Theorems · Theorem · commutative algebra
Subring.list_prod_mem
∀ {R : Type u_1} [inst : Ring R] (s : Subring R) {l : List R}, (∀ x ∈ l, x ∈ s) → l.prod ∈ sProduct of a list of elements in a subring is in the subring.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Subringstatement and proof · cited by 602
- list_prod_memproof · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.