Pair Light Prepared3 — left signatures checked

Proved

D1Bound5.PairLightPrepared3.left_signatures_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared3.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 Mathlib.Data.List.Basic
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData3Left_Definitions_001
import Definitions.Def_D1Bound5_SmallPairLightData3Left_Definitions_002

Formal statement

section
namespace D1Bound5.PairLightPrepared3
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.PairLightPrepared3.left_signatures_checked :
    (leftCached.all fun x => decide (x.2 = pairLightCoordinateSignature sieve x.1)) = true := by sorry





end D1Bound5.PairLightPrepared3
end

Source

D1Bound5/SmallPairLightLeft3.lean, lines 15-17, SHA-256 1770bf0be106ea0293f60a3735aac7731bcb6a6d6f3ccfc30bbf853b9350e773. Project: https://github.com/tomislav-math/d1-bound5-lean

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