Theorems · Theorem · linear algebra

linearIndepOn_biUnion_of_directed

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] {η : Type u_6} {s : Set η} {t : η → Set ι},
  DirectedOn (t ⁻¹'o fun x1 x2 => x1 ⊆ x2) s → (∀ a ∈ s, LinearIndepOn R v (t a)) → LinearIndepOn R v (⋃ a ∈ s, t a)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule