Theorems · Theorem · general algebraic systems

Finsupp.sum_mapDomain_index_addMonoidHom

∀ {α : Type u_1} {β : Type u_2} {M : Type u_5} {N : Type u_6} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N]
  {f : α → β} {s : α →₀ M} (h : β → M →+ N),
  ((Finsupp.mapDomain f s).sum fun b m => (h b) m) = s.sum fun a m => (h (f a)) m

A version of sum_mapDomain_index that takes a bundled AddMonoidHom, rather than separate linearity hypotheses.

Defined in

Mathlib.Data.Finsupp.Basic

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoid