Theorems · Theorem · real analysis
CauSeq.inv_aux
∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
[inst_3 : DivisionRing β] {abv : β → α} [IsAbsoluteValue abv] {f : CauSeq β abv},
¬f.LimZero → ∀ ε > 0, ∃ i, ∀ j ≥ i, abv ((↑f j)⁻¹ - (↑f i)⁻¹) < ε- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_rflproof · cited by 1,558
- DivisionRingstatement and proof · cited by 1,062
- CauSeqstatement and proof · cited by 189
- IsAbsoluteValuestatement and proof · cited by 160
- IsCauSeqstatement · cited by 91
- CauSeq.LimZerostatement and proof · cited by 46
- exists_forall_ge_andproof · cited by 15
- CauSeq.abv_pos_of_not_limZeroproof · cited by 6
- CauSeq.cauchy₃proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- CauSeq.invproof · cited by 8