theorem Th59:
  still_not-bound_in <*p*> = still_not-bound_in p
proof
A1: now
    1 in Seg 1 by FINSEQ_1:2,TARSKI:def 1;
    then
A2: 1 in dom <*p*> by FINSEQ_1:38;
A3: p = <*p*>.1;
    let b be object;
    assume b in still_not-bound_in p;
    hence b in still_not-bound_in <*p*> by A2,A3,Def5;
  end;
  now
    let b be object;
    assume b in still_not-bound_in <*p*>;
    then consider i,q such that
A4: i in dom <*p*> and
A5: q = <*p*>.i & b in still_not-bound_in q by Def5;
    i in Seg 1 by A4,FINSEQ_1:38;
    then i = 1 by FINSEQ_1:2,TARSKI:def 1;
    hence b in still_not-bound_in p by A5;
  end;
  hence thesis by A1,TARSKI:2;
end;
