Theorems · Definition · order theory

MulArchimedeanClass.liftOrderHom

{M : Type u_1} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] →
      [inst_2 : IsOrderedMonoid M] →
        {α : Type u_2} →
          [inst_3 : PartialOrder α] →
            (f : M → α) →
              (∀ (a b : M), MulArchimedeanClass.mk a ≤ MulArchimedeanClass.mk b → f a ≤ f b) →
                MulArchimedeanClass M →o α

Lift a function M → α that's monotone along archimedean classes to a monotone function MulArchimedeanClass M →o α.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoidPartialOrder