Theorems · Theorem · linear algebra

Submodule.disjoint_span_singleton

∀ {K : Type u_3} {V : Type u_6} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  {s : Submodule K V} {x : V}, Disjoint s (K ∙ x) ↔ x ∈ s → x = 0

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule