Theorems · Theorem · general topology
closure_of_rat_image_lt
∀ {q : ℚ}, closure (Rat.cast '' {x | q < x}) = {r | ↑q ≤ r}- Defined in
- Mathlib.Topology.Instances.Real.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Set.ofPredstatement and proof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Set.rangeproof · cited by 4,705
- Nat.cast_oneproof · cited by 2,501
- Set.extproof · cited by 2,266
- Nat.cast_zeroproof · cited by 1,870
- Set.Ioiproof · cited by 1,463
- closurestatement and proof · cited by 1,254
- lt_of_not_geproof · cited by 374
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