Theorems · Theorem · real analysis

CauSeq.abv_pos_of_not_limZero

∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
  [inst_3 : Ring β] {abv : β → α} [IsAbsoluteValue abv] {f : CauSeq β abv},
  ¬f.LimZero → ∃ K > 0, ∃ i, ∀ j ≥ i, K ≤ abv (↑f j)

Defined in

Mathlib.Algebra.Order.CauSeq.Basic

Cited by

6 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingRingIsAbsoluteValue