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;

theorem Th32:
  X c= Rank A iff X in Rank succ A
proof
  thus X c= Rank A implies X in Rank succ A
  proof
    assume X c= Rank A;
then  X in bool Rank A;
    hence thesis by Lm2;
  end;
  assume X in Rank succ A;
then  X in bool Rank A by Lm2;
  hence thesis;
end;
