Window overlap of ratio
ProvedD1Bound5.window_overlap_of_ratiodiophantine-tuplesnumber-theory
Auxiliary result window_overlap_of_ratio 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 Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.BigOperators.Group.Finset.Sigma import Mathlib.Algebra.BigOperators.NatAntidiagonal import Mathlib.Algebra.CharZero.Infinite import Mathlib.Algebra.Order.Archimedean.Real.Basic import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Operations import Mathlib.Algebra.Polynomial.Div import Mathlib.Algebra.Polynomial.PartialFractions import Mathlib.Algebra.Polynomial.Reverse import Mathlib.Algebra.Polynomial.RingDivision import Mathlib.Algebra.Polynomial.Roots import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Analytic.Binomial import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Analysis.Normed.Ring.InfiniteSum import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral import Mathlib.Analysis.SpecialFunctions.Pow.Real import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Combinatorics.Enumerative.Catalan.Basic import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Insert import Mathlib.Data.Int.GCD import Mathlib.Data.Sym.Basic import Mathlib.Data.Sym.Card import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Lagrange import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.LinearAlgebra.Matrix.Polynomial import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.RingTheory.Binomial import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.RingTheory.PowerSeries.Binomial import Mathlib.RingTheory.PowerSeries.Trunc import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.FinCases import Mathlib.Tactic.GCongr import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring import Mathlib.Topology.Algebra.InfiniteSum.Order
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.window_overlap_of_ratio (l u q : ℝ) (hl : 0 < l)
(heq : u/l=q) (hq : 1 < q) : l < u := by sorry
end D1Bound5
end
Source
D1Bound5/AllLargeWindows.lean, lines 40-43, SHA-256 8a55028f795f579ca9d48bce231b9a089c1b85f46e7e028019c12a2849cb716c. Project: https://github.com/tomislav-math/d1-bound5-lean