NW_ext (KFV §14: the uniform record product `recU`)
ProvedNLogN.KFV.NW_extThe following holds (Lean statement, in the scope of module Solutions.KFV10Rec):
theorem NLogN.KFV.NW_ext {c r' KG B BJ D2 : ℤ} {O : Fin HS} (hO : O.val < 50) {e : Ex HS} {b r Δ : ℕ} :
NW (πR c r' KG B BJ D2) (extI e O b r Δ : IStmt HS Pp)
Context. The lemma belongs to the part KFV §14: the uniform record product recU.
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.unusedVariables false
set_option linter.unusedSimpArgs false
open NLogN
open NLogN.KFV
open IntMul KIL KFD KFT KFB KFC RS
variable {Pp : ℕ} {I : List Sym} {iprog : Fin Pp → IStmt HS Pp}
theorem NLogN.KFV.NW_ext {c r' KG B BJ D2 : ℤ} {O : Fin HS} (hO : O.val < 50) {e : Ex HS} {b r Δ : ℕ} :
NW (πR c r' KG B BJ D2) (extI e O b r Δ : IStmt HS Pp) := by sorry