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

<b>let </b><font color="Maroon">L</font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relset_1.html#NM3">Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>;<br/>





<b>set </b><font color="Maroon">X</font> =  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>;<br/>
<a NAME="E1:30"/><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1">WELLORD2:def 1</a></i>;<br/>
<b>thus </b><a NAME="E2:30"/><i><font color="Green">E31</font></i>: 
 <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font> <a href="waybel35.html#NR1" target="_self">is_inductive_wrt</a>  <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D9">ORDERS_1:def 9</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:30_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:30_1"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">Y</font> <a href="orders_1.html#NR3" target="_self">is_linear-order</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_1_1"/>
( <font color="Maroon">Y</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">Y</font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1"><b>suppose </b></a><a NAME="E1:30_1_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">Y</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>take </b>
<font color="Maroon">C</font>
;<br/><b>thus </b><a NAME="E2:30_1_1_1"/>
( <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">C</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span> ) ) )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2"><b>suppose </b></a><a NAME="E1:30_1_1_2"/><i><font color="Green">E61</font></i>: 
not <font color="Maroon">Y</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>take </b><font color="Maroon">Z</font> =  <a href="tarski.html#K3">union</a> <font color="Maroon">Y</font>;<br/><a NAME="E2:30_1_1_2"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:30_1_1_2_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:30_1_1_2_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:30_1_1_2_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E5:30_1_1_2_1"/>
<font color="Maroon">A</font> is    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:30_1_1_2_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">S</font> = <font color="Maroon">Z</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/><a NAME="E4:30_1_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">S</font> is    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel35.html#D3" target="_self">WAYBEL35:def 3</a><br/>

<b>assume </b><a NAME="E1:30_1_1_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:30_1_1_2_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:30_1_1_2_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>assume </b><a NAME="E5:30_1_1_2_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:30_1_1_2_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E8:30_1_1_2_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E9:30_1_1_2_2"/>
<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">Y</font> is <a href="relat_2.html#V6">connected</a>
 
<b>by </b><i>, <a class="ref" href="orders_1.html#D5">ORDERS_1:def 5</a></i>;<br/>
<a NAME="E10:30_1_1_2_2"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">Y</font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p3">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D14">RELAT_2:def 14</a></i>;<br/>
<a NAME="E11:30_1_1_2_2"/><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="wellord2.html#T8">WELLORD2:8</a></i>;<br/>
<a NAME="E12:30_1_1_2_2"/><i><font color="Green">E75</font></i>: 
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1">WELLORD2:def 1</a></i>;<br/>
<a NAME="E13:30_1_1_2_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">A</font> is    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E14:30_1_1_2_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">B</font> is    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>
 
<b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_1_1_2_2_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:30_1_1_2_2_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><a NAME="E2:30_1_1_2_2_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">Y</font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">A</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, , , , <a class="txt" href="waybel35.html#E2"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/><a NAME="E3:30_1_1_2_2_1_1"/><b>then </b>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> or <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i>, , <a class="ref" href="wellord2.html#D1">WELLORD2:def 1</a></i>;<br/><b>hence </b><a NAME="E4:30_1_1_2_2_1_1"/>
( <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> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 <b>by </b><i>, <a class="txt" href="waybel35.html#E1"><i><font color="Green">Lemma22</font></i></a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:30_1_1_2_2_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_2_2_1_2"/>
( <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> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 <b>by </b><i>, <a class="txt" href="waybel35.html#E1"><i><font color="Green">Lemma22</font></i></a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E5:30_1_1_2"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</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="E1:30_1_1_2_3"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/>

<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:30_1_1_2_3"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E4:30_1_1_2_3"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:30_1_1_2_3"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:30_1_1_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#R2">in</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 <b>by </b><i>, </i>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E7:30_1_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/><a NAME="E8:30_1_1_2"/><b>then </b>
<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/><b>hence </b><a NAME="E9:30_1_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">Z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="wellord2.html#D1">WELLORD2:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<a NAME="E3:30"/>
 <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span> <a href="orders_1.html#R2">partially_orders</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:30_2"/>
 <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span> <a href="relat_2.html#R1">is_reflexive_in</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D7">ORDERS_1:def 7</a><br/>

<b>thus </b><a NAME="E2:30_2"/>
 <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span> <a href="relat_2.html#R8">is_transitive_in</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E3:30_2"/>
 <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span> <a href="relat_2.html#R4">is_antisymmetric_in</a>  <a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">D</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:30"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">D</font> <a href="orders_1.html#R6">is_maximal_in</a>  <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="orders_1.html#T173">ORDERS_1:173</a></i>;<br/>
<b>take </b>
<font color="Maroon">D</font>
;<br/>

<b>thus </b><a NAME="E6:30"/>
<font color="Maroon">D</font> <a href="orders_1.html#R6">is_maximal_in</a>  <a href="yellow_1.html#K1">RelIncl</a> <span class="p1">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span>
 <b>by </b><i/>;<br/>

<a NAME="E7:30"/>
<font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="waybel35.html#K2" target="_self">Strict_Chains</a> <font color="Maroon">R</font>,<font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="orders_1.html#D11">ORDERS_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:30"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 <b>by </b><i>, </i>;<br/>


</div>
