Theorems · Theorem · order theory
exists_int_gt
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R] (x : R), ∃ n, x < ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 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.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Archimedeanstatement and proof · cited by 603
- Int.cast_natCastproof · cited by 393
- exists_nat_gtproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- Real.exists_isLUBproof · cited by 3
- Pell.exists_of_not_isSquareproof · cited by 3
- exists_int_ltproof · cited by 2
- exists_floorproof · cited by 1
- archimedean_iff_int_ltproof · cited by 1