Theorems · Theorem · group theory
Finset.sum_eq_add_of_mem
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] {s : Finset ι} {f : ι → M} (a b : ι),
a ∈ s → b ∈ s → a ≠ b → (∀ c ∈ s, c ≠ a ∧ c ≠ b → f c = 0) → ∑ x ∈ s, f x = f a + f b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Classical.decEqproof · cited by 134
- Finset.sum_subsetproof · cited by 79
- Finset.sum_pairproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_eq_addproof · cited by 1