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SetTheory/Cardinal/Cofinality Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -291,18 +291,14 @@ end Preorder
291291section PartialOrder
292292variable [PartialOrder α]
293293
294- theorem DirSupClosed.singleton (a : α) : DirSupClosed {a} := by
294+ theorem dirSupClosed_singleton (a : α) : DirSupClosed {a} := by
295295 intro d hda hdn _ b hb
296296 rw [hdn.subset_singleton_iff] at hda
297297 subst hda
298298 exact mem_singleton_of_eq (hb.unique isLUB_singleton)
299299
300- @ [deprecated (since := "2026-05-22" )] alias dirSupClosed_singleton := DirSupClosed.singleton
301-
302- theorem DirSupClosedOn.singleton (a : α) : DirSupClosedOn D {a} :=
303- (DirSupClosed.singleton a).dirSupClosedOn
304-
305- @ [deprecated (since := "2026-05-22" )] alias dirSupClosedOn_singleton := DirSupClosedOn.singleton
300+ theorem dirSupClosedOn_singleton (a : α) : DirSupClosedOn D {a} :=
301+ (dirSupClosed_singleton a).dirSupClosedOn
306302
307303end PartialOrder
308304
Original file line number Diff line number Diff line change @@ -131,9 +131,6 @@ theorem cof_congr_of_strictMono {f : α → γ} (hf : StrictMono f) (hf' : IsCof
131131 cof α = cof γ := by
132132 simpa using lift_cof_congr_of_strictMono hf hf'
133133
134- theorem cof_eq_of_isCofinal {s : Set α} (hs : IsCofinal s) : cof s = cof α :=
135- cof_congr_of_strictMono (Subtype.strictMono_coe _) (by simpa)
136-
137134@[simp]
138135theorem cof_lt_aleph0_iff : Order.cof α < ℵ₀ ↔ Order.cof α ≤ 1 := by
139136 refine ⟨fun h ↦ ?_, (lt_of_le_of_lt · one_lt_aleph0)⟩
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