theorem
  [x,z] in (g*f) implies [x,f.x] in f & [f.x,z] in g
proof
  assume [x,z] in (g*f);
  then ex y being object st [x,y] in f & [y,z] in g by RELAT_1:def 8;
  hence thesis by FUNCT_1:1;
end;
