Theorems · Theorem · order theory
exists_rat_lt
∀ {K : Type u_4} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] [Archimedean K] (x : K), ∃ q, ↑q < x- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Rat.cast_intCastproof · cited by 74
- exists_int_ltproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- EReal.exists_rat_btwn_of_ltproof · cited by 5
- LinearOrderedField.cutMap_nonemptyproof · cited by 3
- ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iicproof · cited by 1
- ENNReal.exists_upcrossings_of_not_bounded_underproof · cited by 1
- Real.not_bddBelow_coeproof · cited by 1