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 Th2:
  i <= j implies max(0,i-j) = 0
proof
  assume i <= j;
  then i-i <= j-i by XREAL_1:9;
  then -(j-i) <= -0;
  hence thesis by XXREAL_0:def 10;
end;
