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Theorems · Theorem · real analysis

CauSeq.exists_lt

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] (f : CauSeq α abs),
  ∃ a, CauSeq.const abs a < f
Defined in
Mathlib.Algebra.Order.CauSeq.Basic
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRing
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Around this declaration

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

Real.cauSeq_converges · cited by 0Real.cauSeq_convergesLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingabs · cited by 1814absadd_comm · cited by 1535add_commsub_neg_eq_add · cited by 264sub_neg_eq_addCauSeq · cited by 189CauSeqCauSeq.const · cited by 58CauSeq.constCauSeq.Pos · cited by 13CauSeq.PosCauSeq.const_neg · cited by 3CauSeq.const_negCauSeq.exists_gt · cited by 2CauSeq.exists_gtCauSeq.exists_ltCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.