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

<a NAME="E1:36_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T66">FINSEQ_1:66</a></i>;<br/>
<a NAME="E2:36_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">s</font> <a href="funcop_1.html#K2">--&gt;</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">s</font>, <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> </span>)</span> <b>by </b><i><a class="ref" href="funcop_1.html#T57">FUNCOP_1:57</a></i>;<br/>
<a NAME="E4:36_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">x</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font><br/> for <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> holds <br/><font color="Olive">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font>;<br/><b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:36_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:36_1_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E3:36_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:36_1_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">x</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font> holds   <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font>;<br/>

<a NAME="E1:36_1_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E2:36_1_1_2"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:36_1_1"/><i><font color="Green">E38</font></i>: 
 <a href="xboole_0.html#K1">{}</a>  is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T66">FINSEQ_1:66</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font>;<br/>



<b>thus </b><a NAME="E7:36_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> , <font color="Olive">b</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> ) </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:36_1_1_3"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Maroon">y</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> , <font color="Olive">b</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> ) </span>}</span> 
  <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="36_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</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="E1:36_1_1_3_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Maroon">y</font></span>)</span>
 ;<br/>

<a NAME="E2:36_1_1_3_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:36_1_1_3_1"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<b>hence </b><a NAME="E4:36_1_1_3_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> , <font color="Olive">b</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> ) </span>}</span> 
 ;<br/>


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

<b>let </b><font color="Maroon">t</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="E2:36_1_1_3"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font></span>)</span> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> , <font color="Olive">b</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> , <font color="Maroon">b</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E4:36_1_1_3"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> )
 ;<br/>
<a NAME="E5:36_1_1_3"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:36_1_1_3"/><b>then </b>
<font color="Maroon">a</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<b>hence </b><a NAME="E7:36_1_1_3"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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

<b>thus </b><a NAME="E8:36_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_4"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:36_1_1_4"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Maroon">y</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
  <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="36_1_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</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="E1:36_1_1_4_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Maroon">y</font></span>)</span>
 ;<br/>

<a NAME="E2:36_1_1_4_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> ;<br/><b>assume </b><a NAME="E1:36_1_1_4_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/><a NAME="E2:36_1_1_4_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><a NAME="E3:36_1_1_4_1_1"/><b>then </b>
<a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E4:36_1_1_4_1_1"/>
<a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36_1_1_4_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/>


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

<b>let </b><font color="Maroon">t</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="E2:36_1_1_4"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E4:36_1_1_4"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; ( for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Maroon">a</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> ) )
 ;<br/>
<a NAME="E5:36_1_1_4"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:36_1_1_4"/><b>then </b>
<font color="Maroon">a</font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:36_1_1_4"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E8:36_1_1_4"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:36_1_1_4"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="prelamb.html#K2" target="_self">/"</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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

<b>thus </b><a NAME="E9:36_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">b</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_5"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:36_1_1_5"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Maroon">x</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">b</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
  <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="36_1_1_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</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="E1:36_1_1_5_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Maroon">x</font></span>)</span>
 ;<br/>

<a NAME="E2:36_1_1_5_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_5_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> ;<br/><b>assume </b><a NAME="E1:36_1_1_5_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/><a NAME="E2:36_1_1_5_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><a NAME="E3:36_1_1_5_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E4:36_1_1_5_1_1"/>
<font color="Maroon">b</font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36_1_1_5_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">b</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/>


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

<b>let </b><font color="Maroon">t</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="E2:36_1_1_5"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  : for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">b</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E4:36_1_1_5"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; ( for <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> holds <br/><font color="Olive">b</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> ) )
 ;<br/>
<a NAME="E5:36_1_1_5"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:36_1_1_5"/><b>then </b>
<a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:36_1_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E8:36_1_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:36_1_1_5"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="prelamb.html#K1" target="_self">\</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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


</div>
