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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:159"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T97" target="_self">Th97</a></i>;<br/>
<a NAME="E3:159"/>
(  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E2:159"><i><font color="Green">E89</font></i></a>, <a class="ref" href="funct_5.html#T13">FUNCT_5:13</a></i>;<br/>
<b>hence </b><a NAME="E4:159"/>
(  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></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="E5:159"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E6:159"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E2:159"><i><font color="Green">E89</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<a NAME="E7:159"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E5:159"><i><font color="Green">E90</font></i></a>, <a class="ref" href="funct_5.html#T4">FUNCT_5:4</a></i>;<br/>
<b>hence </b><a NAME="E8:159"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E6:159"><i><font color="Green">E91</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div>
