Theorems · Definition · order theory

HahnSeries.finiteArchimedeanClassOrderIsoLex

(Γ : Type u_1) →
  (R : Type u_2) →
    [inst : LinearOrder Γ] →
      [inst_1 : LinearOrder R] →
        [inst_2 : AddCommGroup R] →
          [inst_3 : IsOrderedAddMonoid R] →
            FiniteArchimedeanClass (Lex (HahnSeries Γ R)) ≃o Lex (Γ × FiniteArchimedeanClass R)

The correspondence between finite archimedean classes of Lex R⟦Γ⟧ and lexicographical pairs of HahnSeries.orderTop and the finite archimedean class of HahnSeries.leadingCoeff.

Defined in

Mathlib.RingTheory.HahnSeries.Lex

Cited by

2 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLinearOrderAddCommGroupIsOrderedAddMonoid