Theorems · Theorem · ring theory
Finset.dvd_sum
∀ {ι : Type u_1} {R : Type u_4} {s : Finset ι} [inst : NonUnitalSemiring R] {f : ι → R} {a : R},
(∀ i ∈ s, a ∣ f i) → a ∣ ∑ i ∈ s, f i- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Finset.sumstatement · cited by 5,195
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- NonUnitalSemiringstatement and proof · cited by 339
- Multiset.mem_mapproof · cited by 72
- Multiset.dvd_sumproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- Int.erdos_ginzburg_zivproof · cited by 2
- WittVector.pow_dvd_ghostComponent_of_dvd_coeffproof · cited by 1
- Polynomial.dvd_term_of_dvd_eval_of_dvd_termsproof · cited by 1
- sub_one_dvd_natCast_of_pow_eq_oneproof · cited by 1
- Nat.exists_mem_span_nat_finset_of_geproof · cited by 1
- Int.sum_divproof · cited by 1
- sq_dvd_add_pow_sub_subproof · cited by 1
- Commute.pow_dvd_add_pow_of_pow_eq_zero_rightproof · cited by 1
- pow_pow_modEq_oneproof · cited by 1
- Nat.sum_divproof · cited by 0
- Matrix.IsHadamard.four_dvd_cardproof · cited by 0