Theorems · Theorem · approximation theory
LinearGrowth.tendsto_atTop_of_linearGrowthInf_natCast_pos
∀ {v : ℕ → ℕ}, (LinearGrowth.linearGrowthInf fun n => ↑(v n)) ≠ 0 → Filter.Tendsto v Filter.atTop Filter.atTop- Cited by
- 3 results in Mathlib
- Foundations
- Depth 140 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.
- Top.topproof · cited by 9,680
- nhdsproof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- le_of_ltproof · cited by 1,175
- ERealstatement · cited by 793
- Filter.Eventually.monoproof · cited by 646
- LinearGrowth.linearGrowthInfstatement and proof · cited by 41
- Filter.tendsto_atTopproof · cited by 24
- LinearGrowth.linearGrowthInf_natCast_nonnegproof · cited by 7
- Ne.lt_of_le'proof · cited by 6
- EReal.tendsto_nhds_top_iff_realproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Monotone.linearGrowthInf_compproof · cited by 2
- Monotone.linearGrowthSup_compproof · cited by 2
- Monotone.le_linearGrowthSup_compproof · cited by 2