Theorems · Theorem · order theory
Set.Finite.bddBelow
∀ {α : Type u} [inst : Preorder α] [IsCodirectedOrder α] [Nonempty α] {s : Set α}, s.Finite → BddBelow sA finite set is bounded below.
- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 7 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.
Cites8
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
- IsCodirectedOrderstatement and proof · cited by 95
- Set.Finite.induction_onproof · cited by 39
- bddBelow_emptyproof · cited by 5
- BddBelow.insertproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- Filter.IsBoundedUnder.bddBelow_range_of_cofiniteproof · cited by 2
- Finset.bddBelowproof · cited by 0
- Set.infinite_of_not_bddBelowproof · cited by 0
- Set.Finite.lt_ciInf_iffproof · cited by 0
- Filter.IsBoundedUnder.ge_of_finiteproof · cited by 0
- Set.Finite.map_sInf_of_monotoneproof · cited by 0