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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: LIOUVIL2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">S</font> being    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">g</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g</font> holds <br/> <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b4">g</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="liouvil2.html#T8" target="_self" onmouseover="rs('liouvil2/T8')" onmouseout="rh()">Th9</a></span>;<br/></div></div>
