Kernel check of half of segment 13 of stage 2 (`chk2_13b`)

Proved

IntMul.Kappa.R6.Cx.NetData.chk2_13b

by xuanji · Oct 20, 2026 · Mathlib 0df444a (Lean v4.33.1)

complexity-theoryinteger-multiplicationkappa-improvement

Kernel check of the second half of segment 13 of stage 2 (scratch wires 24604 .. 49207, the y wires): 24604 moves.

The following holds (Lean statement, in the scope of module R6Pk.R6CxNetChk2_13b):

theorem IntMul.Kappa.R6.Cx.NetData.chk2_13b : mvK NL (mvOK2R dat) wd2R 0 (finK H2_13b 24604 S2_14)
    ((List.range 24604).map (fun q => aw (24604 + q)) ++ allY) S2_13m 0 0 = true

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*).

Preamble

-- Round-six κ development (integer-multiplication-kappa), generated by skeleton subtraction.

import Definitions.Def_IntMul_Kappa_R6_Defs25
import Definitions.Def_IntMul_Kappa_R6_Data_CxNetData_1
import Definitions.Def_IntMul_Kappa_R6_Data_CxNetDataS2_14
import Definitions.Def_IntMul_Kappa_R6_Data_CxNetDataS2_13
import Definitions.Def_IntMul_Kappa_R6_Data_CxNetDataS2_13m

set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000

open IntMul IntMul.Kappa IntMul.Kappa.R6 IntMul.Kappa.R6.Cx IntMul.Kappa.R6.Cx.NetData
open IntMul.Kappa.R6.Cx.NetBT IntMul.Kappa.R6.Cx.NetLoc IntMul.Kappa.R6.Cx.NetSpec IntMul.Kappa.R6.Cx.NetFast IntMul.Kappa.R6.Cx.NetRaw

Formal statement

theorem IntMul.Kappa.R6.Cx.NetData.chk2_13b : mvK NL (mvOK2R dat) wd2R 0 (finK H2_13b 24604 S2_14)
    ((List.range 24604).map (fun q => aw (24604 + q)) ++ allY) S2_13m 0 0 = true := by sorry

Source

S. Jain, round-six networks for the integer-multiplication κ-improvement campaign (https://github.com/Swapnil-jain/integer-mult-kappa, commit 5868dc7) and D. Colkitt, integer-mult-bounds (https://github.com/CrocSwap/integer-mult-bounds); target `IntMul.Kappa.jain_round6_framework`. Lean declaration `IntMul.Kappa.R6.Cx.NetData.chk2_13b`, R6Pk/R6CxNetChk2_13b.lean of the round-six development.

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