The value pushed for a register of a push list
ProvedNLogN.KFY.pushL_GThe value pushed for a register of a push list.
The following holds (Lean statement, in the scope of module Solutions.KFY6Gen):
theorem NLogN.KFY.pushL_G (l : List (Fin HS × Ex HS)) (t : IState HS) (hl : PushOk l t) (r : Fin HS)
(e : Ex HS) (hr : (r, e) ∈ l) : ((NLogN.KFY.pushL l).run t).G r = .int (e.eval t) :: t.G r
Context. The lemma belongs to the part KFY 6: generic combinators for the line passes.
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 set_option linter.unusedSectionVars false open NLogN open NLogN.KFY open IntMul NLogN
theorem NLogN.KFY.pushL_G (l : List (Fin HS × Ex HS)) (t : IState HS) (hl : PushOk l t) (r : Fin HS)
(e : Ex HS) (hr : (r, e) ∈ l) : ((NLogN.KFY.pushL l).run t).G r = .int (e.eval t) :: t.G r := by sorry