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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th9</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: HILB10_5:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b2">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Olive" title="b1">n</font><br/>  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">r</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> for <font color="Olive" title="b4">x</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">n</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st (  for <font color="Olive" title="b5">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b4">x</font> holds <br/><span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">r</font> ) holds <br/><span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">eval</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">x</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">r</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default"><a href="uproots.html#K3" title="UPROOTS:func.3">degree</a> <font color="Olive" title="b2">b</font></span>)</span></div></div>
