Theorems · Theorem · linear algebra

LinearIndepOn.eq_zero_of_smul_mem_span

∀ {ι : Type u'} {R : Type u_2} {s : Set ι} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] {i : ι},
  LinearIndepOn R v s → i ∈ s → ∀ (a : R), a • v i ∈ Submodule.span R (v '' (s \ {i})) → a = 0

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule