Theorems · Theorem · group theory

DirectSum.decompose_of_mem

∀ {ι : Type u_1} {M : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddCommMonoid M] [inst_2 : SetLike σ M]
  [inst_3 : AddSubmonoidClass σ M] (ℳ : ι → σ) [inst_4 : DirectSum.Decomposition ℳ] {x : M} {i : ι} (hx : x ∈ ℳ i),
  (DirectSum.decompose ℳ) x = (DirectSum.of (fun i => ↥(ℳ i)) i) ⟨x, hx⟩

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

7 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.Decomposition