Theorems · Theorem · order theory
Order.PFilter.nonempty
∀ {P : Type u_1} [inst : Preorder P] (F : Order.PFilter P), (↑F).Nonempty- Defined in
- Mathlib.Order.PFilter
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptystatement · cited by 2,627
- Order.PFilterstatement and proof · cited by 32
- Order.PFilter.dualproof · cited by 5
- Order.Ideal.nonemptyproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- IdealFilter.isTorsionQuot_selfproof · cited by 2
- Order.Ideal.PrimePair.I_isProperproof · cited by 1
- IdealFilter.isPFilter_gabrielCompositionproof · cited by 0
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0