theorem
  A c= B+ implies A+ c= B+
proof
  assume A c= B+;
  then A c= B |^.. 1 by Th50;
  then A |^.. 1 c= B |^.. 1 by Th29;
  then A+ c= B |^.. 1 by Th50;
  hence thesis by Th50;
end;
