reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

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;
