Theorems · Theorem · commutative algebra
CauSeq.le_lim
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
[inst_3 : CauSeq.IsComplete α abs] {f : CauSeq α abs} {x : α}, CauSeq.const abs x ≤ f → x ≤ f.lim- Defined in
- Mathlib.Algebra.Order.CauSeq.Completion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- absstatement and proof · cited by 1,814
- CauSeqstatement and proof · cited by 189
- CauSeq.conststatement and proof · cited by 58
- CauSeq.limstatement · cited by 35
- CauSeq.IsCompletestatement and proof · cited by 21
- CauSeq.equiv_limproof · cited by 15
- CauSeq.const_leproof · cited by 2
- CauSeq.le_of_le_of_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.sum_le_exp_of_nonnegproof · cited by 5