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 Th66:
  r <=' s & s <=' r implies r = s
proof
  given x such that
A1: s = r+x;
  given y such that
A2: r = s+y;
  r+{} = r by Th50
    .= r+(x+y) by A1,A2,Th51;
  then x = {} by Th62,Th63;
  hence thesis by A1,Th50;
end;
