Theorems · Theorem · order theory
exists_rat_gt
∀ {K : Type u_4} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] [Archimedean K] (x : K), ∃ q, x < ↑q- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Archimedeanstatement and proof · cited by 603
- archimedean_iff_rat_ltproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- EReal.exists_rat_btwn_of_ltproof · cited by 5
- LinearOrderedField.cutMap_bddAboveproof · cited by 4
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonnegproof · cited by 2
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_oneproof · cited by 2
- ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRatproof · cited by 2
- Real.iInf_Ioi_eq_iInf_rat_gtproof · cited by 2
- ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAuxproof · cited by 2
- ENNReal.exists_upcrossings_of_not_bounded_underproof · cited by 1
- Real.not_bddAbove_coeproof · cited by 1
- ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iicproof · cited by 1