Theorems · Theorem · linear algebra

Submodule.finrank_lt

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [FiniteDimensional K V] {s : Submodule K V}, s ≠ ⊤ → Module.finrank K ↥s < Module.finrank K V

The dimension of a strict submodule is strictly bounded by the dimension of the ambient space. See also Submodule.length_lt.

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Lemmas

Cited by

3 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFiniteDimensional