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 st f is one-to-one holds card dom f = card rng f
proof
  let f be Function;
  assume
A1:  f is one-to-one;
  f .: dom f = rng f by RELAT_1:113;
  hence thesis by A1,Th4,Th32;
end;
