Theorems · Theorem · ring theory
Subalgebra.list_sum_mem
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A)
{L : List A}, (∀ x ∈ L, x ∈ S) → L.sum ∈ S- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- list_sum_memproof · cited by 10
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