Theorems · Theorem · order theory
Filter.Eventually.natCast_atTop
∀ {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [IsOrderedRing R] [Archimedean R] {p : R → Prop},
(∀ᶠ (x : R) in Filter.atTop, p x) → ∀ᶠ (n : ℕ) in Filter.atTop, p ↑n- Cited by
- 6 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- PartialOrderstatement and proof · cited by 6,410
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- IsOrderedRingstatement and proof · cited by 777
- Archimedeanstatement and proof · cited by 603
- Filter.Tendsto.eventuallyproof · cited by 174
- tendsto_natCast_atTop_atTopproof · cited by 51
Cited by6
Results whose statement or proof uses this declaration.
- AkraBazziRecurrence.eventually_one_add_smoothingFn_posproof · cited by 3
- AkraBazziRecurrence.isBigO_apply_r_sub_bproof · cited by 2
- AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_constproof · cited by 2
- AkraBazziRecurrence.eventually_one_sub_smoothingFn_posproof · cited by 2
- AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le_natproof · cited by 1
- AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge_natproof · cited by 1