theorem
  (i * a) * b = i * (a * b)
proof
  per cases;
  suppose
    i >= 0;
    then i = |.i.| by ABSVALUE:def 1;
    hence thesis by Lm4;
  end;
  suppose
A1: i < 0;
    hence (i * a) * b = (-(|.i.| * a)) * b by Th29
      .= -((|.i.| * a) * b) by Th26
      .= -(|.i.| * (a * b)) by Lm4
      .= i * (a * b) by A1,Th29;
  end;
end;
