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;

theorem
 for x,y,z being object holds
  f.z <> x implies (f+~(x,y)).z = f.z
proof let x,y,z be object;
  assume f.z <> x;
  then not f.z in dom(x.-->y) by FUNCOP_1:75;
  then not z in dom((x.-->y)*f) by FUNCT_1:11;
  hence thesis by Th11;
end;
