One more level: a node of J over the level-k claim

One more level: a node of J over the level-k claim.

The following holds (Lean statement, in the scope of module Solutions.KFNInd):

theorem NLogN.KFN.lv_succ (hGc : GClass J A) (hrow : RowHyp Isym iprog K m r Z Ψ CR τ) (hCR : 0 ≤ CR) (hτ : 0 ≤ τ)
    (hW : 1 ≤ W) (hr : 1 ≤ r) (hΨm : Monotone Ψ) (hZΨ : ∀ v, Z + 2 ≤ Ψ v)
    {k Ek DWk Wk : ℕ} {ck : ℝ} (hck : 0 ≤ ck) (IH : Lv Isym iprog K W m r Z Ψ k Ek DWk Wk ck) :
    Lv Isym iprog K W m r Z Ψ (k + 1) (J.net.length + s * Ek)
      (s * (DWk + (Ek + 2) * W) + J.net.length * dwloc W A)
      (s * (DWk + (Ek + 2) * W) + J.net.length * dwloc W A +
        (DWk + (Ek + 2) * W + Ek + dwloc W A + 10) + Wk)
      ((s / W : ℝ) * ck + ((s + J.net.length : ℕ) : ℝ) *
        ((alN W A : ℝ) + CR * ((m : ℝ) ^ k + 1) ^ τ) + 1)

Context. The lemma belongs to the part KFN: the recursion over the levels.

Formalization Note. This lemma belongs to the item-language (IL) layer of the integer-multiplication-kappa campaign: tape-level programs (register programs over 64 item stacks of the NLogN multitape framework, definition bundles IntMul_HvdH_M_Defs1–IntMul_HvdH_M_Defs8) that implement the data-movement primitives of the OpenAI preprint Integer multiplication below $n\log n$ (field moves, row split/merge, shifts, the uniform Proposition 11 interchange, Lemma 12 with fine $O(1)$-per-element costs, Gaussian record primitives, Proposition 14 pieces) with exact list denotations from the array-model bundles IntMul_Kappa_K_Defs* and explicit cost bounds. All names refer to the definition bundles up to IntMul_Kappa_K_Defs20.