Theorems · Inductive type · commutative algebra

CauSeq.IsComplete

{α : Type u_1} →
  [inst : Field α] →
    [inst_1 : LinearOrder α] →
      [IsStrictOrderedRing α] → (β : Type u_2) → [inst_3 : Ring β] → (abv : β → α) → [IsAbsoluteValue abv] → Prop

A class stating that a ring with an absolute value is complete, i.e. every Cauchy sequence has a limit.

Defined in

Mathlib.Algebra.Order.CauSeq.Completion

Cited by

21 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingRingIsAbsoluteValue