theorem Th2:
  k+1 in Seg n iff k < n
  proof
    thus k+1 in Seg n implies k < n
    proof
      assume k+1 in Seg n; then
      k + 1 <= n by FINSEQ_1:1;
      hence k < n by NAT_1:13;
    end;
    thus thesis by FINSEQ_3:11;
  end;
