Theorems · Theorem · linear algebra

Submodule.range_lsum_smul

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} {σ : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (φ : M →ₗ[R] N) (f : σ → R),
  ((Finsupp.lsum R) fun x => f x • φ).range = Set.range f • φ.range

Defined in

Mathlib.LinearAlgebra.Finsupp.Span

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule