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

<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">H1</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">H2</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green">E31</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green">E34</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font> or  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font> )
 ;<br/>

<b>set </b><font color="Maroon">cH1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>;<br/>
<b>set </b><font color="Maroon">cH2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>;<br/>
<b>set </b><font color="Maroon">IH1</font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>;<br/>
<b>set </b><font color="Maroon">IH2</font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>;<br/>
<b>set </b><font color="Maroon">H1H2</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>set </b><font color="Maroon">H2H1</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1"/>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font> or  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><b>suppose </b></a><a NAME="E1:20_1_1"/><i><font color="Green">E35</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K1">union_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font>
 ;<br/><div class="add"><a NAME="E2:20_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 <b>by </b><i><a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/><a NAME="E3:20_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:20_1_1"/><i><font color="Green">E41</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/><a NAME="E5:20_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E6:20_1_1"/><i><font color="Green">E43</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E7:20_1_1"/><i><font color="Green">E60</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E8:20_1_1"/><i><font color="Green">E61</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_1_1_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
  <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="20_1_1_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="E1:20_1_1_1_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<a NAME="E3:20_1_1_1_1"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:20_1_1_1_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 ;<br/>


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

<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="E2:20_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 ;<br/>

<a NAME="E3:20_1_1_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<a NAME="E4:20_1_1_1"/><b>then </b><i><font color="Green">E63</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:20_1_1_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1_1_1_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_1_2_1"><b>suppose </b></a><a NAME="E1:20_1_1_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_1_1_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_1_2_2"><b>suppose </b></a><a NAME="E1:20_1_1_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_1_1_2_2"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_1_1_2_2"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_1_1_2_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E7:20_1_1_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E9:20_1_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_1_1_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
  <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="20_1_1_2_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="E1:20_1_1_2_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:20_1_1_2_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<a NAME="E3:20_1_1_2_1"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:20_1_1_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 ;<br/>


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

<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="E2:20_1_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E3:20_1_1_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<a NAME="E4:20_1_1_2"/><b>then </b><i><font color="Green">E94</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:20_1_1_2"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D2">NECKLA_2:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1_1_2_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_2_2_1"><b>suppose </b></a><a NAME="E1:20_1_1_2_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_1_2_2_1"/><i><font color="Green">E105</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_1_2_2_1"/><i><font color="Green">E106</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_1_2_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_1_2_2_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_1_2_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1_2_2_2"><b>suppose </b></a><a NAME="E1:20_1_1_2_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_1_1_2_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E10:20_1_1"/>
( <font color="Maroon">H1</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">H2</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">G</font> )
 <b>by </b><i>, , , , , <a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><b>suppose </b></a><a NAME="E1:20_1_2"/><i><font color="Green">E107</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="neckla_2.html#K2">sum_of</a> <font color="Maroon">H1</font>,<font color="Maroon">H2</font>
 ;<br/><div class="add"><a NAME="E2:20_1_2"/><b>then </b><i><font color="Green">E108</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/><a NAME="E3:20_1_2"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:20_1_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E5:20_1_2"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/><a NAME="E6:20_1_2"/><b>then </b><i><font color="Green">E110</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:20_1_2"/><i><font color="Green">E111</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/><a NAME="E8:20_1_2"/><b>then </b><i><font color="Green">E112</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E9:20_1_2"/><i><font color="Green">E113</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E10:20_1_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E11:20_1_2"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><a NAME="E12:20_1_2"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/><a NAME="E13:20_1_2"/><b>then </b><i><font color="Green">E114</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><a NAME="E14:20_1_2"/><i><font color="Green">E115</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_1_2_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
  <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="20_1_2_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="E1:20_1_2_1_1"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/>

the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>
<br/>.= 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T113">XBOOLE_1:113</a></i>
;<br/>
<a NAME="E3:20_1_2_1_1"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:20_1_2_1_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 ;<br/>


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

<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="E2:20_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 ;<br/>

<a NAME="E3:20_1_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<a NAME="E4:20_1_2_1"/><b>then </b><i><font color="Green">E117</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:20_1_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/>
<a NAME="E6:20_1_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T113">XBOOLE_1:113</a></i>;<br/>
<a NAME="E7:20_1_2_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E8:20_1_2_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E9:20_1_2_1"/><b>then </b><i><font color="Green">E118</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1_2_1_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_2_1"><b>suppose </b></a><a NAME="E1:20_1_2_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_1_2_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_2_2"><b>suppose </b></a><a NAME="E1:20_1_2_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_1_2_2"/><i><font color="Green">E119</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_1_2_2"/><i><font color="Green">E120</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_1_2_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_1_2_2"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_2_3"><b>suppose </b></a><a NAME="E1:20_1_2_1_2_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_1_2_3"/><i><font color="Green">E121</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_1_2_3"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_1_2_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_1_2_3"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_1_2_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_1_2_4"><b>suppose </b></a><a NAME="E1:20_1_2_1_2_4"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_1_2_4"/><i><font color="Green">E123</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_1_2_4"/><i><font color="Green">E124</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_1_2_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_1_2_4"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_1_2_4"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E15:20_1_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_1_2_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
  <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="20_1_2_2_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="E1:20_1_2_2_1"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:20_1_2_2_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/>
<a NAME="E3:20_1_2_2_1"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T113">XBOOLE_1:113</a></i>;<br/>
<a NAME="E4:20_1_2_2_1"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:20_1_2_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_2_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 ;<br/>


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

<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="E2:20_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="wellord1.html#K2">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E3:20_1_2_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<a NAME="E4:20_1_2_2"/><b>then </b><i><font color="Green">E126</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:20_1_2_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="neckla_2.html#D3">NECKLA_2:def 3</a></i>;<br/>
<a NAME="E6:20_1_2_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T113">XBOOLE_1:113</a></i>;<br/>
<a NAME="E7:20_1_2_2"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E8:20_1_2_2"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E9:20_1_2_2"/><b>then </b><i><font color="Green">E127</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1_2_2_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_2_2_1"><b>suppose </b></a><a NAME="E1:20_1_2_2_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_2_2_1"/><i><font color="Green">E128</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_2_2_1"/><i><font color="Green">E129</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_2_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_2_2_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_2_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_2_2_2"><b>suppose </b></a><a NAME="E1:20_1_2_2_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_1_2_2_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_2_2_3"><b>suppose </b></a><a NAME="E1:20_1_2_2_2_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_2_2_3"/><i><font color="Green">E130</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_2_2_3"/><i><font color="Green">E131</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_2_2_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_2_2_3"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_2_2_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2_2_2_4"><b>suppose </b></a><a NAME="E1:20_1_2_2_2_4"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:20_1_2_2_2_4"/><i><font color="Green">E132</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:20_1_2_2_2_4"/><i><font color="Green">E133</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">y1</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E6:20_1_2_2_2_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:20_1_2_2_2_4"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</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="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E8:20_1_2_2_2_4"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">H2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E16:20_1_2"/>
( <font color="Maroon">H1</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">H2</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">G</font> )
 <b>by </b><i>, , , , , , <a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
