Theorems · Theorem · group theory

DirectSum.sum_support_decompose

∀ {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]
  [inst_5 : (i : ι) → (x : ↥(ℳ i)) → Decidable (x ≠ 0)] (r : M),
  ∑ i ∈ DFinsupp.support ((DirectSum.decompose ℳ) r), ↑(((DirectSum.decompose ℳ) r) i) = r

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

9 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.DecompositionDecidable