<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">p</font> =  <a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font>;<br/>
<a NAME="E1:56"/><i><font color="Green" title="E47">A1</font></i>: 
 <a href="polynom5.html#K6" title="POLYNOM5:func.6">Roots</a> <span class="p1">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="uniroots.html#K2" title="UNIROOTS:func.2">-roots_of_1</a> 
 
<b>by </b><i><a class="ref" href="uniroots.html#T46" target="_self" title="UNIROOTS:th.46">Th46</a></i>;<br/>
<a NAME="E2:56"/><i><font color="Green" title="E48">A2</font></i>: 
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><a href="uproots.html#K8" title="UPROOTS:func.8">BRoots</a> <span class="p2">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom5.html#K6" title="POLYNOM5:func.6">Roots</a> <span class="p1">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="uproots.html#D9" title="UPROOTS:def.9">UPROOTS:def 9</a></i>;<br/>
<i><font color="Green" title="E49">A3</font></i>:  <a href="uproots.html#K4" title="UPROOTS:func.4">degree</a> <span class="p1">(<span class="default"><a href="uproots.html#K8" title="UPROOTS:func.8">BRoots</a> <span class="p2">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
<b>by </b><i><a class="ref" href="uproots.html#T61" title="UPROOTS:th.61">UPROOTS:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
<b>by </b><i><a class="ref" href="uniroots.html#T44" target="_self" title="UNIROOTS:th.44">Th44</a></i>
<br/>.= 
<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
;<br/>
<a NAME="E4:56"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="uniroots.html#K2" title="UNIROOTS:func.2">-roots_of_1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="uniroots.html#T30" target="_self" title="UNIROOTS:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
 <a href="uproots.html#K8" title="UPROOTS:func.8">BRoots</a> <span class="p1">(<span class="default"><a href="uniroots.html#K4" title="UNIROOTS:func.4">unital_poly</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="uniroots.html#K2" title="UNIROOTS:func.2">-roots_of_1</a> </span>)</span>,1 <a href="uproots.html#K2" title="UPROOTS:func.2">-bag</a> 
 <b>by </b><i><a class="txt" href="uniroots.html#E1:56"><i><font color="Green" title="E47">A1</font></i></a>, <a class="txt" href="uniroots.html#E2:56"><i><font color="Green" title="E48">A2</font></i></a>, <a class="txt" href="uniroots.html#E3:56"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="uproots.html#T15" title="UPROOTS:th.15">UPROOTS:15</a></i>;<br/>


</div>
