Theorems · Theorem · order theory
tendsto_natCast_atTop_iff
∀ {α : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R]
{f : α → ℕ} {l : Filter α}, Filter.Tendsto (fun n => ↑(f n)) l Filter.atTop ↔ Filter.Tendsto f l Filter.atTop- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Filterstatement and proof · cited by 8,121
- PartialOrderstatement and proof · cited by 6,410
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement · cited by 2,405
- Archimedeanstatement and proof · cited by 603
- Nat.cast_leproof · cited by 159
- exists_nat_geproof · cited by 20
- Filter.tendsto_atTop_embeddingproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- tendsto_div_of_monotone_of_exists_subseq_tendsto_divproof · cited by 1