number_theory.basicMathlib.NumberTheory.Basic

This file has been ported!

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(no changes)

(last sync)

Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -35,7 +35,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h
   by
   induction' k with k ih
   · rwa [pow_one, pow_zero, pow_one, pow_one]
-  rw [pow_succ' p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ]
+  rw [pow_succ p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ']
   refine' mul_dvd_mul _ ih
   let I : Ideal R := span {p}
   let f : R →+* R ⧸ I := mk I
Diff
@@ -40,7 +40,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h
   let I : Ideal R := span {p}
   let f : R →+* R ⧸ I := mk I
   have hp : (p : R ⧸ I) = 0 := by rw [← map_natCast f, eq_zero_iff_mem, mem_span_singleton]
-  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h 
+  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h
   rw [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, RingHom.map_pow,
     RingHom.map_pow, h, geom_sum₂_self, hp, MulZeroClass.zero_mul]
 #align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_sub
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 -/
-import Mathbin.Algebra.GeomSum
-import Mathbin.RingTheory.Ideal.Quotient
+import Algebra.GeomSum
+import RingTheory.Ideal.Quotient
 
 #align_import number_theory.basic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
-
-! This file was ported from Lean 3 source module number_theory.basic
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GeomSum
 import Mathbin.RingTheory.Ideal.Quotient
 
+#align_import number_theory.basic from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Basic results in number theory
 
Diff
@@ -32,6 +32,7 @@ section
 
 open Ideal Ideal.Quotient
 
+#print dvd_sub_pow_of_dvd_sub /-
 theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k :=
   by
@@ -46,6 +47,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h
   rw [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, RingHom.map_pow,
     RingHom.map_pow, h, geom_sum₂_self, hp, MulZeroClass.zero_mul]
 #align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_sub
+-/
 
 end
 
Diff
@@ -42,7 +42,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h
   let I : Ideal R := span {p}
   let f : R →+* R ⧸ I := mk I
   have hp : (p : R ⧸ I) = 0 := by rw [← map_natCast f, eq_zero_iff_mem, mem_span_singleton]
-  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h
+  rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h 
   rw [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, RingHom.map_pow,
     RingHom.map_pow, h, geom_sum₂_self, hp, MulZeroClass.zero_mul]
 #align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_sub
Diff
@@ -32,12 +32,6 @@ section
 
 open Ideal Ideal.Quotient
 
-/- warning: dvd_sub_pow_of_dvd_sub -> dvd_sub_pow_of_dvd_sub is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)) -> (forall (k : Nat), Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)) -> (forall (k : Nat), Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k))))
-Case conversion may be inaccurate. Consider using '#align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_subₓ'. -/
 theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k :=
   by
Diff
@@ -36,7 +36,7 @@ open Ideal Ideal.Quotient
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)) -> (forall (k : Nat), Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)) -> (forall (k : Nat), Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)) -> (forall (k : Nat), Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k))))
 Case conversion may be inaccurate. Consider using '#align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_subₓ'. -/
 theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k :=
Diff
@@ -34,7 +34,7 @@ open Ideal Ideal.Quotient
 
 /- warning: dvd_sub_pow_of_dvd_sub -> dvd_sub_pow_of_dvd_sub is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)) -> (forall (k : Nat), Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)) -> (forall (k : Nat), Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)) -> (forall (k : Nat), Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k))))
 Case conversion may be inaccurate. Consider using '#align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_subₓ'. -/
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
 
 ! This file was ported from Lean 3 source module number_theory.basic
-! leanprover-community/mathlib commit 168ad7fc5d8173ad38be9767a22d50b8ecf1cd00
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Ideal.Quotient
 /-!
 # Basic results in number theory
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file should contain basic results in number theory. So far, it only contains the essential
 lemma in the construction of the ring of Witt vectors.
 
Diff
@@ -29,6 +29,12 @@ section
 
 open Ideal Ideal.Quotient
 
+/- warning: dvd_sub_pow_of_dvd_sub -> dvd_sub_pow_of_dvd_sub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) a b)) -> (forall (k : Nat), Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Nat} {a : R} {b : R}, (Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) a b)) -> (forall (k : Nat), Dvd.dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Nat.cast.{u1} R (NonAssocRing.toNatCast.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) a (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) b (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k))))
+Case conversion may be inaccurate. Consider using '#align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_subₓ'. -/
 theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k :=
   by
Diff
@@ -41,7 +41,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h
   have hp : (p : R ⧸ I) = 0 := by rw [← map_natCast f, eq_zero_iff_mem, mem_span_singleton]
   rw [← mem_span_singleton, ← Ideal.Quotient.eq] at h
   rw [← mem_span_singleton, ← eq_zero_iff_mem, RingHom.map_geom_sum₂, RingHom.map_pow,
-    RingHom.map_pow, h, geom_sum₂_self, hp, zero_mul]
+    RingHom.map_pow, h, geom_sum₂_self, hp, MulZeroClass.zero_mul]
 #align dvd_sub_pow_of_dvd_sub dvd_sub_pow_of_dvd_sub
 
 end

Changes in mathlib4

mathlib3
mathlib4
change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

  • pow_succ and pow_succ' have switched their meanings.
  • Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
  • In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
  • the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.
Diff
@@ -30,7 +30,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type*} [CommRing R] {p : ℕ} {a b : R} (h :
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k := by
   induction' k with k ih
   · rwa [pow_one, pow_zero, pow_one, pow_one]
-  rw [pow_succ' p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ]
+  rw [pow_succ p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ']
   refine' mul_dvd_mul _ ih
   let f : R →+* R ⧸ span {(p : R)} := mk (span {(p : R)})
   have hf : ∀ r : R, (p : R) ∣ r ↔ f r = 0 := fun r ↦ by rw [eq_zero_iff_mem, mem_span_singleton]
chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

  • switching to using explicit lemmas that have the intended level of application
  • (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
  • Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

Diff
@@ -30,7 +30,7 @@ theorem dvd_sub_pow_of_dvd_sub {R : Type*} [CommRing R] {p : ℕ} {a b : R} (h :
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k := by
   induction' k with k ih
   · rwa [pow_one, pow_zero, pow_one, pow_one]
-  rw [pow_succ' p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ, Nat.cast_mul]
+  rw [pow_succ' p k, pow_mul, pow_mul, ← geom_sum₂_mul, pow_succ]
   refine' mul_dvd_mul _ ih
   let f : R →+* R ⧸ span {(p : R)} := mk (span {(p : R)})
   have hf : ∀ r : R, (p : R) ∣ r ↔ f r = 0 := fun r ↦ by rw [eq_zero_iff_mem, mem_span_singleton]
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -26,7 +26,7 @@ section
 
 open Ideal Ideal.Quotient
 
-theorem dvd_sub_pow_of_dvd_sub {R : Type _} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
+theorem dvd_sub_pow_of_dvd_sub {R : Type*} [CommRing R] {p : ℕ} {a b : R} (h : (p : R) ∣ a - b)
     (k : ℕ) : (p ^ (k + 1) : R) ∣ a ^ p ^ k - b ^ p ^ k := by
   induction' k with k ih
   · rwa [pow_one, pow_zero, pow_one, pow_one]
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Kenny Lau
-
-! This file was ported from Lean 3 source module number_theory.basic
-! leanprover-community/mathlib commit 168ad7fc5d8173ad38be9767a22d50b8ecf1cd00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GeomSum
 import Mathlib.RingTheory.Ideal.Quotient
 
+#align_import number_theory.basic from "leanprover-community/mathlib"@"168ad7fc5d8173ad38be9767a22d50b8ecf1cd00"
+
 /-!
 # Basic results in number theory
 
feat: port NumberTheory.Basic (#2773)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

Dependencies 8 + 391

392 files ported (98.0%)
161144 lines ported (98.1%)
Show graph

The unported dependencies are