Theorems · Theorem · general topology
Filter.mem_lift_sets
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {g : Set α → Filter β},
Monotone g → ∀ {s : Set β}, s ∈ f.lift g ↔ ∃ t ∈ f, s ∈ g t- Defined in
- Mathlib.Order.Filter.Lift
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Monotonestatement and proof · cited by 1,397
- Filter.basis_setsproof · cited by 105
- Filter.liftstatement · cited by 45
- Filter.HasBasis.mem_lift_iffproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Filter.mem_lift'_setsproof · cited by 10
- Filter.lift_assocproof · cited by 3
- Filter.lift_iInfproof · cited by 2
- Filter.lift_neBot_iffproof · cited by 1
- Filter.map_lift_eqproof · cited by 1
- Filter.sInter_lift_setsproof · cited by 1
- completeSpace_extensionproof · cited by 0
- Filter.lift_iInf_of_directedproof · cited by 0