Theorems · Theorem · commutative algebra
Subsemiring.list_sum_mem
∀ {R : Type u} [inst : NonAssocSemiring R] (s : Subsemiring R) {l : List R}, (∀ x ∈ l, x ∈ s) → l.sum ∈ sSum of a list of elements in a Subsemiring is in the Subsemiring.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiring
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- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- list_sum_memproof · cited by 10
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