Theorems · Theorem · order theory
Filter.Subsingleton.atTop_eq
∀ (α : Type u_6) [Subsingleton α] [inst : Preorder α], Filter.atTop = ⊤
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubsingletonPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Top.topstatement · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement and proof · cited by 2,405
- Set.Iciproof · cited by 1,070
- Filter.principalproof · cited by 740
- top_uniqueproof · cited by 102
- Set.self_mem_Iciproof · cited by 30
- Filter.mem_principalproof · cited by 10
- ciInf_subsingletonproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Filter.Tendsto.add_atTopproof · cited by 3
- Filter.Tendsto.mul_atTop'proof · cited by 2
- Filter.Subsingleton.atBot_eqproof · cited by 0