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

<b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:137_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">x1</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x2</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y2</font>
 ;<br/><b>thus </b><a NAME="E2:137_1"/>
<font color="Maroon">x1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</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="E1:137_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x1</font>
 ;<br/>

<a NAME="E2:137_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,1</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">x1</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y1</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D15" target="_self">Def15</a></i>;<br/>
<b>hence </b><a NAME="E3:137_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="cohsp_1.html#D15" target="_self">Def15</a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E3:137_1"/>
<font color="Maroon">y1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</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="E1:137_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y1</font>
 ;<br/>

<a NAME="E2:137_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,2</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">x1</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y1</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D16" target="_self">Def16</a></i>;<br/>
<b>hence </b><a NAME="E3:137_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="cohsp_1.html#D16" target="_self">Def16</a></i>;<br/>


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

<b>assume </b><a NAME="E2:137"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">x1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y2</font> )
 ;<br/>

<b>let </b><font color="Maroon">a</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="E3:137"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x1</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y1</font>
 ;<br/>

<a NAME="E4:137"/><b>then </b>
( <font color="Maroon">a</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">a</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; ( ( <font color="Maroon">a</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">a</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">x1</font> ) or ( <font color="Maroon">a</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">a</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">y1</font> ) ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D14" target="_self">Def14</a></i>;<br/>
<b>hence </b><a NAME="E5:137"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x2</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">y2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="cohsp_1.html#D15" target="_self">Def15</a>, <a class="ref" href="cohsp_1.html#D16" target="_self">Def16</a></i>;<br/>


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