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

<b>let </b><font color="Maroon">C1</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>, <font color="Maroon">C2</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="cohsp_1.html#V9" target="_self">U-stable</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>, <font color="Maroon">g</font> be  <a href="cohsp_1.html#V9" target="_self">U-stable</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/>



<b>assume </b><a NAME="E1:82"/><i><font color="Green">E26</font></i>: 
 <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">g</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font>;<br/>

<a NAME="E2:82"/><i><font color="Green">E27</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>let </b><font color="Maroon">z</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="E3:82"/>
<font color="Maroon">z</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/>

<b>then consider </b><font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:82"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">b</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> &amp; ( for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> holds <br/><font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> ) )
 <b>by </b><i>, <a class="ref" href="cohsp_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">b</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <b>by </b><i>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:82_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">c</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> )
 ;<br/><a NAME="E2:82_1"/><b>then </b>
<font color="Maroon">c</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E3:82_1"/><b>then </b>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:82_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:82"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K8" target="_self">Trace</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E9:82"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, , , , <a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E10:82"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 ;<br/>


</div>
