Theorems · Theorem · group theory

DirectSum.decompose_symm_sum

∀ {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] {ι' : Type u_5} (s : Finset ι')
  (f : ι' → DirectSum ι fun i => ↥(ℳ i)),
  (DirectSum.decompose ℳ).symm (∑ i ∈ s, f i) = ∑ i ∈ s, (DirectSum.decompose ℳ).symm (f i)

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

1 results in Mathlib

Foundations

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

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.Decomposition