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

<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<a NAME="E1:11"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> implies  ex <font color="Olive">j1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">F</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>, <font color="Maroon">I</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:11_1"/><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E4:11_1"/><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>and </b><br/><a NAME="E5:11_1"/><i><font color="Green">E51</font></i>: 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="group_4.html#T37">GROUP_4:37</a></i>;<br/>
<i><font color="Green">E61</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/>
<a NAME="E7:11_1"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_2"><b>proof </b></a><div class="add">

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

<a NAME="E1:11_1_2"/><i><font color="Green">E62</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>assume </b><a NAME="E2:11_1_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E3:11_1_2"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>then </b><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> = 
<font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font>
<b>by </b><i>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>
<b>hence </b><a NAME="E5:11_1_2"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font>
 ;<br/>


</div><b>end;</b></div>
<b>then </b><i><font color="Green">E64</font></i>: <font color="Maroon">b</font> = 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="group_4.html#K4">|^</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K2" target="_self">Sum</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i/>
;<br/>
<b>take </b>
 <a href="gr_cy_1.html#K2" target="_self">Sum</a> <font color="Maroon">I</font>
;<br/>

<b>thus </b><a NAME="E9:11_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K2" target="_self">Sum</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:11"/>
(  ex <font color="Olive">j1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j1</font> implies <font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">j1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><a NAME="E1:11_2"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">j1</font>
 ;<br/>

<b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:11_2"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> or <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K7">-</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="int_1.html#T8">INT_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_2_1_1"/>
( <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> or <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K7">-</a> <font color="Maroon">n</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_1_1"><b>suppose </b></a><a NAME="E1:11_2_1_1_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><a NAME="E2:11_2_1_1_1"/>
 ex <font color="Olive">F</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> ex <font color="Olive">I</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Olive">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">I</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="group_4.html#K4">|^</a> <font color="Olive">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">F</font> = <font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font>;<br/>

<i><font color="Green">E68</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> = 
<font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p2">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
;<br/>
<a NAME="E2:11_2_1_1_1_1"/><i><font color="Green">E69</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p3">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span></span>)</span> = 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p3">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
<br/>.= 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_4.html#T31">GROUP_4:31</a></i>
<br/>.= 
<font color="Maroon">b</font>
<b>by </b><i>, , <a class="ref" href="group_4.html#T15">GROUP_4:15</a></i>
;<br/>
<b>hence </b><a NAME="E4:11_2_1_1_1_1"/>
 ex <font color="Olive">I</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">I</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <font color="Olive">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:11_2_1_1_1"/>
<font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="group_4.html#T37">GROUP_4:37</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_1_2"><b>suppose </b></a><a NAME="E1:11_2_1_1_2"/>
<font color="Maroon">j1</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K7">-</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><b>then </b><i><font color="Green">E70</font></i>: <font color="Maroon">b</font> <a href="group_1.html#K3">"</a>  = 
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7">-</a> <span class="p2">(<span class="default"><a href="binop_2.html#K7">-</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="group_1.html#T70">GROUP_1:70</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">n</font>

;<br/><a NAME="E3:11_2_1_1_2"/>
 ex <font color="Olive">F</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> ex <font color="Olive">I</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Olive">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">I</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="group_4.html#K4">|^</a> <font color="Olive">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K3">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1_2_2"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">F</font> = <font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font>;<br/>

<i><font color="Green">E71</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> = 
<font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p2">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
;<br/>
<a NAME="E2:11_2_1_1_2_2"/><i><font color="Green">E72</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p3">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span></span>)</span> = 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p3">(<span class="default"><a href="group_4.html#K2">@</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>
<br/>.= 
 <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finsop_1.html#K1">|-&gt;</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_4.html#T31">GROUP_4:31</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="group_1.html#K3">"</a> 
<b>by </b><i>, <a class="ref" href="group_4.html#T15">GROUP_4:15</a></i>
;<br/>
<b>hence </b><a NAME="E4:11_2_1_1_2_2"/>
 ex <font color="Olive">I</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <br/>(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">I</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4">|^</a> <font color="Olive">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K3">"</a>  )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><a NAME="E4:11_2_1_1_2"/><b>then </b>
<font color="Maroon">b</font> <a href="group_1.html#K3">"</a>  <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="group_4.html#T37">GROUP_4:37</a></i>;<br/><a NAME="E5:11_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K3">"</a>  <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="group_2.html#T60">GROUP_2:60</a></i>;<br/><b>hence </b><a NAME="E6:11_2_1_1_2"/>
<font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="group_1.html#T19">GROUP_1:19</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:11_2"/>
<font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:11"/>
( <font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> iff  ex <font color="Olive">j1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j1</font> )
 <b>by </b><i/>;<br/>


</div>
