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<div><span class="kw">theorem </span><a NAME="T37"><span class="comment"><font color="firebrick">:: ALGGEO_1:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">n</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b3">V</font>, <font color="Olive" title="b4">W</font> being   <a href="alggeo_1.html#NM1" title="ALGGEO_1:NM.1">Algebraic_Set</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font> holds <br/> ( <font color="Olive" title="b3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">W</font> iff  <a href="alggeo_1.html#K10" title="ALGGEO_1:func.10">Ideal_</a> <font color="Olive" title="b3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="alggeo_1.html#K10" title="ALGGEO_1:func.10">Ideal_</a> <font color="Olive" title="b4">W</font> )</div></div>
