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