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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">C</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="triang_1.html#M1" target="_self">Element</a> of  <a href="triang_1.html#K3" target="_self">symplexes</a> <font color="Maroon">C</font>;<br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E34</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="triang_1.html#K2" target="_self">SgmX</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font>,<font color="Maroon">A</font>;<br/>
<a NAME="E2:25"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">A1</font> where <font color="Olive">A1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> : the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Olive">A1</font> </span>}</span> 
 
;<br/>
<a NAME="E3:25"/><b>then </b>
 ex <font color="Olive">A1</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Olive">A1</font> )
 
;<br/>
<a NAME="E4:25"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2" target="_self">SgmX</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2" target="_self">SgmX</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2" target="_self">SgmX</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font>,<font color="Maroon">A</font></span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2" target="_self">SgmX</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">C</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/>


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