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Theorems · Theorem · commutative algebra

CauSeq.complete

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {β : Type u_2}
  [inst_3 : Ring β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] [CauSeq.IsComplete β abv] (s : CauSeq β abv),
  ∃ b, s ≈ CauSeq.const abv b
Defined in
Mathlib.Algebra.Order.CauSeq.Completion
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingRingIsAbsoluteValueCauSeq.IsComplete
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CauSeq.lim · cited by 35CauSeq.limCauSeq.equiv_lim · cited by 15CauSeq.equiv_limLinearOrder · cited by 8572LinearOrderRing · cited by 7463RingField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingCauSeq · cited by 189CauSeqIsAbsoluteValue · cited by 160IsAbsoluteValueCauSeq.const · cited by 58CauSeq.constCauSeq.IsComplete · cited by 21CauSeq.IsCompleteCauSeq.IsComplete.isComplete · cited by 1IsComplete.isCompleteCauSeq.completeCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.