reserve A for QC-alphabet;
reserve k,n,m for Nat;
reserve P for QC-pred_symbol of A;
reserve F for Element of QC-WFF(A);
reserve Q for QC-pred_symbol of A;
reserve F, G for (Element of QC-WFF(A)), s for FinSequence;
reserve p for Element of QC-WFF(A);
reserve F for Element of QC-WFF(A);
reserve p for Element of QC-WFF(A);
reserve j,k for Nat;
reserve k for Nat;
reserve s,t,u,v for QC-symbol of A;

theorem
  t <= t+n
proof
  defpred P[Nat] means t <= t + $1;
A1: P[0]
  proof
    consider f being sequence of QC-symbols(A) such that
A2:  t + 0 = f.0 & f.0 = t & for k holds f.(k+1) = (f.k)++ by Def40;
    thus thesis by A2,Th22;
  end;
A3: for k st P[k] holds P[k+1]
  proof
    let k such that
A4:  t <= t + k;
    consider f being sequence of QC-symbols(A) such that
A5:  t + (k+1) = f.(k+1) & f.0 = t & for k holds f.(k+1) = (f.k)++ by Def40;
    f.k = t + k by A5,Def40;
    then f.(k+1) = (t + k)++ by A5;
    then t < t + (k+1) by A5,A4,Th27,Th29;
    hence thesis;
  end;
  for n holds P[n] from NAT_1:sch 2(A1,A3);
  hence thesis;
end;
