Theorems · Theorem · linear algebra

Finsupp.linearIndependent_single

∀ {R : Type u_1} {M : Type u_2} {ι : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {φ : ι → Type u_4} (f : (i : ι) → φ i → M),
  (∀ (i : ι), LinearIndependent R (f i)) → LinearIndependent R fun ix => fun₀ | ix.fst => f ix.fst ix.snd

Defined in

Mathlib.LinearAlgebra.Finsupp.VectorSpace

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule