Theorems · Theorem · general algebraic systems

Finsupp.sum_option_index

∀ {α : Type u_1} {M : Type u_2} {N : Type u_3} [inst : AddZeroClass M] [inst_1 : AddCommMonoid N] (f : Option α →₀ M)
  (b : Option α → M → N),
  (∀ (o : Option α), b o 0 = 0) →
    (∀ (o : Option α) (m₁ m₂ : M), b o (m₁ + m₂) = b o m₁ + b o m₂) →
      f.sum b = b none (f none) + f.some.sum fun a => b (some a)

Defined in

Mathlib.Data.Finsupp.Option

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddZeroClassAddCommMonoid