Theorems · Theorem · group theory
Finset.sum_union_inter
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
∑ x ∈ s₁ ∪ s₂, f x + ∑ x ∈ s₁ ∩ s₂, f x = ∑ x ∈ s₁, f x + ∑ x ∈ s₂, f x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.fold_union_interproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Finset.sum_unionproof · cited by 40
- HasSum.nat_add_negproof · cited by 10
- finsum_mem_union_interproof · cited by 1
- Nat.sum_primeFactors_gcd_add_sum_primeFactors_mulproof · cited by 0