clean_lit (KIL base: register programs on "managed" stacks)
ProvedNLogN.KIL.clean_litThe following holds (Lean statement, in the scope of module Solutions.KILBase):
theorem NLogN.KIL.clean_lit (c : ℤ) : (Ex.lit (S := HS) c).Clean
Context. The lemma belongs to the part KIL base: register programs on "managed" stacks: encK s f is the state s with the list of integers f j pushed on top of every stack j
(f j = [] for unmanaged stacks). All programs of the KIL files are specified on such states;
updates are Function.updates of f, which keeps the bookkeeping small.
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 open NLogN open IntMul RS open NLogN.KIL
theorem NLogN.KIL.clean_lit (c : ℤ) : (Ex.lit (S := HS) c).Clean := by sorry