Theorems · Theorem · ring theory

DirectSum.coeLinearMap_of

∀ {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) (i : ι) (x : ↥(A i)),
  (DirectSum.coeLinearMap A) ((DirectSum.of (fun i => ↥(A i)) i) x) = ↑x

Defined in

Mathlib.Algebra.DirectSum.Module

Cited by

3 results in Mathlib

Foundations

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

Assumes

SemiringDecidableEqAddCommMonoidModule