Theorems · Theorem · order theory
Set.infinite_iff_exists_gt
∀ {α : Type u_2} [inst : LinearOrder α] [LocallyFiniteOrderBot α] {s : Set α} [Nonempty α],
s.Infinite ↔ ∀ (a : α), ∃ b ∈ s, a < b- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 85 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.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Set.Infinitestatement · cited by 263
- Set.Infinite.exists_gtproof · cited by 5
- Set.infinite_of_forall_exists_gtproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Nat.forall_exists_prime_gt_and_eq_modproof · cited by 1
- Nat.infinite_deficientproof · cited by 0
- Nat.infinite_even_abundantproof · cited by 0
- Nat.infinite_even_deficientproof · cited by 0
- Nat.infinite_odd_abundantproof · cited by 0
- Nat.infinite_odd_deficientproof · cited by 0