Theorems · Theorem · commutative algebra
LaurentSeries.Cauchy.exists_lb_support
∀ {K : Type u_2} [inst : Field K] {ℱ : Filter (LaurentSeries K)} (hℱ : Cauchy ℱ),
∃ N, ∀ n < N, LaurentSeries.Cauchy.coeff hℱ n = 0The support of Cauchy.coeff has a lower bound.
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Bot.botproof · cited by 4,720
- Filter.Eventuallyproof · cited by 3,134
- UniformSpaceproof · cited by 2,040
- Multiplicativestatement · cited by 875
- WithZerostatement · cited by 586
- Filter.mem_of_supersetproof · cited by 308
- HahnSeries.coeffproof · cited by 235
- Cauchystatement and proof · cited by 115
- LaurentSeriesstatement and proof · cited by 64
Cited by2
Results whose statement or proof uses this declaration.
- LaurentSeries.Cauchy.exists_lb_coeff_neproof · cited by 1
- LaurentSeries.Cauchy.coeff_support_bddBelowproof · cited by 0