theorem
  rng f c= rng g & x in dom f implies
   ex y being object st y in dom g & f.x = g. y
proof
  assume that
A1: rng f c= rng g and
A2: x in dom f;
  f.x in rng f by A2,FUNCT_1:3;
  hence thesis by A1,FUNCT_1:def 3;
end;
