Theorems · Theorem · real analysis
CauSeq.const_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} [inst_4 : IsAbsoluteValue abv] {x : β}, (CauSeq.const abv x).LimZero ↔ x = 0- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 50 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
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_rflproof · cited by 1,558
- le_of_ltproof · cited by 1,175
- IsAbsoluteValuestatement and proof · cited by 160
- CauSeq.conststatement and proof · cited by 58
- CauSeq.LimZerostatement and proof · cited by 46
- IsAbsoluteValue.abv_nonnegproof · cited by 9
- eq_of_le_of_forall_lt_imp_le_of_denseproof · cited by 4
- IsAbsoluteValue.abv_eq_zeroproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- CauSeq.const_equivproof · cited by 3
- Padic.const_equivproof · cited by 2
- CauSeq.Completion.ofRat_invproof · cited by 1
- CauSeq.lim_eq_zero_iffproof · cited by 1
- PadicSeq.not_limZero_const_of_nonzeroproof · cited by 1
- CauSeq.Completion.cau_seq_zero_ne_oneproof · cited by 1