Theorems · Theorem · ring theory

DirectSum.coeLinearMap_eq_dfinsuppSum

∀ {R : Type u} [inst : Semiring R] {ι : Type v} [dec_ι : DecidableEq ι] {M : Type u_1} [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] (A : ι → Submodule R M) [inst_3 : DecidableEq M] (x : DirectSum ι fun i => ↥(A i)),
  (DirectSum.coeLinearMap A) x = DFinsupp.sum x fun i x => ↑x

Defined in

Mathlib.Algebra.DirectSum.Module

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqAddCommMonoidModuleDecidableEq