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 s1,t1,s2,t2 being Element of RAT+ st s1 + t1 = s2 + t2 & s1 <=' s2
  holds t2 <=' t1
proof
  let s1,t1,s2,t2 be Element of RAT+ such that
A1: s1 + t1 = s2 + t2;
  given x such that
A2: s2 = s1+x;
  take x;
  s1+t1 = s1+(x+t2) by A1,A2,Th51;
  hence thesis by Th62;
end;
