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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">ZZ1a</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: FIELD_14:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">S</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">F</font><br/>  for <font color="Olive" title="b3">p</font> being   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">q</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>   <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font>  st <font color="Olive" title="b3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b4">q</font> is   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">F</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">S</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</a> <font color="Olive" title="b4">q</font></span>)</span></span>)</span> holds <br/><font color="Olive" title="b4">q</font> is   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">F</font>,<span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</a> <font color="Olive" title="b4">q</font></span>)</span></div></div>
