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
  k <> 0 implies k in Seg(k + n)
proof
  assume k <> 0;
  then
A1: 0 + 1 <= k by NAT_1:13;
  k <= k + n by NAT_1:12;
  hence thesis by A1,FINSEQ_1:1;
end;
