Theorems · Theorem · group theory
Finset.sum_finset_coe
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] (f : ι → M) (s : Finset ι), ∑ i, f ↑i = ∑ i ∈ s, f i- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- Finset.sum_coe_sortproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- summable_sum_mul_antidiagonal_of_summable_mulproof · cited by 3
- Summable.tsum_mul_tsum_eq_tsum_sum_antidiagonalproof · cited by 3
- RootPairing.Base.pos_or_neg_of_sum_smul_root_memproof · cited by 2
- Module.exists_nontrivial_relation_of_finrank_lt_cardproof · cited by 1