Round-six lemma `umt3_eq`
ProvedR6Chk.Bit.umt3_eqAn 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.R6ChkBitDim):
theorem R6Chk.Bit.umt3_eq : allN 64 (fun r => Nat.beq (fieldOf UMT3 1792 r) (umq 3 r 6)) = true
Context. Bit round six (h = 23): soundness of the node-dimension checker
spanS sup = span_ℚ {𝟙_{tri i} : sup.testBit i} (𝟙_{tri i} ∈ ℚ^23 the indicator vector of the
i-th triple). recChk_sound: if recChk sup R = true then finrank ℚ (spanS sup) = d
(the record's claimed dimension); dimChk_sound lifts this to a whole element.
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 open R6Chk Matrix Matrix.Module Module
theorem R6Chk.Bit.umt3_eq : allN 64 (fun r => Nat.beq (fieldOf UMT3 1792 r) (umq 3 r 6)) = true := by sorry