Theorems · Theorem · linear algebra

LinearIndependent.notMem_span

∀ {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] [Nontrivial R], LinearIndependent R v → ∀ (i : ι), v i ∉ Submodule.span R (v '' {i}ᶜ)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleNontrivial