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<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>set </b><font color="Maroon">p</font> =  <a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font>;<br/>
<a NAME="E1:57"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1
 
<b>by </b><i><a class="ref" href="uniroots.html#T2" target="_self">Th2</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i/>
;<br/>
<b>hence </b> <a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font> = 
 <a href="uproots.html#K10">poly_with_roots</a> <span class="p1">(<span class="default"><a href="uproots.html#K8">BRoots</a> <span class="p2">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="uproots.html#T67">UPROOTS:67</a></i>
<br/>.= 
 <a href="uproots.html#K10">poly_with_roots</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="uniroots.html#K2" target="_self">-roots_of_1</a> </span>)</span>,1 <a href="uproots.html#K2">-bag</a> </span>)</span>
<b>by </b><i><a class="ref" href="uniroots.html#T3" target="_self">Th3</a></i>
;<br/><br/>


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