lem13IL_holds (Prop 14 row additions, unconditional)

The following holds (Lean statement, in the scope of module Solutions.KFP14Closed):

theorem NLogN.KFR.lem13IL_holds : Lem13IL

Context. The lemma belongs to the part Prop 14 row additions, unconditional: KFL.lem13_il (proved in KFLMain) discharges KFR.Lem13IL, so the row-addition hypothesis RowHyp of KFN.prop14_il_complex_closed / KFM.prop14Ph_complex_closed holds for the Lemma 12 program table KFL.l12prog.

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_Defs22.