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;

theorem
  for f being Function
  st dom f is infinite & f is one-to-one holds rng f is infinite
proof
  let f be Function;
  assume
A1: dom f is infinite;
  assume f is one-to-one;
  then dom f,rng f are_equipotent;
  hence thesis by A1,Th37;
end;
