Theorems · Theorem · commutative algebra
LaurentSeries.Cauchy.eventually_mem_nhds
∀ {K : Type u_2} [inst : Field K] {ℱ : Filter (LaurentSeries K)} (hℱ : Cauchy ℱ) {U : Set (LaurentSeries K)},
U ∈ nhds (LaurentSeries.Cauchy.limit hℱ) → ∀ᶠ (f : LaurentSeries K) in ℱ, f ∈ UThe main result showing that the Cauchy filter tends to the Cauchy.limit
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Ringproof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement and proof · cited by 3,134
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Multiplicativestatement and proof · cited by 875
- Filter.Eventually.monoproof · cited by 646
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