Theorems · Theorem · order theory
Set.Infinite.exists_gt
∀ {α : Type u_2} [inst : LinearOrder α] [LocallyFiniteOrderBot α] {s : Set α}, s.Infinite → ∀ (a : α), ∃ b ∈ s, a < b- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 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 and proof · cited by 263
- not_bddAbove_iffproof · cited by 15
- Set.Infinite.not_bddAboveproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Set.infinite_iff_exists_gtproof · cited by 6
- AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finiteproof · cited by 3
- Monoid.exponent_ne_zero_iff_range_orderOf_finiteproof · cited by 3
- Set.Infinite.Nat.sSup_eq_zeroproof · cited by 3
- Nat.le_nth_countproof · cited by 0