Theorems · Theorem · group theory
IsCompl.sum_add_sum
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Fintype ι] {s t : Finset ι},
IsCompl s t → ∀ (f : ι → M), ∑ i ∈ s, f i + ∑ i ∈ t, f i = ∑ i, f i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidFintype
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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topproof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- IsComplstatement and proof · cited by 351
- IsCompl.disjointproof · cited by 42
- IsCompl.sup_eq_topproof · cited by 20
- Finset.disjUnion_eq_unionproof · cited by 12
- Finset.sum_disjUnionproof · cited by 8
- Finset.sup_eq_unionproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Finset.sum_add_sum_complproof · cited by 9
- Finset.sum_compl_add_sumproof · cited by 4