T0c_XLc (KFL §2: Lemma 13 on chunk triples (canonical layout `x, y, z` = slots `0, 1, 2`))
ProvedNLogN.KFL.T0c_XLcThe following holds (Lean statement, in the scope of module Solutions.KFLMath):
theorem NLogN.KFL.T0c_XLc (hK : 1 ≤ K) (hf : 1 ≤ f) (c : Tr) : T0c K ρ f (XLc K ρ f c) = RAc K ρ f c
Context. The lemma belongs to the part KFL §2: Lemma 13 on chunk triples (canonical layout x, y, z = slots 0, 1, 2).
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 (field moves, row split/merge, shifts, the uniform Proposition 11 interchange, Lemma 12 with fine -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_Defs18.
-- OpenAI-preprint / κ-improvement development (integer-multiplication-kappa), generated by skeleton subtraction.
import Definitions.Def_IntMul_Kappa_K_Defs18
set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000
set_option linter.unusedSimpArgs false
set_option linter.unusedVariables false
open NLogN
open NLogN.KFL
open Butterfly
variable {K ρ f : ℕ}
theorem NLogN.KFL.T0c_XLc (hK : 1 ≤ K) (hf : 1 ≤ f) (c : Tr) : T0c K ρ f (XLc K ρ f c) = RAc K ρ f c := by sorry