theorem Th9:
  rng a c= dom (f2*f1) implies rng a c= dom f1 & rng (f1/*a) c= dom f2
proof
  assume
A1: rng a c= dom (f2*f1);
  then
A2: f1.:(rng a) c= dom f2 by FUNCT_1:101;
  rng a c= dom f1 by A1,FUNCT_1:101;
  hence thesis by A2,VALUED_0:30;
end;
