apply Finset.prod_congr rfl
f : ℕ → ℝ
n : ℕ
ih : ∏ i ∈ Finset.range (n + 1), ∏ j ∈ (Finset.range (n + 1)).erase i, f j = ∏ i ∈ Finset.range (n + 1), f i ^ ↑n
⊢ ∏ x ∈ Finset.range (n + 1), ∏ j ∈ (Finset.range (n.succ + 1)).erase x, f j =
    ∏ x ∈ Finset.range (n + 1), (∏ j ∈ (Finset.range (n + 1)).erase x, f j) * f (n + 1)
f : ℕ → ℝ
n : ℕ
ih : ∏ i ∈ Finset.range (n + 1), ∏ j ∈ (Finset.range (n + 1)).erase i, f j = ∏ i ∈ Finset.range (n + 1), f i ^ ↑n
⊢ ∀ x ∈ Finset.range (n + 1),
    ∏ j ∈ (Finset.range (n.succ + 1)).erase x, f j = (∏ j ∈ (Finset.range (n + 1)).erase x, f j) * f (n + 1)