Theorems · Theorem · group theory
Finset.sum_union_eq_right
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
(∀ a ∈ s₁, a ∉ s₂ → f a = 0) → ∑ a ∈ s₁ ∪ s₂, f a = ∑ a ∈ s₂, f a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 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.
Cites5
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 and proof · cited by 5,195
- Finset.union_commproof · cited by 25
- Finset.sum_union_eq_leftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Finset.sum_congr_of_eq_on_interproof · cited by 6
- sum_mul_eq_sub_integral_mul₁proof · cited by 2
- Finpartition.sum_ofPairwiseDisjoint_eq_sumproof · cited by 1