Two small M window brackets

Proved

D1Bound5.two_small_M_window_brackets

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

diophantine-tuplesnumber-theory

Auxiliary result two_small_M_window_brackets 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.Algebra.Order.Floor.Semiring
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_OrdinaryLog10_Definitions
import Definitions.Def_D1Bound5_TwoSmallHeightScalar_Definitions

Formal statement

section
namespace D1Bound5



theorem _root_.D1Bound5.two_small_M_window_brackets
    (C D : ℝ) (hC : (10 : ℝ)^100 ≤ C)
    (hlow : C^7/(10 : ℝ)^50 < D)
    (hhigh : ordinaryLog10 D < twoSmallHeightEnvelope (ordinaryLog10 C))
    (hD : 0 < D) :
    (10 : ℝ)^143*C^5 ≤ D ∧ D ≤ C^11/(10 : ℝ)^87 := by sorry

end D1Bound5
end

Source

D1Bound5/TwoSmallMWindow.lean, lines 41-84, SHA-256 01923ebf8661b40e7df02a892c03d641336b952c4de01415c43f072023fbf04f. Project: https://github.com/tomislav-math/d1-bound5-lean

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