Theorems · Theorem · order theory
exists_nat_ge
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [IsOrderedRing R] [Archimedean R] (x : R), ∃ n, x ≤ ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialproof · cited by 2,416
- IsOrderedRingstatement and proof · cited by 777
- Archimedeanstatement and proof · cited by 603
- one_posproof · cited by 102
- nsmul_oneproof · cited by 34
- Archimedean.archproof · cited by 19
Cited by20
Results whose statement or proof uses this declaration.
- tendsto_natCast_atTop_atTopproof · cited by 51
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- EReal.exists_nat_ge_mulproof · cited by 3
- tendsto_natCast_atTop_iffproof · cited by 2
- Int.comap_cast_atBotproof · cited by 2
- Int.comap_cast_atTopproof · cited by 2
- Metric.iUnion_closedBall_natproof · cited by 2
- Rat.comap_cast_atBotproof · cited by 2
- Rat.comap_cast_atTopproof · cited by 2
- LinearGrowth.EReal.eventually_atTop_exists_nat_betweenproof · cited by 2
- Function.Periodic.intervalIntegrableproof · cited by 2
- exists_int_geproof · cited by 1