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 Th8:
  not k + 1 in Seg k
proof
  assume k + 1 in Seg k;
  then
A1: k + 1 <= k by FINSEQ_1:1;
  k <= k + 1 by NAT_1:12;
  then k + 0 = k + 1 by A1,XXREAL_0:1;
  hence thesis;
end;
