Theorems · Theorem · ring theory
NonUnitalSubring.multiset_sum_mem
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] (s : NonUnitalSubring R) (m : Multiset R),
(∀ a ∈ m, a ∈ s) → m.sum ∈ sSum of a multiset of elements in a NonUnitalSubring of a NonUnitalRing is
in the NonUnitalSubring.
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- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocRing
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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
- Multiset.sumstatement · cited by 388
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement and proof · cited by 185
- multiset_sum_memproof · cited by 10
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