Theorems · Theorem · group theory
finsum_mem_zero
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] (s : Set α), ∑ᶠ (i : α) (_ : i ∈ s), 0 = 0The sum of the constant function 0 over any set equals 0.
- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites4
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
- finsum_zeroproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- finsum_mem_of_eqOn_zeroproof · cited by 1