Theorems · Theorem · linear algebra

Finsupp.linearIndependent_single_iff

∀ {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},
  (LinearIndependent R fun ix => fun₀ | ix.fst => f ix.fst ix.snd) ↔ ∀ (i : ι), LinearIndependent R (f i)

Defined in

Mathlib.LinearAlgebra.Finsupp.VectorSpace

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule