Theorems · Theorem · general topology
Filter.map_val_atTop_of_Ici_subset
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] {a : α} {s : Set α},
Set.Ici a ⊆ s → Filter.map Subtype.val Filter.atTop = Filter.atTop- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.Elemproof · cited by 7,166
- LE.le.transproof · cited by 3,151
- Filter.atTopstatement · cited by 2,405
- Set.Icistatement and proof · cited by 1,070
- Filter.mapstatement · cited by 819
- IsDirectedOrderstatement and proof · cited by 316
- DirectedOnproof · cited by 271
- exists_ge_geproof · cited by 22
- Subtype.mono_coeproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- Filter.map_val_Ici_atTopproof · cited by 3
- Filter.map_val_Ioi_atTopproof · cited by 2
- Filter.atTop_Ioi_eqproof · cited by 1