disk_pull (KFV §31: one layout primitive on the record array)
ProvedNLogN.KFV.disk_pullThe following holds (Lean statement, in the scope of module Solutions.KFV28LayStep):
theorem NLogN.KFV.disk_pull {xs : List (Fin r → ℂ)} (h : Disk xs) (sh sh' : Shape) (g : List ℕ → List ℕ) :
Disk (pull sh sh' g 0 xs)
Context. The lemma belongs to the part KFV §31: one layout primitive on the record array: The records xs (shape binSh n, each r coefficients) are stored as zs (shape
binSh n ++ [r]) and on stack 0 as gflat zs (shape binSh n ++ [r, 2]). A layout
primitive o acts on the records by pull (binSh n) (permIdx o.inv).
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.unusedSectionVars false
set_option linter.unusedSimpArgs false
set_option linter.unusedVariables false
open NLogN
open NLogN.KFV
open IntMul KIL KFB KFH Synth AModel AModelL12
variable {r F : ℕ}
theorem NLogN.KFV.disk_pull {xs : List (Fin r → ℂ)} (h : Disk xs) (sh sh' : Shape) (g : List ℕ → List ℕ) :
Disk (pull sh sh' g 0 xs) := by sorry