Prove2Me

Phase Half Polynomial deriv

Proved
D1Bound5.phaseHalfPolynomial_deriv

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

diophantine-tuplesnumber-theory

Auxiliary result phaseHalfPolynomial_deriv 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.Analysis.Calculus.Deriv.MeanValue
import Mathlib.Analysis.Calculus.Deriv.Pow
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_CoupledPhaseBounds_Definitions
Formal statement
section
namespace D1Bound5




theorem _root_.D1Bound5.phaseHalfPolynomial_deriv (q x : ℝ) :
    HasDerivAt (phaseHalfPolynomial q) (-(4-x^2)*phaseCritical q x) x := by sorry











end D1Bound5
end
Source
D1Bound5/CoupledPhaseBounds.lean, lines 10-29, SHA-256 14ad3644c7d0af80f0ec212461e5adea70bec57470ae7e0a8a0ee48d46ce9bc9. Project: https://github.com/tomislav-math/d1-bound5-lean

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