Pair Light Adaptive Prepared9 — left signatures checked

Proved

D1Bound5.PairLightAdaptivePrepared9.left_signatures_checked

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result PairLightAdaptivePrepared9.left_signatures_checked in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Init
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData9_Definitions_001

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared9
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.PairLightAdaptivePrepared9.left_signatures_checked :
    (PairLightPrepared9.leftCached.all fun x =>
      decide (x.2 = pairLightCoordinateSignature PairLightPrepared9.sieve x.1)) = true := by sorry






end D1Bound5.PairLightAdaptivePrepared9
end

Source

D1Bound5/SmallPairLightAdaptiveValidation9.lean, lines 11-14, SHA-256 d9314bf52983f4e24aa6ebb4747df3e0b262bbfcf418314de945cc7966c01d52. Project: https://github.com/tomislav-math/d1-bound5-lean

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