reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;
reserve i,j,k for Element of omega;
reserve x,y,z for Element of RAT+;
reserve i,j,k for natural Ordinal;
reserve r,s,t for Element of RAT+;

theorem
  for r1,r2,s1,s2 being Element of RAT+ st r1+r2 = s1+s2 holds r1 <=' s1
  or r2 <=' s2
proof
  let r1,r2,s1,s2 be Element of RAT+ such that
A1: r1+r2 = s1+s2;
  assume that
A2: s1 < r1 and
A3: s2 < r2;
  s1+s2 < r1+s2 by A2,Th76;
  hence thesis by A1,A3,Th76;
end;
