Finite PAdaptive Rate pos

Proved

D1Bound5.finitePAdaptiveRate_pos

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finitePAdaptiveRate_pos 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.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FinitePAdaptiveResidual_Definitions

Formal statement

section
namespace D1Bound5











theorem _root_.D1Bound5.finitePAdaptiveRate_pos (x : ℝ) (hx : 0 ≤ x) : 0 < finitePAdaptiveRate x := by sorry



end D1Bound5
end

Source

D1Bound5/FinitePAdaptiveResidual.lean, lines 42-44, SHA-256 25fa69daa14e28209c09660c5858b952ff9e39422be6b297ad69d024782cb11b. Project: https://github.com/tomislav-math/d1-bound5-lean

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