Theorems · Definition · order theory

LocallyFiniteOrder.orderAddMonoidEquiv

(G : Type u_2) →
  [inst : AddCommGroup G] →
    [inst_1 : LinearOrder G] → [IsOrderedAddMonoid G] → [LocallyFiniteOrder G] → [Nontrivial G] → G ≃+o ℤ

Any nontrivial linearly ordered abelian group that is locally finite is isomorphic to ℤ.

Defined in

Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidLocallyFiniteOrderNontrivial