reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;
reserve S for Sequence;
reserve k,n,m for Nat;
reserve l for Element of omega;

theorem
 for f being Function, x,y being object
 holds card(f+~(x,y)) = card f
proof let f be Function,x,y be object;
 thus card(f+~(x,y)) = card dom(f+~(x,y)) by Th60
    .= card dom f by FUNCT_4:99
    .= card f by Th60;
end;
