Theorems · Theorem · order theory
BddBelow.finite_of_bddAbove
∀ {α : Type u_3} [inst : Preorder α] [LocallyFiniteOrder α] {s : Set α}, BddBelow s → BddAbove s → s.Finite- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
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
- LocallyFiniteOrderstatement and proof · cited by 658
- BddAbovestatement and proof · cited by 620
- BddBelowstatement and proof · cited by 401
- Set.Finite.subsetproof · cited by 285
- upperBoundsproof · cited by 263
- lowerBoundsproof · cited by 212
- Set.finite_Iccproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBeforeproof · cited by 3
- Set.Nonempty.ordConnected_iff_of_bddproof · cited by 3
- Set.finite_iff_bddBelow_bddAboveproof · cited by 0