Pair Graph Prepared28 — indexed coverage checked
ProvedD1Bound5.PairGraphPrepared28.indexed_coverage_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairGraphPrepared28.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_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.PairGraphPrepared28
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairGraphPrepared28.indexed_coverage_checked :
decide (anchorRoot * anchorRoot = smallPairA_28 * smallPairB_28 + 1 ∧
witnesses.map PairRootWitness.vertex = smallPairClosure_28) = true := by sorry
end D1Bound5.PairGraphPrepared28
end
Source
D1Bound5/SmallPairGraphClosure28Coverage.lean, lines 9-29, SHA-256 19e8d6ac1e2633f9b0400c64db2fd87b2ce3eb6a077bf71b1af1e2168b430053. Project: https://github.com/tomislav-math/d1-bound5-lean