Theorems · Theorem · linear algebra

Submodule.rank_sup_add_rank_inf_eq

∀ {R : Type u_1} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [HasRankNullity.{u, u_1} R] (s t : Submodule R M),
  Module.rank R ↥(s ⊔ t) + Module.rank R ↥(s ⊓ t) = Module.rank R ↥s + Module.rank R ↥t

Defined in

Mathlib.LinearAlgebra.Dimension.RankNullity

Cited by

2 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleHasRankNullity