Rational Cutoff mem
ProvedD1Bound5.rationalCutoff_memdiophantine-tuplesnumber-theory
Auxiliary result rationalCutoff_mem 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 Lean.Elab.Tactic.Omega import Lean.Util.CollectAxioms import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.BigOperators.NatAntidiagonal import Mathlib.Algebra.CharP.Frobenius import Mathlib.Algebra.CharP.Two import Mathlib.Algebra.Group.Int.Units import Mathlib.Algebra.Order.BigOperators.Ring.Finset 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.Analytic.Binomial import Mathlib.Analysis.CStarAlgebra.Matrix import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Data.Complex.Basic import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Insert 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.Range import Mathlib.Data.Real.Basic import Mathlib.Data.Sym.Basic import Mathlib.Data.Sym.Card import Mathlib.Data.ZMod.Basic import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Lagrange import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.LinearAlgebra.Matrix.Permutation import Mathlib.LinearAlgebra.Matrix.SchurComplement import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.RingTheory.Binomial import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.Tactic import Mathlib.Tactic.Convert import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.FinCases import Mathlib.Tactic.GCongr import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001 import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_002
Formal statement
section open scoped NumberField namespace D1Bound5 open QuadInt theorem _root_.D1Bound5.rationalCutoff_mem : oneSmallCutoffRow_56 ∈ oneSmallCutoffRows := by sorry end D1Bound5 end
Source
D1Bound5/RationalCutoffHeights.lean, lines 27-27, SHA-256 887e635eec7648e8edc3fcbe9cbb33e7e5e7ef6738dfaf41dfb1deb286dc6f8f. Project: https://github.com/tomislav-math/d1-bound5-lean