Theorems · Theorem · linear algebra

LinearIndepOn.singleton

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {v : ι → M} {i : ι} [IsDomain R] [Module.IsTorsionFree R M], v i ≠ 0 → LinearIndepOn R v {i}

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

6 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleIsDomainModule.IsTorsionFree