Theorems · Theorem · ring theory
Multiset.dvd_sum
∀ {R : Type u_4} [inst : NonUnitalSemiring R] {s : Multiset R} {a : R}, (∀ x ∈ s, a ∣ x) → a ∣ s.sum- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- Multiset.sumstatement and proof · cited by 388
- NonUnitalSemiringstatement and proof · cited by 339
- Multiset.consproof · cited by 313
- Multiset.induction_onproof · cited by 109
- dvd_zeroproof · cited by 63
- Multiset.sum_consproof · cited by 45
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_consproof · cited by 29
- dvd_addproof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- Finset.dvd_sumproof · cited by 11
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Equiv.Perm.two_dvd_card_supportproof · cited by 1