top_eq (Expressions over register stacks)
ProvedNLogN.IState.top_eqThe following holds (Lean statement, in the scope of module NLogN.HExpr):
theorem NLogN.IState.top_eq {s : IState S} {i : Fin S} {a : ℤ} {L : List Item} (h : s.G i = .int a :: L) :
s.top i = a
Context. The lemma belongs to the part Expressions over register stacks: Ex S are integer expressions whose leaves read the top item of a register stack. Ex.code z e
evaluates e onto the value stack z.V, using the scratch stacks of z and leaving every other
stack unchanged (Ex.code_runs).
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
open NLogN
open IntMul
variable {S P : ℕ} {I : List Sym} {iprog : Fin P → IStmt S P}
theorem NLogN.IState.top_eq {s : IState S} {i : Fin S} {a : ℤ} {L : List Item} (h : s.G i = .int a :: L) :
s.top i = a := by sorry