reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;
reserve x for set;
reserve x for object;

theorem
  for f, g, h being Function st f c= g & dom f misses dom h holds f c= g +* h
proof
  let f, g, h be Function;
  assume f c= g;
  then
A1: f +* h c= g +* h by Th123;
  assume dom f misses dom h;
  then f c= f +* h by Th32;
  hence thesis by A1;
end;
