reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem
  X c= Y implies Lim X c= Lim Y
proof
  assume
A1: X c= Y;
  let x be object;
  assume x in Lim X;
  then x in X & ex A st x = A & A is limit_ordinal by ORDINAL1:def 10;
  hence thesis by A1,ORDINAL1:def 10;
end;
