Theorems · Theorem · group theory
finsum_mem_singleton
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] {f : α → M} {a : α}, ∑ᶠ (i : α) (_ : i ∈ {a}), f i = f aThe sum of f i over i ∈ {a} equals f a.
- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- finsumstatement and proof · cited by 286
- Finset.sum_singletonproof · cited by 251
- Finset.coe_singletonproof · cited by 145
- finsum_mem_coe_finsetproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- finsum_cond_eq_leftproof · cited by 2
- finsum_mem_insert'proof · cited by 2
- finsum_mem_pairproof · cited by 0