Theorems · Theorem · logic and foundations
Hyperreal.ofSeq_lt_ofSeq
∀ {f g : ℕ → ℝ}, Hyperreal.ofSeq f < Hyperreal.ofSeq g ↔ ∀ᶠ (n : ℕ) in ↑(Filter.hyperfilter ℕ), f n < g n- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filter.Eventuallystatement · cited by 3,134
- Hyperrealstatement · cited by 172
- Ultrafilter.toFilterstatement · cited by 172
- Filter.hyperfilterstatement · cited by 30
- Hyperreal.ofSeqstatement · cited by 24
- Filter.Germ.coe_ltproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Hyperreal.isSt_ofSeq_iff_tendstoproof · cited by 7
- Hyperreal.lt_of_tendsto_atBotproof · cited by 3
- Hyperreal.lt_of_tendsto_atTopproof · cited by 3
- Hyperreal.IsSt.ltproof · cited by 2
- Hyperreal.coe_lt_omegaproof · cited by 2
- Hyperreal.lt_of_tendsto_zero_of_posproof · cited by 1