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Mathlib/SetTheory/Cardinal/Arithmetic.lean

Lines changed: 1 addition & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -383,8 +383,7 @@ protected theorem ciSup_mul (c : Cardinal.{v}) : (⨆ i, f i) * c = ⨆ i, f i *
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refine le_antisymm ?_ (ciSup_le' this)
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have bdd : BddAbove (range (f · * c)) := ⟨_, forall_mem_range.mpr this⟩
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obtain hs | hs := lt_or_ge (⨆ i, f i) ℵ₀
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· obtain ⟨i, hi⟩ := exists_eq_of_iSup_eq_of_not_isSuccLimit
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f hf (not_isSuccLimit_of_lt_aleph0 hs) rfl
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· obtain ⟨i, hi⟩ := exists_eq_ciSup_of_not_isSuccLimit hf (not_isSuccLimit_of_lt_aleph0 hs)
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exact hi ▸ le_ciSup bdd i
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rw [mul_eq_max_of_aleph0_le_left hs h0, max_le_iff]
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obtain ⟨i, hi⟩ := exists_lt_of_lt_ciSup' (one_lt_aleph0.trans_le hs)

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