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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: ALGGEO_1:20</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">F</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="ring_2.html#K2" title="RING_2:func.2">Ideals</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Polynom-Ring</a> (<font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span></span>)</span> holds   <a href="alggeo_1.html#K6" title="ALGGEO_1:func.6">Zero_</a> <span class="p1">(<span class="default"><a href="alggeo_1.html#K7" title="ALGGEO_1:func.7">union</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="alggeo_1.html#K6" title="ALGGEO_1:func.6">Zero_</a> <font color="Olive" title="b4">I</font></span>)</span> where <font color="Olive" title="b4">I</font> is   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Polynom-Ring</a> (<font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span> : <font color="Olive" title="b4">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">F</font> </span> } </span> </div></div>
