Pair Light Closure Prepared6 — original witnesses checked
ProvedD1Bound5.PairLightClosurePrepared6.original_witnesses_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairLightClosurePrepared6.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_SmallPairGraphInputs6_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphInputs6_Definitions_002 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData6_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData6_Definitions_003
Formal statement
section
namespace D1Bound5.PairLightClosurePrepared6
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairLightClosurePrepared6.original_witnesses_checked :
pairIndexedWitnessesCheckedBool smallPairA_6 smallPairB_6 PairGraphPrepared6.anchorRoot
(10^1100) smallPairClosure_6 PairGraphPrepared6.witnesses PairGraphPrepared6.destinations = true := by sorry
end D1Bound5.PairLightClosurePrepared6
end
Source
D1Bound5/SmallPairPureClosureAdapter6.lean, lines 17-29, SHA-256 3bc9090e96edc7c62853a7dae56534f9ddc63473766945ac647cc9e4f2c93c73. Project: https://github.com/tomislav-math/d1-bound5-lean