theorem Th29:
  i <= 0 implies h |^ i = (h |^ |.i.|)"
proof
  assume
A1: i <= 0;
  per cases by A1;
  suppose
    i < 0;
    hence thesis by Def8;
  end;
  suppose
A2: i = 0;
    hence h |^ i = 1_G by Lm3
      .= (1_G)" by Th8
      .= (h |^ 0)" by Def7
      .= (h |^ |.i.|)" by A2,ABSVALUE:def 1;
  end;
end;
