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;
