The uniform Proposition 18 from the uniform Proposition 14

The uniform Proposition 18 from the uniform Proposition 14.

The following holds (Lean statement, in the scope of module Solutions.KFV56Final):

theorem NLogN.KFV.p18IL_of (A : ℕ) (HU : P14Uat A) (HE : EwB18 A) (HPar : Par18Need) (HCost : Cost18) :
    KFM.P18IL

Context. The lemma belongs to the part KFV §56: the uniform Proposition 18 (P18IL) from the uniform Proposition 14: The table is kTable (ext18 nU U e su td q): the Proposition 14 procedures, the uniform swap KFW.swGU q and the body body18; the entry is ent18 nU, the descriptor stack dS18 = 33.

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.