theorem Th34:
  G is idempotent implies H is idempotent
proof
  assume
A1: G is idempotent;
A2: carr(H) c= carr(G) by Th23;
  now
    let a be Element of H;
    reconsider a9 = a as Element of G by A2;
    thus a*a = a9*a9 by Th25
      .= a by A1,Th7;
  end;
  hence thesis by Th7;
end;
