Theorems · Theorem · order theory
exists_int_lt
∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R] (x : R), ∃ n, ↑n < x- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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.
- 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_negproof · cited by 224
- neg_ltproof · cited by 21
- exists_int_gtproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- exists_rat_ltproof · cited by 5
- exists_floorproof · cited by 1