
theorem Th2:
  for X being infinite set ex f being sequence of  X st f is one-to-one
proof
  let X be infinite set;
  card NAT c= card X by CARD_3:85;
  then consider f being Function such that
A1: f is one-to-one and
A2: dom f = NAT and
A3: rng f c= X by CARD_1:10;
  for x being object st x in NAT holds f.x in X by A3,A2,FUNCT_1:3;
  then reconsider f as sequence of X by A2,FUNCT_2:3;
  take f;
  thus thesis by A1;
end;
