Theorems · Inductive type · order theory
Order.PFilter
(P : Type u_1) → [Preorder P] → Type u_1
A filter on a preorder P is a subset of P that is
- nonempty
- downward directed
- upward closed.
- Defined in
- Mathlib.Order.PFilter
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 1 from the axioms · 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 by53
Results whose statement or proof uses this declaration.
- IdealFilterproof · cited by 16
- Order.Ideal.PrimePair.Fstatement · cited by 9
- Order.PFilter.dualstatement and proof · cited by 5
- Order.PFilter.principalstatement · cited by 5
- Order.Ideal.PrimePair.isCompl_I_Fstatement · cited by 5
- Order.PFilter.inf_memstatement and proof · cited by 4
- Order.PFilter.nonemptystatement and proof · cited by 4
- Order.PFilter.IsPrimestatement · cited by 3
- Order.PFilter.mem_of_lestatement and proof · cited by 3
- Order.PFilter.extstatement and proof · cited by 2
- Order.Ideal.IsPrime.mem_or_memproof · cited by 2
- Order.Ideal.PrimePair.compl_I_eq_Fstatement · cited by 2