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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="gcd_1.html#NM3">gcdDomain</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="gcd_1.html#M2" target="_self">AmpleSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1"><b>case </b></a><a NAME="E1:63_1_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_1_1_1_1_1"/>
(  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:63_1_1_1_1_1_1"/><i><font color="Green">E47</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E2:63_1_1_1_1_1_1"/>
(  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E3:63_1_1_1_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="gcd_1.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E4:63_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:63_1_1_1_1_1_1"/><i><font color="Green">E48</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E7:63_1_1_1_1_1_1"/><i><font color="Green">E49</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E8:63_1_1_1_1_1_1"/><i><font color="Green">E50</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E9:63_1_1_1_1_1_1"/>
( <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:63_1_1_1_1_1_1_1"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E6:63_1_1_1_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gcd_1.html#E7:63_1_1_1_1_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E3:63_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E2:63_1_1_1_1_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<a NAME="E4:63_1_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:63_1_1_1_1_1_1_1"/><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E6:63_1_1_1_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="gcd_1.html#E8:63_1_1_1_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:63_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E6:63_1_1_1_1_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<a NAME="E8:63_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E9:63_1_1_1_1_1_1_1"/>
( <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:63_1_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="gcd_1.html#E4:63_1_1_1_1_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="gcd_1.html#T15" target="_self">Th15</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:63_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E11:63_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:63_1_1_1_1_1_1_2"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E2:63_1_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:63_1_1_1_1_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="gcd_1.html#E10:63_1_1_1_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="gcd_1.html#T15" target="_self">Th15</a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:63_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is <a href="gcd_1.html#V1" target="_self">unital</a>
 <b>by </b><i><a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E13:63_1_1_1_1_1_1"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E6:63_1_1_1_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="gcd_1.html#T18" target="_self">Th18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:63_1_1_1_1_1_2"/><i><font color="Green">E47</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:63_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="gcd_1.html#T34" target="_self">Th34</a></i>;<br/><a NAME="E3:63_1_1_1_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:63_1_1_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/> <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="gcd_1.html#E2:63_1_1_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E3:63_1_1_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="gcd_1.html#T32" target="_self">Th32</a></i>
;<br/><b>hence </b><a NAME="E5:63_1_1_1_1_1_2"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:63_1_1_1"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_2"><b>case </b></a><a NAME="E1:63_1_1_2"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:63_1_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><a NAME="E3:63_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:63_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><b>then </b> <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="gcd_1.html#E2:63_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="gcd_1.html#T32" target="_self">Th32</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E1:63_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/><b>hence </b><a NAME="E5:63_1_1_2"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:63"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


</div>
