Theorems · Theorem · linear algebra

Submodule.finrank_sup_span_singleton

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [Module.Finite K V]
  {p : Submodule K V} {v : V}, v ∉ p → Module.finrank K ↥(p ⊔ K ∙ v) = Module.finrank K ↥p + 1

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Lemmas

Cited by

2 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleModule.Finite