theorem
  x in dom f implies x .--> f.x c= f
proof
A1: now
    let y be object;
    assume y in dom (x .--> f.x);
    then x = y by FUNCOP_1:75;
    hence (x .--> f.x).y = f.y by FUNCOP_1:72;
  end;
  assume
A2: x in dom f;
  dom (x .--> f.x) c= dom f
  by A2,FUNCOP_1:75;
  hence thesis by A1,GRFUNC_1:2;
end;
