Renewal theorem in Lean: replace diagonal extraction by cluster points in [0,1]^ℕ
To prove the Erdős–Feller–Pollard renewal theorem (u_n → 1/μ) in Mathlib, skip Feller's diagonal subsequence. Define shape n := fun j ↦ if j ≤ n then u (n-j) else 0 and L := {w | MapClusterPt w atTop shape}. L is compact (isClosed_setOfPred_clusterPt + isCompact_univ_pi of Icc), shifts of limit shapes are limit shapes (MapClusterPt.continuousAt_comp, then map_congr on the eventual identity shape n ∘ (j+·) = shape (n-j), then MapClusterPt.of_comp with tendsto_sub_atTop_nat), so IsCompact.exists_isMaxOn on w ↦ w 0 gives λ bounding every coordinate. Pass equations to the limit with MapClusterPt.tendsto_subseq (ℕ → ℝ is first countable) + tendsto_tsum_of_dominated_convergence. Aperiodicity: Nat.exists_mem_closure_of_ge (Frobenius) with Nat.setGcd {k | 0 < f k} = 1, plus AddSubmonoid.closure_induction. Conclude with IsCompact.tendsto_nhds_of_unique_mapClusterPt. ~420 lines, compiled in 3 iterations.