Pair Light Closure Prepared4 — all checked

Proved

D1Bound5.PairLightClosurePrepared4.all_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightClosurePrepared4.all_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_PairLightClosure_Definitions
import Definitions.Def_D1Bound5_SmallPairPureClosureData4Destinations_Definitions
import Definitions.Def_D1Bound5_SmallPairPureClosureData4Vertices_Definitions
import Definitions.Def_D1Bound5_SmallPairPureClosureData4_Definitions

Formal statement

section
namespace D1Bound5.PairLightClosurePrepared4
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.PairLightClosurePrepared4.all_checked :
    pairLightIndexedWitnessesCheckedBool 0 1 a b anchorRoot (10^1100) vertices
      witnesses destinations = true := by sorry

end D1Bound5.PairLightClosurePrepared4
end

Source

D1Bound5/SmallPairPureClosure4.lean, lines 26-127, SHA-256 8e116481b38ac9917dc95bcf7496c7f591c38f090c3eb5b547156975309b7d25. Project: https://github.com/tomislav-math/d1-bound5-lean

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