bnd_sZ (KFUU §8c: reading the `Φ` descriptor)

The following holds (Lean statement, in the scope of module Solutions.KFUUSet3):

theorem NLogN.KFUU.bnd_sZ (sF : ℕ → ℕ) (d B : ℕ) (hB : ∀ j < d, zsz ((sF j : ℕ) : ℤ) ≤ B) : Bnd B (sZ sF d)

Context. The lemma belongs to the part KFUU §8c: reading the Φ descriptor: readD Ys Ym (register code) reads descPhi w h d bL sF μ from dP and restores it: rW = w, rU = h, oD = d, oPi = P_d; the bits reversed on bT; the sizes [s_{d-1}, …, s_0] on Ys, pSR, xA; the multipliers [μ_{d-1}, …, μ_0] on Ym.

Formalization Note. This lemma belongs to layer 5 of the Lean formalization (integer-multiplication-kappa campaign) of the OpenAI preprint Integer multiplication below $n\log n$: the uniform item-language machine (register programs over the NLogN multitape framework) assembling the Proposition 14 / Lemma 13 / Proposition 18 pieces, the resampling and chirp stages and the cost recurrences into one fixed machine, culminating in NLogN.KFTop.kappa_bound : IntMul.KappaBound (1 / 2 ^ 182) (the bound of Def_IntMul_MultitapeModel). All names refer to the definition bundles up to IntMul_Kappa_K_Defs33.