Round-six lemma `seg1_9`
ProvedR6Chk.Bit.Loc.seg1_9complexity-theoryinteger-multiplicationkappa-improvement
An auxiliary lemma of the round-six development, published as a separate node because its proof is long or shared.
The following holds (Lean statement, in the scope of module Solutions.R6BitNBG1_9):
theorem R6Chk.Bit.Loc.seg1_9 : segChk SG1_9 SG1_10 CN1_9 (segW1 9) = true
Context. Round-six bit invocation: kernel check of the label generator, stage 1, segment 9.
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_Defs51 import Definitions.Def_IntMul_Kappa_R6_Data_BitNBGenData_1 set_option autoImplicit false set_option relaxedAutoImplicit false set_option maxHeartbeats 1000000 open R6Chk R6Chk.Bit R6Chk.Bit.Loc
Formal statement
theorem R6Chk.Bit.Loc.seg1_9 : segChk SG1_9 SG1_10 CN1_9 (segW1 9) = 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 `R6Chk.Bit.Loc.seg1_9`, Solutions/R6BitNBG1_9.lean (lines 10–10) of the round-six development.