Pair Light Closure Prepared14 — original witnesses checked
ProvedD1Bound5.PairLightClosurePrepared14.original_witnesses_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairLightClosurePrepared14.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_SmallPairGraphInputs14_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphInputs14_Definitions_002 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData14_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData14_Definitions_003
Formal statement
section
namespace D1Bound5.PairLightClosurePrepared14
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairLightClosurePrepared14.original_witnesses_checked :
pairIndexedWitnessesCheckedBool smallPairA_14 smallPairB_14 PairGraphPrepared14.anchorRoot
(10^1100) smallPairClosure_14 PairGraphPrepared14.witnesses PairGraphPrepared14.destinations = true := by sorry
end D1Bound5.PairLightClosurePrepared14
end
Source
D1Bound5/SmallPairPureClosureAdapter14.lean, lines 17-29, SHA-256 dcbec461e3834bd41ce1a122d5dc0b892beaa11b2dcd99196523459ba8dfaa81. Project: https://github.com/tomislav-math/d1-bound5-lean