Theorems · Theorem · general topology
Filter.lift_principal
∀ {α : Type u_1} {β : Type u_2} {g : Set α → Filter β} {s : Set α}, Monotone g → (Filter.principal s).lift g = g s- Defined in
- Mathlib.Order.Filter.Lift
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- le_rflproof · cited by 1,558
- Monotonestatement and proof · cited by 1,397
- Filter.principalstatement and proof · cited by 740
- LE.le.antisymmproof · cited by 507
- Filter.liftstatement · cited by 45
- Filter.mem_principal_selfproof · cited by 37
- Filter.lift_leproof · cited by 6
- Filter.le_liftproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Filter.lift'_principalproof · cited by 3
- Filter.lift_lift'_assocproof · cited by 2