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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">r58</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: FIELD_14:28</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">S1</font>, <font color="Olive" title="b3">S2</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">p</font> being   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S1</font><br/>  for <font color="Olive" title="b5">q</font> being   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b3">S2</font>  st <font color="Olive" title="b2">S1</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Olive" title="b3">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><font color="Olive" title="b4">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b5">q</font> is   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">R</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">S1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">S2</font></span>)</span></div></div>
