reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem
  i in Seg (l+1) implies i in Seg l or i = l+1
proof
A0: i is Nat by TARSKI:1;
  assume
A1: i in Seg(l+1);
  then i <= l+1 by FINSEQ_1:1;
  then 1 <= i & i <= l or i = l+1 by A1,FINSEQ_1:1,NAT_1:8;
  hence thesis by A0;
end;
