zl_shP (KFUU §9a: the passes on managed states)

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

theorem NLogN.KFUU.zl_shP (d h : ℕ) (bL : ℕ → Bool) : NLogN.KFUU.zl (shP h (bsL d bL)) = tZ h bL d

Context. The lemma belongs to the part KFUU §9a: the passes on managed states: The pass lemmas (padAllU_runs, unpadAllU_runs, revU_runs, rotsFU_runs, rotsBU_runs) restated on managed states encK s F (data xs ++ l on stack 0).

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.