
theorem Th13:
  for i being Integer holds |.i.| divides i & i divides |.i.|
proof
  let i be Integer;
  per cases by ABSVALUE:1;
  suppose
    |.i.| = i;
    hence thesis;
  end;
  suppose
A1: |.i.| = -i;
    then
A2: i * (-1) = |.i.|;
    |.i.| * (-1) = i by A1;
    hence thesis by A2,INT_1:def 3;
  end;
end;
