Theorems · Theorem · group theory
AddSubgroup.zsmul_mem
∀ {G : Type u_1} [inst : AddGroup G] (K : AddSubgroup G) {x : G}, x ∈ K → ∀ (n : ℤ), n • x ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- zsmul_memproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.span_int_eq_addSubgroupClosureproof · cited by 5
- AddSubgroup.cyclic_of_minproof · cited by 2
- AddSubgroup.int_mul_memproof · cited by 0