Ordinary Log10 pow

Proved

D1Bound5.ordinaryLog10_pow

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

diophantine-tuplesnumber-theory

Auxiliary result ordinaryLog10_pow 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_pow (x : ℝ) (n : ℕ) :
    ordinaryLog10 (x^n) = n*ordinaryLog10 x := by sorry















end D1Bound5
end

Source

D1Bound5/OrdinaryLog10.lean, lines 15-18, SHA-256 09aeaea7ebd8948074c88ecfb8ed793209871b3b024d7443a02f1048da4ea91c. Project: https://github.com/tomislav-math/d1-bound5-lean

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