bnd_pull (KFU §2: padding / deletion of every field)
ProvedNLogN.KFU.bnd_pullThe following holds (Lean statement, in the scope of module Solutions.KFUPadAll):
theorem NLogN.KFU.bnd_pull {w : ℕ} (sh sh' : Shape) (g : List ℕ → List ℕ) {xs : List ℤ} (h : Bnd w xs) :
Bnd w (AModel.pull sh sh' g 0 xs)
Context. The lemma belongs to the part KFU §2: padding / deletion of every field: padAllC S T n runs one padding scan per field k < n (S ≤ T pointwise); after all
|S| scans stack 0 holds embed S T 0 xs (padAll_spec). unpadAllC S T n runs the deletion
scans and computes extract S T 0 ys (unpadAll_spec). Cost ≤ |S| · 10^4 (w+1)(2 vol T + 1).
Formalization Note. This lemma belongs to layer 5 of the Lean formalization (integer-multiplication-kappa campaign) of the OpenAI preprint Integer multiplication below : 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.
-- OpenAI-preprint / κ-improvement development (integer-multiplication-kappa), generated by skeleton subtraction.
import Definitions.Def_IntMul_Kappa_K_Defs33
set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000
set_option linter.unusedSimpArgs false
set_option linter.unnecessarySeqFocus false
open NLogN
open NLogN.KFU
open IntMul KFC KFT AModel AModelL12
variable {Pp : ℕ} {I : List Sym} {iprog : Fin Pp → IStmt HS Pp}
theorem NLogN.KFU.bnd_pull {w : ℕ} (sh sh' : Shape) (g : List ℕ → List ℕ) {xs : List ℤ} (h : Bnd w xs) :
Bnd w (AModel.pull sh sh' g 0 xs) := by sorry