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;
