Theorems · Theorem · order theory
exists_int_ge
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [IsOrderedRing R] [Archimedean R] (x : R), ∃ n, x ≤ ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 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
- IsOrderedRingstatement and proof · cited by 777
- Archimedeanstatement and proof · cited by 603
- Int.cast_natCastproof · cited by 393
- exists_nat_geproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- exists_int_leproof · cited by 1