parQ_bnd (KFM SetC: the cost of the parameter pushes)
ProvedNLogN.KFM.parQ_bndThe following holds (Lean statement, in the scope of module Solutions.KFMSetC):
theorem NLogN.KFM.parQ_bnd {n : ℕ} (hn : IntMul.OpenAI.Glue.n0 ≤ n) (S : ℕ) (hS : S < 2 ^ bP n) (t : IState HS)
(h : QRegs t n S) : PBnd (8 * bP n + 8) Lq t
Context. The lemma belongs to the part KFM SetC: the cost of the parameter pushes.
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.unusedVariables false open NLogN open NLogN.KFM open IntMul IntMul.OpenAI.Glue RS set_option maxHeartbeats 4000000
theorem NLogN.KFM.parQ_bnd {n : ℕ} (hn : IntMul.OpenAI.Glue.n0 ≤ n) (S : ℕ) (hS : S < 2 ^ bP n) (t : IState HS)
(h : QRegs t n S) : PBnd (8 * bP n + 8) Lq t := by sorry