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

<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">PA</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PB</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PC</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>



<b>consider </b><font color="Maroon">PD</font> being    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PE</font> being    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E2:20"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">PD</font> <a href="hidden.html#R1">=</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PB</font>
 <b>and </b><br/><a NAME="E3:20"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">PE</font> <a href="hidden.html#R1">=</a> <font color="Maroon">PB</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font>
 ;<br/>
<a NAME="E4:20"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1"/>
for <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> holds <br/> ex <font color="Olive">v</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font>
 ;<br/>

<a NAME="E2:20_1_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PD</font>,<font color="Maroon">PC</font></span>)</span> <a href="subset_1.html#K6">\</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>
 
;<br/>
<a NAME="E3:20_1_1"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PD</font>,<font color="Maroon">PC</font>
 
;<br/>
<b>then consider </b><font color="Maroon">u1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">u2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">u1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font>
 <b>and </b><br/><a NAME="E6:20_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">u2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PC</font>
 <b>and </b><br/><a NAME="E7:20_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u2</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E8:20_1_1"/>
<font color="Maroon">u1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PB</font></span>)</span> <a href="subset_1.html#K6">\</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>, </i>;<br/>
<a NAME="E9:20_1_1"/><b>then </b>
<font color="Maroon">u1</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PB</font>
 
;<br/>
<b>then consider </b><font color="Maroon">u3</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">u4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:20_1_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">u3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font>
 <b>and </b><br/><a NAME="E12:20_1_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">u4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PB</font>
 <b>and </b><br/><a NAME="E13:20_1_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u3</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u4</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">v</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">v1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">v2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:20_1_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u4</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u2</font>
 <b>and </b><br/><a NAME="E16:20_1_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u3</font>
 <b>and </b><br/><a NAME="E17:20_1_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">u3</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u4</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u2</font>
 ;<br/>
<a NAME="E18:20_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">v1</font>
 
<b>by </b><i>, , , <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>
<a NAME="E19:20_1_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PB</font>,<font color="Maroon">PC</font>
 
<b>by </b><i>, , , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E20:20_1_1"/><i><font color="Green">E79</font></i>: 
not <font color="Maroon">u</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E21:20_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u3</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">v1</font>
 
<b>by </b><i>, , , <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>
<a NAME="E22:20_1_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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/>
<a NAME="E23:20_1_1"/><b>then </b>
not <font color="Maroon">v1</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E24:20_1_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PB</font>,<font color="Maroon">PC</font></span>)</span> <a href="subset_1.html#K6">\</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E25:20_1_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PE</font>
 
<b>by </b><i/>;<br/>
<a NAME="E26:20_1_1"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PE</font>
 
<b>by </b><i>, , , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E27:20_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PE</font></span>)</span> <a href="subset_1.html#K6">\</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">v</font>
;<br/>

<b>thus </b><a NAME="E28:20_1_1"/>
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font> &amp; <font color="Maroon">u</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">v</font> )
 <b>by </b><i>, , , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_1"/>
<font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D2">SETFAM_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:20"/>
<font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_2"/>
for <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font> holds <br/> ex <font color="Olive">v</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:20_2_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font>
 ;<br/>

<a NAME="E2:20_2_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PE</font></span>)</span> <a href="subset_1.html#K6">\</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>
 
;<br/>
<a NAME="E3:20_2_1"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PE</font>
 
;<br/>
<b>then consider </b><font color="Maroon">u1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">u2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_2_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">u1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font>
 <b>and </b><br/><a NAME="E6:20_2_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">u2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PE</font>
 <b>and </b><br/><a NAME="E7:20_2_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u2</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E8:20_2_1"/>
<font color="Maroon">u2</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PB</font>,<font color="Maroon">PC</font></span>)</span> <a href="subset_1.html#K6">\</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>, </i>;<br/>
<a NAME="E9:20_2_1"/><b>then </b>
<font color="Maroon">u2</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PB</font>,<font color="Maroon">PC</font>
 
;<br/>
<b>then consider </b><font color="Maroon">u3</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">u4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:20_2_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">u3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PB</font>
 <b>and </b><br/><a NAME="E12:20_2_1"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">u4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PC</font>
 <b>and </b><br/><a NAME="E13:20_2_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">u2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u3</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u4</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E14:20_2_1"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u4</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>
<b>consider </b><font color="Maroon">v</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">v1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">v2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E16:20_2_1"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u3</font>
 <b>and </b><br/><a NAME="E17:20_2_1"/>
<font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u4</font>
 <b>and </b><br/><a NAME="E18:20_2_1"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">u4</font>
 ;<br/>
<a NAME="E19:20_2_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PB</font>
 
<b>by </b><i>, , , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E20:20_2_1"/><i><font color="Green">E92</font></i>: 
not <font color="Maroon">u</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E21:20_2_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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/>
<a NAME="E22:20_2_1"/><b>then </b>
not <font color="Maroon">v1</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E23:20_2_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PA</font>,<font color="Maroon">PB</font></span>)</span> <a href="subset_1.html#K6">\</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E24:20_2_1"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font>
 
<b>by </b><i/>;<br/>
<a NAME="E25:20_2_1"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PD</font>,<font color="Maroon">PC</font>
 
<b>by </b><i>, , , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E26:20_2_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">PD</font>,<font color="Maroon">PC</font></span>)</span> <a href="subset_1.html#K6">\</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="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">v</font>
;<br/>

<b>thus </b><a NAME="E27:20_2_1"/>
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> &amp; <font color="Maroon">u</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">v</font> )
 <b>by </b><i>, , , , <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_2"/>
<font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PE</font> <a href="partit1.html#NR1" target="_self">'&lt;'</a> <font color="Maroon">PD</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D2">SETFAM_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:20"/>
<span class="p1">(<span class="default"><font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PB</font></span>)</span> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font> <a href="hidden.html#R1">=</a> <font color="Maroon">PA</font> <a href="partit1.html#K2" target="_self">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">PB</font> <a href="partit1.html#K2" target="_self">'/\'</a> <font color="Maroon">PC</font></span>)</span>
 <b>by </b><i>, , , </i>;<br/>


</div>
