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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="orders_1.html#NM2">Order</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">R</font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">A</font>
 ;<br/>

<i><font color="Green">E36</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <font color="Maroon">R</font>,<font color="Maroon">A</font></span>)</span> = 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">A</font>
<b>by </b><i>, <a class="ref" href="triang_1.html#T9">TRIANG_1:9</a></i>
<br/>.= 
1
<b>by </b><i>, <a class="ref" href="card_1.html#T50">CARD_1:50</a></i>
;<br/>
<a NAME="E4:20"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <font color="Maroon">R</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:20"/>
 <a href="triang_1.html#K2">SgmX</a> <font color="Maroon">R</font>,<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>


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