Theorems · Definition · order theory

FiniteMulArchimedeanClass.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 : { a // a ≠ 1 } → α) →
              (∀ (a b : { a // a ≠ 1 }),
                  FiniteMulArchimedeanClass.mk ↑a ⋯ ≤ FiniteMulArchimedeanClass.mk ↑b ⋯ → f a ≤ f b) →
                FiniteMulArchimedeanClass M →o α

Lift a function {a : M // a ≠ 1} → α that's monotone along archimedean classes to a monotone function FiniteMulArchimedeanClass M →o α.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

1 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoidPartialOrder