Theorems · Theorem · group theory
Finset.sum_disjSum
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] (s : Finset ι) (t : Finset κ) (f : ι ⊕ κ → M),
∑ x ∈ s.disjSum t, f x = ∑ x ∈ s, f (Sum.inl x) + ∑ x ∈ t, f (Sum.inr x)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 64 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.mapproof · cited by 747
- Finset.sum_mapproof · cited by 115
- Finset.disjSumstatement · cited by 55
- Function.Embedding.inlproof · cited by 32
- Function.Embedding.inrproof · cited by 30
- Finset.sum_disjUnionproof · cited by 8
- Finset.disjoint_map_inl_map_inrproof · cited by 3
- Finset.map_inl_disjUnion_map_inrproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Fintype.sum_sum_typeproof · cited by 22
- convexHull_eqproof · cited by 3
- HasSum.sumproof · cited by 2
- Finset.sum_sumElimproof · cited by 1
- Finset.sum_sum_eq_sum_toLeft_add_sum_toRightproof · cited by 0
- Fintype.sum_sumElimproof · cited by 0
- Finsupp.sum_sumElimproof · cited by 0