Theorems · Theorem · linear algebra

Finsupp.submodule_eq_iSup

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {α : Type u_5}
  (p : α → Submodule R M), Finsupp.submodule p = ⨆ i, Submodule.map (Finsupp.lsingle i) (p i)

Defined in

Mathlib.LinearAlgebra.Finsupp.Pi

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule