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Fix Riemann rearrangement scaffold (Theorem 8.2.8) #467

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teorth merged 1 commit into from
Mar 9, 2026
Merged

Fix Riemann rearrangement scaffold (Theorem 8.2.8) #467

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8 changes: 4 additions & 4 deletions analysis/Analysis/Section_8_2.lean
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Expand Up @@ -471,21 +471,21 @@ theorem permute_convergesTo_of_divergent {a: ℕ → ℝ} (ha: (a:Series).conver
obtain ⟨ a_plus, ha_plus_bij, ha_plus_mono ⟩ := (Nat.monotone_enum_of_infinite A_plus).exists
obtain ⟨ a_minus, ha_minus_bij, ha_minus_mono ⟩ := (Nat.monotone_enum_of_infinite A_minus).exists
let F : (n : ℕ) → ((m : ℕ) → m < n → ℕ) → ℕ :=
fun j n' ↦ if ∑ i:Fin j, n' i (by simp) > L then
fun j n' ↦ if ∑ i:Fin j, a (n' i (by simp)) < L then
Nat.min { n ∈ A_plus | ∀ i:Fin j, n ≠ n' i (by simp) }
else
Nat.min { n ∈ A_minus | ∀ i:Fin j, n ≠ n' i (by simp) }
let n' : ℕ → ℕ := Nat.strongRec F
have hn' (j:ℕ) : n' j = if ∑ i:Fin j, n' i > L then
have hn' (j:ℕ) : n' j = if ∑ i:Fin j, a (n' i) < L then
Nat.min { n ∈ A_plus | ∀ i:Fin j, n ≠ n' i }
else
Nat.min { n ∈ A_minus | ∀ i:Fin j, n ≠ n' i }
:= Nat.strongRec.eq_def _ j
have hn'_plus_inf (j:ℕ) : Infinite { n ∈ A_plus | ∀ i:Fin j, n ≠ n' i } := by sorry
have hn'_minus_inf (j:ℕ) : Infinite { n ∈ A_minus | ∀ i:Fin j, n ≠ n' i } := by sorry
have hn'_inj : Injective n' := by sorry
have h_case_I : Infinite { j | ∑ i:Fin j, n' i > L } := by sorry
have h_case_II : Infinite { j | ∑ i:Fin j, n' i ≤ L } := by sorry
have h_case_I : Infinite { j | ∑ i:Fin j, a (n' i) < L } := by sorry
have h_case_II : Infinite { j | ∑ i:Fin j, a (n' i) ≥ L } := by sorry
have hn'_surj : Surjective n' := by sorry
have hconv : atTop.Tendsto (a ∘ n') (nhds 0) := by sorry
have hsum : (a ∘ n':Series).convergesTo L := by sorry
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