
theorem lemiso:
for X,Y being non empty finite set st card Y = card X
ex f being Function of X,Y st f is bijective
proof
  let X,Y be non empty finite set;
assume card Y = card X;
then X,Y are_equipotent by CARD_1:5;
then consider f be Function such that
   F: f is one-to-one & dom f = X & rng f = Y by WELLORD2:def 4;
reconsider f as Function of X,Y by F,FUNCT_2:1;
take f;
f is onto by F,FUNCT_2:def 3;
hence thesis by F;
end;
