Theorems · Theorem · group theory

DirectSum.toAddMonoid_of

∀ {ι : Type v} {β : ι → Type w} [inst : (i : ι) → AddCommMonoid (β i)] [inst_1 : DecidableEq ι] {γ : Type u₁}
  [inst_2 : AddCommMonoid γ] (φ : (i : ι) → β i →+ γ) (i : ι) (x : β i),
  (DirectSum.toAddMonoid φ) ((DirectSum.of β i) x) = (φ i) x

Defined in

Mathlib.Algebra.DirectSum.Basic

Cited by

8 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidDecidableEqAddCommMonoid