Theorems · Theorem · linear algebra

LinearMap.lift_rank_quot_map_le

∀ {R : Type u_1} {M : Type u} {M' : Type v} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup M']
  [inst_3 : Module R M] [inst_4 : Module R M'] [HasRankNullity.{v, u_1} R] {f : M →ₗ[R] M'} (p : Submodule R M),
  Cardinal.lift.{u, v} (Module.rank R (M' ⧸ Submodule.map f p)) ≤
    Cardinal.lift.{u, v} (Module.rank R (M' ⧸ f.range)) + Cardinal.lift.{v, u} (Module.rank R (M ⧸ p))

Defined in

Mathlib.LinearAlgebra.Dimension.RankNullity

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleHasRankNullity