irun (KFD base: fine compilation of register programs)
ProvedNLogN.KFD.FSp.irunThe following holds (Lean statement, in the scope of module Solutions.KFDBase):
theorem NLogN.KFD.FSp.irun {p : RS} {s t : IState HS} {c : ℕ} (hf : NLogN.KFD.fok p = true) (h : FSp p s t c) :
IRuns I iprog (fcode p) s t c
Context. The lemma belongs to the part KFD base: fine compilation of register programs.
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 IntMul RS
open NLogN.KFD
open KFC (marks marks_zero isMk NM toUL cUL uK uR uY uB)
variable {Pp : ℕ} {I : List Sym} {iprog : Fin Pp → IStmt HS Pp}
theorem NLogN.KFD.FSp.irun {p : RS} {s t : IState HS} {c : ℕ} (hf : NLogN.KFD.fok p = true) (h : FSp p s t c) :
IRuns I iprog (fcode p) s t c := by sorry