Small Pair Table 0 2 graph property full ring
ProvedD1Bound5.smallPairTable_0_2_graph_property_full_ringdiophantine-tuplesnumber-theory
Auxiliary result smallPairTable_0_2_graph_property_full_ring 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.Group.Int.Units import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Squarefree.Basic import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.List.Basic import Mathlib.Data.List.Range 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.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_SmallExtensionSymmetry_Definitions import Definitions.Def_D1Bound5_SmallPairClassificationData_Definitions import Definitions.Def_D1Bound5_SmallPairGraphSymmetry_Definitions
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.smallPairTable_0_2_graph_property_full_ring
{K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
(hK : finrank ℚ K = 2) (phi : K →+* ℂ)
(e : QuadInt 0 2 ≃+* 𝓞 K)
(row : Finset (ℤ × ℤ)) (hrow : row ∈ smallPairTable 0 2) :
SmallPairGraphProperty (smallCoordinateSet 0 2 row) := by sorry
end D1Bound5
end
Source
D1Bound5/SmallPairOrbitProperties.lean, lines 82-113, SHA-256 4aaf9e9c32b323b6121de5e879d561ffcd195b5099816cb6c0736c14b2987a2e. Project: https://github.com/tomislav-math/d1-bound5-lean