Theorems · Definition · order theory

FiniteMulArchimedeanClass.subgroup

{M : Type u_1} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] → [inst_2 : IsOrderedMonoid M] → UpperSet (FiniteMulArchimedeanClass M) → Subgroup M

The MulArchimedeanClass.subsemigroup associated to an upper set in FiniteMulArchimedeanClass M is a subgroup.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

4 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoid