Theorems · Theorem · linear algebra

DFinsupp.linearIndependent_single

∀ {ι : Type u_1} {R : Type u_2} {M : ι → Type u_3} [inst : Semiring R] [inst_1 : (i : ι) → AddCommMonoid (M i)]
  [inst_2 : (i : ι) → Module R (M i)] [inst_3 : DecidableEq ι] {φ : ι → Type u_4} (f : (i : ι) → φ i → M i),
  (∀ (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

3 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleDecidableEq