Ordinary Log10 mul

Proved

D1Bound5.ordinaryLog10_mul

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

diophantine-tuplesnumber-theory

Auxiliary result ordinaryLog10_mul 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_mul (x y : ℝ) (hx : x ≠ 0) (hy : y ≠ 0) :
    ordinaryLog10 (x*y) = ordinaryLog10 x+ordinaryLog10 y := by sorry

















end D1Bound5
end

Source

D1Bound5/OrdinaryLog10.lean, lines 10-13, SHA-256 09aeaea7ebd8948074c88ecfb8ed793209871b3b024d7443a02f1048da4ea91c. Project: https://github.com/tomislav-math/d1-bound5-lean

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