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
  r <=' s + t implies ex s0,t0 being Element of RAT+ st r = s0 + t0 & s0
  <=' s & t0 <=' t
proof
  assume
A1: r <=' s + t;
  per cases;
  suppose
    s <=' r;
    then
    s <=' s & ex t0 being Element of RAT+ st r = s + t0 & t0 <=' t by A1,Th86;
    hence thesis;
  end;
  suppose
A2: r <=' s;
    r = r+{} & {} <=' t by Th50,Th64;
    hence thesis by A2;
  end;
end;
