theorem
  idseq n | Seg m = idseq m iff m <= n
proof
  thus idseq n | Seg m = idseq m implies m <= n
  proof
    assume idseq n | Seg m = idseq m;
    then len idseq m <= len idseq n by FINSEQ_1:79;
    then m <= len idseq n by CARD_1:def 7;
    hence thesis by CARD_1:def 7;
  end;
  assume m <= n;
  then ex j being Nat st n = m + j by NAT_1:10;
  hence thesis by Th48;
end;
