cIte_le (KFV §25: the prefix and top rounds of the paper's layout, uniform)
ProvedNLogN.KFV.cIte_leThe following holds (Lean statement, in the scope of module Solutions.KFV21Rounds):
theorem NLogN.KFV.cIte_le {st : IState HS} {B : ℕ} {e : Ex HS} {v : ℤ} (h : EV st B e v) :
cIte e st ≤ cIteB e.size B
Context. The lemma belongs to the part KFV §25: the prefix and top rounds of the paper's layout, uniform.
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 RS KIL KFD KFB KFH AModel Butterfly
variable {Pp : ℕ} {I : List Sym} {iprog : Fin Pp → IStmt HS Pp}
theorem NLogN.KFV.cIte_le {st : IState HS} {B : ℕ} {e : Ex HS} {v : ℤ} (h : EV st B e v) :
cIte e st ≤ cIteB e.size B := by sorry