Theorems · Theorem · commutative algebra
Subsemiring.multiset_sum_mem
∀ {R : Type u} [inst : NonAssocSemiring R] (s : Subsemiring R) (m : Multiset R), (∀ a ∈ m, a ∈ s) → m.sum ∈ sSum of a multiset of elements in a Subsemiring of a NonAssocSemiring is
in the Subsemiring.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
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Cites5
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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Multiset.sumstatement · cited by 388
- multiset_sum_memproof · cited by 10
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