Round-six lemma `cov_chk`
ProvedR6Chk.Bit.Loc.cov_chkAn 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.R6BitNBDimCov):
theorem R6Chk.Bit.Loc.cov_chk : (fun r : Bool × ℕ => r.1 && Nat.ble 36513 r.2) (dimAll.foldl covStep (true, 0)) = true
Context. Round six, bit network: the node dimension table DIMT is certified
The dimension records of R6ChkBitDim0..2 list the nodes 0, 1, 2, … in order; the kernel
checks that they cover all 36513 nodes and agree with dimN (the 5-bit table used by the
local programs). Hence finrank ℚ (spanS (supG n)) = dimN n for every node n.
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_Defs51 set_option autoImplicit false set_option relaxedAutoImplicit false set_option maxHeartbeats 1000000 open R6Chk R6Chk.Bit R6Chk.Bit.Loc open R6Chk R6Chk.Bit
theorem R6Chk.Bit.Loc.cov_chk : (fun r : Bool × ℕ => r.1 && Nat.ble 36513 r.2) (dimAll.foldl covStep (true, 0)) = true := by sorry