Theorems · Definition · field theory

ArchimedeanClass.FiniteResidueField.ofArchimedean

{K : Type u_1} →
  [inst : LinearOrder K] →
    [inst_1 : Field K] →
      [inst_2 : IsOrderedRing K] →
        {R : Type u_2} →
          [inst_3 : LinearOrder R] →
            [inst_4 : CommRing R] →
              [IsStrictOrderedRing R] → [Archimedean R] → R →+*o K → R →+*o ArchimedeanClass.FiniteResidueField K

An embedding from an Archimedean field into K induces an embedding into FiniteResidueField K.

Defined in

Mathlib.Algebra.Order.Ring.StandardPart

Cited by

7 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderFieldIsOrderedRingLinearOrderCommRingIsStrictOrderedRingArchimedean