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Mathlib/Order/DirSupClosed.lean

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@@ -291,18 +291,14 @@ end Preorder
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section PartialOrder
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variable [PartialOrder α]
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theorem DirSupClosed.singleton (a : α) : DirSupClosed {a} := by
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theorem dirSupClosed_singleton (a : α) : DirSupClosed {a} := by
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intro d hda hdn _ b hb
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rw [hdn.subset_singleton_iff] at hda
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subst hda
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exact mem_singleton_of_eq (hb.unique isLUB_singleton)
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@[deprecated (since := "2026-05-22")] alias dirSupClosed_singleton := DirSupClosed.singleton
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theorem DirSupClosedOn.singleton (a : α) : DirSupClosedOn D {a} :=
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(DirSupClosed.singleton a).dirSupClosedOn
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@[deprecated (since := "2026-05-22")] alias dirSupClosedOn_singleton := DirSupClosedOn.singleton
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theorem dirSupClosedOn_singleton (a : α) : DirSupClosedOn D {a} :=
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(dirSupClosed_singleton a).dirSupClosedOn
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end PartialOrder
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Mathlib/SetTheory/Cardinal/Cofinality/Basic.lean

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@@ -131,9 +131,6 @@ theorem cof_congr_of_strictMono {f : α → γ} (hf : StrictMono f) (hf' : IsCof
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cof α = cof γ := by
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simpa using lift_cof_congr_of_strictMono hf hf'
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theorem cof_eq_of_isCofinal {s : Set α} (hs : IsCofinal s) : cof s = cof α :=
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cof_congr_of_strictMono (Subtype.strictMono_coe _) (by simpa)
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@[simp]
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theorem cof_lt_aleph0_iff : Order.cof α < ℵ₀ ↔ Order.cof α ≤ 1 := by
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refine ⟨fun h ↦ ?_, (lt_of_le_of_lt · one_lt_aleph0)⟩

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