Theorems · Theorem · general topology
Real.exists_seq_rat_strictMono_tendsto
∀ (x : ℝ), ∃ u, StrictMono u ∧ (∀ (n : ℕ), ↑(u n) < x) ∧ Filter.Tendsto (fun x => ↑(u x)) Filter.atTop (nhds x)
- Defined in
- Mathlib.Topology.Instances.Real.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- StrictMonostatement · cited by 706
- StrictMono.monotoneproof · cited by 118
- Rat.denseRange_castproof · cited by 6
- Rat.cast_strictMonoproof · cited by 5
- DenseRange.exists_seq_strictMono_tendstoproof · cited by 2
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