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<b>let </b><font color="Maroon">r</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">s</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:44"/><i><font color="Green">E26</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">r</font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E2:44"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">r</font> is <a href="dickson.html#V4" target="_self">Dickson</a>
 <b>and </b><br/><a NAME="E3:44"/><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">s</font>
 ;<br/>

<b>let </b><font color="Maroon">N</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">s</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="dickson.html#D10" target="_self">DICKSON:def 10</a><br/>

<b>reconsider </b><font color="Maroon">N'</font> = <font color="Maroon">N</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">r</font> <b>by </b><i><a class="txt" href="dickson.html#E6:44"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:44"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">B</font> <a href="dickson.html#R1" target="_self">is_Dickson-basis_of</a> <font color="Maroon">N'</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">B</font> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i><a class="txt" href="dickson.html#E3:44"><i><font color="Green">E30</font></i></a>, <a class="txt" href="dickson.html#E1:44"><i><font color="Green">E26</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>thus </b><a NAME="E7:44"/>
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 <b>by </b><i>, <a class="ref" href="dickson.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="dickson.html#D9" target="_self">DICKSON:def 9</a><br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">s</font>;<br/><b>assume </b><a NAME="E1:44_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font>
 ;<br/><b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">r</font> <b>by </b><i><a class="txt" href="dickson.html#E6:44"><i><font color="Green">E31</font></i></a></i>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">r</font><b> such that </b><br/><a NAME="E4:44_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a'</font> )
 <b>by </b><i><a class="txt" href="dickson.html#E1:44_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="dickson.html#E4:44_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="dickson.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">s</font> <b>by </b><i><a class="txt" href="dickson.html#E6:44"><i><font color="Green">E31</font></i></a></i>;<br/><b>take </b><font color="Maroon">b'</font> = <font color="Maroon">b'</font>;<br/><a NAME="E6:44_1"/>
<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> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/><b>hence </b><a NAME="E7:44_1"/>
( <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">b'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="txt" href="dickson.html#E2:44"><i><font color="Green">E29</font></i></a>, , <a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E9:44"/>
<font color="Maroon">B</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i/>;<br/>


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