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<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">ni</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>let </b><font color="Maroon" title="c3">q</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:70"/><i><font color="Green" title="E62">A1</font></i>: 
( <font color="Maroon" title="c2">ni</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">ni</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">qc</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E2:70"/><i><font color="Green" title="E63">A2</font></i>: 
<font color="Maroon" title="c4">qc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">j</font>, <font color="Maroon" title="c6">k</font>, <font color="Maroon" title="c7">l</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:70"/><i><font color="Green" title="E64">A3</font></i>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c4">qc</font>
 <b>and </b><br/><a NAME="E4:70"/><i><font color="Green" title="E65">A4</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</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>,<font color="Maroon" title="c4">qc</font>
 <b>and </b><br/><a NAME="E5:70"/><i><font color="Green" title="E66">A5</font></i>: 
<font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</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="c2">ni</font></span>)</span>,<font color="Maroon" title="c4">qc</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">ttt</font> = <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="c2">ni</font></span>)</span> <a href="polynom3.html#K15" title="POLYNOM3:func.15">*'</a> <span class="p1">(<span class="default"><a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c9">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>, <font color="Maroon" title="c10">p</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> <b> such that </b><br/><a NAME="E7:70"/><i><font color="Green" title="E67">A6</font></i>: 
<font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <font color="Maroon" title="c9">f</font>
 <b>and </b><br/><a NAME="E8:70"/><i><font color="Green" title="E68">A7</font></i>: 
 <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 <b>and </b><br/><a NAME="E9:70"/><i><font color="Green" title="E69">A8</font></i>: 
for <font color="Olive" title="b1">i</font> being 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>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/>( ( (  not <font color="Olive" title="b1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> or <font color="Olive" title="b1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> or <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> ) implies <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">%&gt;</a></span> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> &amp; not <font color="Olive" title="b1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font> implies <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Olive" title="b1">i</font> ) )
 <b>and </b><br/><a NAME="E10:70"/><i><font color="Green" title="E70">A9</font></i>: 
 <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> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><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="c2">ni</font></span>)</span> <a href="polynom3.html#K15" title="POLYNOM3:func.15">*'</a> <span class="p2">(<span class="default"><a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="polynom3.html#K15" title="POLYNOM3:func.15">*'</a> <font color="Maroon" title="c10">p</font>
 <b>by </b><i><a class="txt" href="uniroots.html#E1:70"><i><font color="Green" title="E62">A1</font></i></a>, <a class="ref" href="uniroots.html#T58" target="_self" title="UNIROOTS:th.58">Th58</a></i>;<br/>
<a NAME="E11:70"/><i><font color="Green" title="E71">A10</font></i>: 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</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>,<font color="Maroon" title="c4">qc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p2">(<span class="default"><span class="p3">(<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="c2">ni</font></span>)</span> <a href="polynom3.html#K15" title="POLYNOM3:func.15">*'</a> <span class="p3">(<span class="default"><a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">qc</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c4">qc</font></span>)</span>
 
<b>by </b><i><a class="txt" href="uniroots.html#E10:70"><i><font color="Green" title="E70">A9</font></i></a>, <a class="ref" href="polynom4.html#T27" title="POLYNOM4:th.27">POLYNOM4:27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">i</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>assume </b><a NAME="E1:70_1"/><i><font color="Green" title="E72">A11</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c9">f</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_1_1"/>
(  not <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> or <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> or <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> or ( <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> &amp; not <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> &amp; <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_1"><b>suppose </b></a><a NAME="E1:70_1_1_1"/>
(  not <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> or <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> or <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_1_1_1"/>
( <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">%&gt;</a></span> or <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c11">i</font> )
 <b>by </b><i><a class="txt" href="uniroots.html#E8:70"><i><font color="Green" title="E68">A7</font></i></a>, <a class="txt" href="uniroots.html#E9:70"><i><font color="Green" title="E69">A8</font></i></a>, <a class="txt" href="uniroots.html#E1:70_1"><i><font color="Green" title="E72">A11</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_2"><b>suppose </b></a><a NAME="E1:70_1_1_2"/>
( <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> &amp; not <font color="Maroon" title="c11">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">ni</font> &amp; <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_1_1_2"/>
( <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="algseq_1.html#K5" title="ALGSEQ_1:func.5">%&gt;</a></span> or <font color="Maroon" title="c9">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="uniroots.html#K6" title="UNIROOTS:func.6">cyclotomic_poly</a> <font color="Maroon" title="c11">i</font> )
 <b>by </b><i><a class="txt" href="uniroots.html#E8:70"><i><font color="Green" title="E68">A7</font></i></a>, <a class="txt" href="uniroots.html#E9:70"><i><font color="Green" title="E69">A8</font></i></a>, <a class="txt" href="uniroots.html#E1:70_1"><i><font color="Green" title="E72">A11</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E13:70"/><b>then </b>
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c4">qc</font> is <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>
 
<b>by </b><i><a class="txt" href="uniroots.html#E2:70"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="uniroots.html#E7:70"><i><font color="Green" title="E67">A6</font></i></a>, <a class="ref" href="uniroots.html#T59" target="_self" title="UNIROOTS:th.59">Th59</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">m</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E15:70"/><i><font color="Green" title="E72">A12</font></i>: 
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c4">qc</font>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">jc</font> = <font color="Maroon" title="c5">j</font>, <font color="Maroon" title="c13">lc</font> = <font color="Maroon" title="c7">l</font>, <font color="Maroon" title="c14">mc</font> = <font color="Maroon" title="c11">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">jcf</font> = <font color="Maroon" title="c12">jc</font>, <font color="Maroon" title="c16">lcf</font> = <font color="Maroon" title="c13">lc</font>, <font color="Maroon" title="c17">mcf</font> = <font color="Maroon" title="c14">mc</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>;<br/>
<a NAME="E18:70"/><i><font color="Green" title="E73">A13</font></i>: 
<font color="Maroon" title="c16">lcf</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c15">jcf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">lc</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c12">jc</font>
 
<b>by </b><i><a class="ref" href="complfld.html#T6" title="COMPLFLD:th.6">COMPLFLD:6</a></i>;<br/>
<i><font color="Green" title="E74">A14</font></i>: <font color="Maroon" title="c6">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">lcf</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c15">jcf</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c17">mcf</font>
<b>by </b><i><a class="txt" href="uniroots.html#E3:70"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="uniroots.html#E4:70"><i><font color="Green" title="E65">A4</font></i></a>, <a class="txt" href="uniroots.html#E5:70"><i><font color="Green" title="E66">A5</font></i></a>, <a class="txt" href="uniroots.html#E11:70"><i><font color="Green" title="E71">A10</font></i></a>, <a class="txt" href="uniroots.html#E15:70"><i><font color="Green" title="E72">A12</font></i></a>, <a class="ref" href="polynom4.html#T27" title="POLYNOM4:th.27">POLYNOM4:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">l</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">m</font>
<b>by </b><i><a class="txt" href="uniroots.html#E18:70"><i><font color="Green" title="E73">A13</font></i></a>, <a class="ref" href="complfld.html#T6" title="COMPLFLD:th.6">COMPLFLD:6</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_3_1"/>
( <font color="Maroon" title="c7">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 or <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_3_1_1"><b>suppose </b></a><a NAME="E1:70_3_1_1"/><i><font color="Green" title="E75">A15</font></i>: 
<font color="Maroon" title="c7">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:70_3_1_1"/>
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">l</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="uniroots.html#E19:70"><i><font color="Green" title="E74">A14</font></i></a></i>;<br/><a NAME="E3:70_3_1_1"/><b>then </b>
<font color="Maroon" title="c7">l</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="ref" href="int_1.html#D9" title="INT_1:def.9">INT_1:def 9</a></i>;<br/><a NAME="E4:70_3_1_1"/><b>then </b>
<font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">l</font> is <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>
 <b>by </b><i><a class="txt" href="uniroots.html#E1:70_3_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="ref" href="wsierp_1.html#T22" title="WSIERP_1:th.22">WSIERP_1:22</a></i>;<br/><a NAME="E5:70_3_1_1"/><b>then </b>
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">l</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">l</font>
 <b>by </b><i><a class="ref" href="int_1.html#T47" title="INT_1:th.47">INT_1:47</a></i>;<br/><a NAME="E6:70_3_1_1"/><b>then </b>
<font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">l</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c7">l</font>
 <b>by </b><i><a class="txt" href="uniroots.html#E19:70"><i><font color="Green" title="E74">A14</font></i></a>, <a class="ref" href="int_1.html#D7" title="INT_1:def.7">INT_1:def 7</a></i>;<br/><a NAME="E7:70_3_1_1"/><b>then </b>
<font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">j</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">m</font>
 <b>by </b><i><a class="txt" href="uniroots.html#E1:70_3_1_1"><i><font color="Green" title="E75">A15</font></i></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>;<br/><b>hence </b><a NAME="E8:70_3_1_1"/>
<font color="Maroon" title="c5">j</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font>
 <b>by </b><i><a class="ref" href="int_1.html#D9" title="INT_1:def.9">INT_1:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_3_1_2"><b>suppose </b></a><a NAME="E1:70_3_1_2"/>
<font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:70_3_1_2"/><b>then </b>
<font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="int_1.html#T75" title="INT_1:th.75">INT_1:75</a></i>;<br/><b>hence </b><a NAME="E3:70_3_1_2"/>
<font color="Maroon" title="c5">j</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font>
 <b>by </b><i><a class="ref" href="int_2.html#T16" title="INT_2:th.16">INT_2:16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E21:70"/>
<font color="Maroon" title="c5">j</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c6">k</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c7">l</font>
 ;<br/>


</div>
