Theorems · Theorem · order theory
BddBelow.finite
∀ {α : Type u_2} [inst : Preorder α] [LocallyFiniteOrderTop α] {s : Set α}, BddBelow s → s.Finite- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Preorderstatement and proof · cited by 7,952
- Set.Finitestatement and proof · cited by 1,814
- BddBelowstatement and proof · cited by 401
- Set.Finite.subsetproof · cited by 285
- lowerBoundsproof · cited by 212
- Finset.finite_toSetproof · cited by 210
- LocallyFiniteOrderTopstatement and proof · cited by 114
- Finset.Iciproof · cited by 105
- Finset.mem_Iciproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- BddAbove.finiteproof · cited by 2
- Set.Infinite.not_bddBelowproof · cited by 1