Theorems · Theorem · order theory
exists_nat_gt
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R] (x : R),
∃ n, x < ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Archimedeanstatement and proof · cited by 603
- zero_lt_oneproof · cited by 598
- nsmul_oneproof · cited by 34
- exists_lt_nsmulproof · cited by 4
Cited by26
Results whose statement or proof uses this declaration.
- exists_rat_btwnproof · cited by 26
- exists_nat_one_div_ltproof · cited by 7
- PadicInt.exists_pow_neg_ltproof · cited by 6
- exists_int_gtproof · cited by 5
- archimedean_iff_nat_ltproof · cited by 5
- ENNReal.exists_nat_gtproof · cited by 5
- Metric.iUnion_ball_natproof · cited by 4
- Complex.differentiable_one_div_Gammaproof · cited by 4
- Real.exists_isLUBproof · cited by 3
- Asymptotics.isLittleO_iff_nat_mul_le_auxproof · cited by 3
- archimedean_iff_rat_ltproof · cited by 2
- Padic.exi_rat_seq_convproof · cited by 2