Theorems · Theorem · order theory
Filter.blimsup_eq_iInf_biSup
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β} {p : β → Prop} {u : β → α},
Filter.blimsup u f p = ⨅ s ∈ f, ⨆ b, ⨆ (_ : p b ∧ b ∈ s), u b- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
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.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- iSupstatement and proof · cited by 2,415
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iSup_congr_Propproof · cited by 247
- iInf_congr_Propproof · cited by 218
- Filter.basis_setsproof · cited by 105
- Filter.blimsupstatement · cited by 40
- iSup_and'proof · cited by 4
- Filter.HasBasis.blimsup_eq_iInf_iSupproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- sSupHom.apply_blimsup_leproof · cited by 2
- Filter.exists_forall_mem_of_hasBasis_mem_blimsupproof · cited by 1
- Filter.bliminf_eq_iSup_biInfproof · cited by 1