Theorems · Theorem · group theory
Subgroup.list_prod_mem
∀ {G : Type u_1} [inst : Group G] (K : Subgroup G) {l : List G}, (∀ x ∈ l, x ∈ K) → l.prod ∈ KProduct of a list of elements in a subgroup is in the subgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- list_prod_memproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.reflections_generateproof · cited by 0