Theorems · Theorem · order theory
Order.PFilter.inf_mem
∀ {P : Type u_1} [inst : SemilatticeInf P] {x y : P} {F : Order.PFilter P}, x ∈ F → y ∈ F → x ⊓ y ∈ FA specific witness of pfilter.directed when P has meets.
- Defined in
- Mathlib.Order.PFilter
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- Order.PFilterstatement and proof · cited by 32
- Order.Ideal.sup_memproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Order.Ideal.IsPrime.mem_or_memproof · cited by 2
- IdealFilter.IsTorsionQuot.infproof · cited by 1
- IdealFilter.isPFilter_gabrielCompositionproof · cited by 0
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0