span_singleton_toAddSubgroup_eq_zmultiples

English

For a ∈ Z, the AddSubgroup generated by the span of {a} equals the subgroup of multiples: (Ideal.span {a}).toAddSubgroup = AddSubgroup.zmultiples a.

Русский

Для a ∈ Z порожденный порожденный добавочный подгруппой (Ideal.span {a}).toAddSubgroup равен zmultiples a.

LaTeX

$$$ (\mathrm{Ideal}.span\{a\}) \toAddSubgroup = \mathrm{AddSubgroup}.zmultiples\ a $$$

Lean4

@[simp]
theorem _root_.Ideal.span_singleton_toAddSubgroup_eq_zmultiples (a : ℤ) :
    (Ideal.span { a }).toAddSubgroup = AddSubgroup.zmultiples a :=
  Submodule.span_singleton_toAddSubgroup_eq_zmultiples _

Похожие утверждения