Theorems · Inductive type · order theory
LocallyFiniteOrderTop
(α : Type u_1) → [Preorder α] → Type u_1
This mixin class describes an order where all intervals bounded below are finite. This is
slightly weaker than LocallyFiniteOrder + OrderTop as it allows empty types.
- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
Cited by130
Results whose statement or proof uses this declaration.
- Finset.Ioistatement and proof · cited by 106
- Finset.Icistatement and proof · cited by 105
- Finset.coe_Ioistatement and proof · cited by 28
- Finset.coe_Icistatement and proof · cited by 27
- Finset.mem_Icistatement and proof · cited by 12
- Finset.mem_Ioistatement and proof · cited by 9
- Finset.notMem_Ioi_selfstatement and proof · cited by 4
- Finset.Ioi_eq_emptystatement and proof · cited by 4
- Finset.disjoint_Ioi_Iiostatement and proof · cited by 3
- Finset.Ici_eq_cons_Ioistatement and proof · cited by 3
- Finset.filter_le_eq_Icistatement and proof · cited by 2
- BddBelow.finitestatement and proof · cited by 2