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

<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>set </b><font color="Maroon">q</font> =  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span>;<br/>
<a NAME="E1:68"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</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">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E2:68"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>thus </b><a NAME="E3:68"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:68_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
 ;<br/>

<a NAME="E2:68_1"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="txt" href="finseq_3.html#E1:68_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:68_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
 <b>and </b><br/><a NAME="E4:68_1_1"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T15" target="_self">Th15</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>set </b><font color="Maroon">z</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>;<br/><a NAME="E5:68_1_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_3.html#E2:68_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_3.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E6:68_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E7:68_1_1"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="txt" href="finseq_3.html#E2:68_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_3.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E8:68_1_1"/><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_3.html#E2:68_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="finseq_3.html#E3:68_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/><a NAME="E9:68_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</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">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E10:68_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_3.html#E4:68_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="finseq_1.html#D13">FINSEQ_1:def 13</a></i>;<br/><a NAME="E11:68_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E12:68_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="finseq_3.html#T20" target="_self">Th20</a>, <a class="txt" href="finseq_3.html#E1:68_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="finseq_3.html#T24" target="_self">Th24</a>, <a class="ref" href="finseq_3.html#T26" target="_self">Th26</a>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:68_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:68"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E5:68"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 
;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:68"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E8:68"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E9:68"/>
not <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T15" target="_self">Th15</a>, <a class="ref" href="finseq_3.html#T20" target="_self">Th20</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E10:68"/><b>then </b><i><font color="Green">E77</font></i>: 
not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E11:68"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</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">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E12:68"/><b>then </b>
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</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">p</font></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="finseq_1.html#D13">FINSEQ_1:def 13</a></i>;<br/>
<a NAME="E13:68"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T19" target="_self">Th19</a>, <a class="ref" href="finseq_3.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:68"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E16:68"/><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E17:68"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T19" target="_self">Th19</a>, , , <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<a NAME="E18:68"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T20" target="_self">Th20</a>, , , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E19:68"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


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