Pair Light Closure Prepared28 — original witnesses checked
ProvedD1Bound5.PairLightClosurePrepared28.original_witnesses_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairLightClosurePrepared28.original_witnesses_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.Algebra.Order.Ring.Abs import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.ZMod.Basic import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_PairClosureIndexedWitness_Definitions import Definitions.Def_D1Bound5_SmallPairGraphInputs28_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphInputs28_Definitions_002 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData28_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData28_Definitions_003
Formal statement
section
namespace D1Bound5.PairLightClosurePrepared28
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairLightClosurePrepared28.original_witnesses_checked :
pairIndexedWitnessesCheckedBool smallPairA_28 smallPairB_28 PairGraphPrepared28.anchorRoot
(10^1100) smallPairClosure_28 PairGraphPrepared28.witnesses PairGraphPrepared28.destinations = true := by sorry
end D1Bound5.PairLightClosurePrepared28
end
Source
D1Bound5/SmallPairPureClosureAdapter28.lean, lines 17-29, SHA-256 d9201a8656a6d59646eca9f2677b2d6eade0b4907b0942cb3d044c5c407e86af. Project: https://github.com/tomislav-math/d1-bound5-lean