theorem Th74:
  g1 in carr(H) & g2 in carr(H) implies g1 + g2 in carr(H)
proof
  assume g1 in carr(H) & g2 in carr(H);
  then g1 in H & g2 in H;
  then g1 + g2 in H by Th50;
  hence thesis;
end;
