Kernel range checks of the readout data (`chkRd`)

Proved

IntMul.Kappa.R6.Cx.NetData.chkRd

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

complexity-theoryinteger-multiplicationkappa-improvement

Kernel range checks of the readout data.

The following holds (Lean statement, in the scope of module Solutions.R6CxNetChkMR):

theorem IntMul.Kappa.R6.Cx.NetData.chkRd : (allR (fun j => Nat.blt (dat.rs j) NR) (List.range 24) && Nat.beq dat.pieces.length NV &&
    allR (fun ps => allR (fun p => Nat.blt p.1 NR) ps) dat.pieces) = 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_Defs24
import Definitions.Def_IntMul_Kappa_R6_Data_CxNetData_1

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.NetSpec IntMul.Kappa.R6.Cx.NetFast IntMul.Kappa.R6.Cx.NetMask

Formal statement

theorem IntMul.Kappa.R6.Cx.NetData.chkRd : (allR (fun j => Nat.blt (dat.rs j) NR) (List.range 24) && Nat.beq dat.pieces.length NV &&
    allR (fun ps => allR (fun p => Nat.blt p.1 NR) ps) dat.pieces) = 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.chkRd`, Solutions/R6CxNetChkMR.lean (lines 22–26) of the round-six development.

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