Pair Graph Prepared5 — indexed coverage checked
ProvedD1Bound5.PairGraphPrepared5.indexed_coverage_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairGraphPrepared5.indexed_coverage_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 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_Coordinates_Definitions import Definitions.Def_D1Bound5_PairClosureWitness_Definitions import Definitions.Def_D1Bound5_SmallPairGraphInputs5_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphInputs5_Definitions_002 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData5_Definitions_001 import Definitions.Def_D1Bound5_SmallPairGraphWitnessData5_Definitions_003
Formal statement
section
namespace D1Bound5.PairGraphPrepared5
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairGraphPrepared5.indexed_coverage_checked :
decide (anchorRoot * anchorRoot = smallPairA_5 * smallPairB_5 + 1 ∧
witnesses.map PairRootWitness.vertex = smallPairClosure_5) = true := by sorry
end D1Bound5.PairGraphPrepared5
end
Source
D1Bound5/SmallPairGraphClosure5Coverage.lean, lines 9-29, SHA-256 0aaa2d7ada192fdd32f641f50b6643c28bf90681f2f9f3bbc105b9aa512c9b30. Project: https://github.com/tomislav-math/d1-bound5-lean