Theorems · Theorem · ring theory
Subalgebra.multiset_sum_mem
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A)
{m : Multiset A}, (∀ x ∈ m, x ∈ S) → m.sum ∈ S- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Multisetstatement and proof · cited by 2,627
- Subalgebrastatement and proof · cited by 1,353
- Multiset.sumstatement · cited by 388
- multiset_sum_memproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegral.multiset_sumproof · cited by 2