reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem Th3:
  for f,g being Function st X c= dom f & f.:X c= dom g holds X c= dom(g*f)
proof
  let f,g be Function such that
A1: X c= dom f and
A2: f.:X c= dom g;
  let x be object;
  assume
A3: x in X;
  then f.x in f.:X by A1,FUNCT_1:def 6;
  hence thesis by A1,A2,A3,FUNCT_1:11;
end;
