Theorems · Theorem · approximation theory
LinearGrowth.linearGrowthInf_le_iff
∀ {u : ℕ → EReal} {a : EReal}, LinearGrowth.linearGrowthInf u ≤ a ↔ ∀ b > a, ∃ᶠ (n : ℕ) in Filter.atTop, u n ≤ b * ↑n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 138 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.
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
- ERealstatement and proof · cited by 793
- Filter.Frequentlystatement and proof · cited by 414
- Filter.eventually_atTopproof · cited by 112
- Filter.isBounded_ge_of_botproof · cited by 55
- LinearGrowth.linearGrowthInfstatement · cited by 41
- Filter.isCobounded_ge_of_topproof · cited by 38
- EReal.natCast_ne_topproof · cited by 19
- EReal.div_le_iff_le_mulproof · cited by 6
- Filter.frequently_congrproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Frequently.linearGrowthInf_leproof · cited by 2
- LinearGrowth.frequently_le_mulproof · cited by 1