The layer of round h, dispatched at run time

The layer of round h, dispatched at run time.

The following holds (Lean statement, in the scope of module Solutions.KFV24Proc):

theorem NLogN.KFV.layerU_layC (hK : 0 < K) (hℓ : 1 ≤ ℓ) {e14 : Fin Pp} {p W Z B cCh : ℕ}
    (HC : ChunkU D ℓ K long I iprog e14 hK hℓ p W Z cCh) {h : ℕ} (hh : h < ℓ) (hW : p + 1 ≤ W)
    (hB : bL D ℓ K long ≤ B) :
    LayerU (r := 2 ^ ℓ) I iprog (RX (pLP D ℓ K long) (flOf D long) h p W Z) (layC e14)
      (layerQc p (paperSel D ℓ K long hK hℓ h)) (2 ^ NLogN.KFV.nB D ℓ K long) p W
      (cLayC D ℓ K long h W B cCh)

Context. The lemma belongs to the part KFV §28: the uniform rounds and Lemma 16 (forward and opposite) as fixed IL code.

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.