theorem Th50:
  A c= B & C c= D implies commutators(A,C) c= commutators(B,D)
proof
  assume
A1: A c= B & C c= D;
  let x be object;
  assume x in commutators(A,C);
  then ex a,c st x = [.a,c.] & a in A & c in C;
  hence thesis by A1;
end;
