Theorems · Theorem · field theory

ArchimedeanClass.FiniteResidueField.ofArchimedean_apply

∀ {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] [inst_5 : IsStrictOrderedRing R] [inst_6 : Archimedean R]
  (f : R →+*o K) (r : R),
  (ArchimedeanClass.FiniteResidueField.ofArchimedean f) r =
    ArchimedeanClass.FiniteResidueField.mk (ArchimedeanClass.FiniteElement.mk (f r) ⋯)

Defined in

Mathlib.Algebra.Order.Ring.StandardPart

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderFieldIsOrderedRingLinearOrderCommRingIsStrictOrderedRingArchimedean