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
  t <> {} & s *' t <=' r *' t implies s <=' r
proof
  assume that
A1: t <> {} and
A2: s *' t <=' r *' t;
  ex x st s*'t = t*'x & x <=' r by A2,Th79;
  hence thesis by A1,Th56;
end;
