Theorems · Theorem · order theory
Rat.denseRange_cast
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
[OrderTopology 𝕜] [Archimedean 𝕜], DenseRange Rat.castRational numbers are dense in a linear ordered archimedean field.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- OrderTopologystatement and proof · cited by 1,355
- Archimedeanstatement and proof · cited by 603
- DenseRangestatement · cited by 164
- exists_rat_btwnproof · cited by 26
- Set.exists_range_iffproof · cited by 22
- dense_of_exists_betweenproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Rat.isDenseEmbedding_coe_realproof · cited by 5
- ProbabilityTheory.Kernel.HasSubgaussianMGF.of_ratproof · cited by 1
- Real.subfield_eq_of_closedproof · cited by 1
- MeasureTheory.tendsto_of_uncrossing_lt_topproof · cited by 1
- Real.exists_seq_rat_strictAnti_tendstoproof · cited by 0
- Real.exists_seq_rat_strictMono_tendstoproof · cited by 0