On `Wp`, the coordinates in `Q` determine the vector (round six, `eq_zero_of_Q`)
ProvedR6Chk.Bit.eq_zero_of_QOn Wp, the coordinates in Q determine the vector.
The following holds (Lean statement, in the scope of module Solutions.R6ChkBitDim):
theorem R6Chk.Bit.eq_zero_of_Q {c Q : ℕ} (hc : c < 23) {L : List (ℕ × ℕ × ℕ)} (hcf : ∀ e ∈ L, CompFacts c Q e)
{x : Fin 23 → ℚ} (hx : x ∈ Wp c L) (hQ : ∀ p ∈ F Q, x p = 0) : x = 0
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.eq_zero_of_Q {c Q : ℕ} (hc : c < 23) {L : List (ℕ × ℕ × ℕ)} (hcf : ∀ e ∈ L, CompFacts c Q e)
{x : Fin 23 → ℚ} (hx : x ∈ Wp c L) (hQ : ∀ p ∈ F Q, x p = 0) : x = 0 := by sorry