Ordinary Log10 two small parameters

Proved

D1Bound5.ordinaryLog10_two_small_parameters

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

diophantine-tuplesnumber-theory

Auxiliary result ordinaryLog10_two_small_parameters 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

Formal statement

section
namespace D1Bound5













theorem _root_.D1Bound5.ordinaryLog10_two_small_parameters :
    ordinaryLog10 1134 < (31/10 : ℝ) ∧
      -(9/10 : ℝ) < ordinaryLog10 (2/15) ∧
      ordinaryLog10 2277 < (17/5 : ℝ) := by sorry

end D1Bound5
end

Source

D1Bound5/TwoSmallHeightScalar.lean, lines 56-67, SHA-256 2fc4438e81abf1fb9766cd269fcc8b00c95036ba7e21a2aa00ca22bc65122f73. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph