reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

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;
