Theorems · Theorem · linear algebra

rank_range_of_surjective

∀ {R : Type u} {M : Type v} {M' : Type v'} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid M'] [inst_4 : Module R M'] (f : M →ₗ[R] M'),
  Function.Surjective ⇑f → Module.rank R ↥f.range = Module.rank R M'

Defined in

Mathlib.LinearAlgebra.Dimension.Basic

Cited by

4 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModule