reserve W,X,Y,Z for set,
  f,g for Function,
  a,x,y,z for set;
reserve u,v for Element of Tarski-Class(X),
  A,B,C for Ordinal,
  L for Sequence;
reserve n for Element of omega;

theorem Th65:
  X c= Rank A iff the_rank_of X c= A
proof
  thus X c= Rank A implies the_rank_of X c= A by Def9;
  assume the_rank_of X c= A;
then A1: Rank the_rank_of X c= Rank A by Th37;
 X c= Rank the_rank_of X by Def9;
  hence thesis by A1;
end;
