`AIL6s` from the per-axis `A` program and the `GB` invariant (round six, `AIL6s_of_axis`)
ProvedJ6Seg.AIL6s_of_axisAIL6s from the per-axis A program and the GB invariant.
The following holds (Lean statement, in the scope of module Solutions.J6LineTopA3):
theorem J6Seg.AIL6s_of_axis (P : Prm) (hP : P.Ok) (tab : Fin 1 → IStmt HS 1) (hX : AxisUA6 P tab)
(hG : PipeGBA6 P) : AIL6s P tab
Context. A lines by an axis sweep, part 3: AIL6s_of_axis
The table is the machine's own procedures only (extL ext0 U body, J6LineTop4): the per-axis
family U of AxisUA6 and, last, the sweep swp (sgm dS dA) dS dA (idx eX) with the descriptor
on dS = 20. sweep_runF with pf = pipeA6 P n src D and the invariant "length ∏ t and
GB (p + 2)" (PipeGBA6), then pipeA6_sweep, gives AIL6s P tab at cost (C_X + 10^12) cU6.
Formalization Note. Part of the Lean formalization of the round-six κ-improvement (integer-multiplication-kappa campaign, target IntMul.Kappa.jain_round6_framework). The statement is copied verbatim from the Lean development; the platform node carries the same declaration name. Definitions it mentions live in the IntMul_Kappa_R6_Defs* bundles (on top of the published κ bundles IntMul_Kappa_K_Defs*).
-- Round-six κ development (integer-multiplication-kappa), generated by skeleton subtraction. import Definitions.Def_IntMul_Kappa_R6_Defs63 set_option autoImplicit false set_option relaxedAutoImplicit false set_option maxHeartbeats 1000000 open J6Seg open IntMul NLogN NLogN.KIL NLogN.KFB IntMul.Kappa.R6 Function
theorem J6Seg.AIL6s_of_axis (P : Prm) (hP : P.Ok) (tab : Fin 1 → IStmt HS 1) (hX : AxisUA6 P tab)
(hG : PipeGBA6 P) : AIL6s P tab := by sorry