Theorems · Theorem · linear algebra

LinearMap.finrank_range_le

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
  {M' : Type u_2} [inst_4 : AddCommMonoid M'] [inst_5 : Module R M'] [Module.Finite R M] (f : M →ₗ[R] M'),
  Module.finrank R ↥f.range ≤ Module.finrank R M

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

2 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankConditionAddCommMonoidModuleModule.Finite