_union_iff

∀ {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},
  Disjoint s t →
    (LinearIndepOn R v (s ∪ t) ↔
      LinearIndepOn R v s ∧ LinearIndepOn R v t ∧ Disjoint (Submodule.span R (v '' s)) (Submodule.span R (v '' t)))

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Basic

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule