reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem
  max(0,i-j) is Element of NAT
proof
  per cases;
  suppose
    i <= j;
    hence thesis by Th2;
  end;
  suppose
A1: j <= i;
    then i - j is Element of NAT by NAT_1:21;
    hence thesis by A1,Th3;
  end;
end;
