Pair Light Prepared7 — left signatures checked

Proved

D1Bound5.PairLightPrepared7.left_signatures_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared7.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_SmallPairLightData7LeftCached_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData7Sieve_Definitions

Formal statement

section
namespace D1Bound5.PairLightPrepared7
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.PairLightPrepared7.left_signatures_checked :
    (leftCached.all fun x => decide (x.2 = pairLightCoordinateSignature sieve x.1)) = true := by sorry





end D1Bound5.PairLightPrepared7
end

Source

D1Bound5/SmallPairLightLeft7.lean, lines 15-17, SHA-256 fa341391c689760774753aa543fae5a4aa3060e7402ca421f1073319ec6a4dcb. Project: https://github.com/tomislav-math/d1-bound5-lean

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