Round-six lemma `c40_ok`
ProvedR6Chk.Bit.Dim2.c40_okcomplexity-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.R6ChkBitDim2):
theorem R6Chk.Bit.Dim2.c40_ok : allL (dimChk supG) c40 = true
Context. Bit round six, h = 23: node dimension records, part 2 of 3 (1521 elements of 8 nodes). Generated by bit_dimexp.py.
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_ChkBitDim2_1 set_option autoImplicit false set_option relaxedAutoImplicit false set_option maxHeartbeats 1000000 open R6Chk R6Chk.Bit R6Chk.Bit.Dim2 open R6Chk R6Chk.Bit
Formal statement
theorem R6Chk.Bit.Dim2.c40_ok : allL (dimChk supG) c40 = 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.Dim2.c40_ok`, Solutions/R6ChkBitDim2.lean (lines 1199–1199) of the round-six development.