Theorems · Theorem · approximation theory
LinearGrowth.linearGrowthSup_le_iff
∀ {u : ℕ → EReal} {a : EReal}, LinearGrowth.linearGrowthSup 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.Eventuallystatement and proof · cited by 3,134
- 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.eventually_atTopproof · cited by 112
- Filter.isBounded_le_of_topproof · cited by 75
- Filter.isCobounded_le_of_botproof · cited by 58
- LinearGrowth.linearGrowthSupstatement · cited by 38
- Filter.eventually_congrproof · cited by 20
- EReal.natCast_ne_topproof · cited by 19
- EReal.div_le_iff_le_mulproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Eventually.linearGrowthSup_leproof · cited by 2
- LinearGrowth.eventually_le_mulproof · cited by 1