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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="jordan12.html#R2" target="_self">are_in_general_position</a> 
 ;<br/>

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E2:18"/><i><font color="Green">E43</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">g</font>,<font color="Maroon">k</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="topreal3.html#T26">TOPREAL3:26</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, </i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<b>hence </b><a NAME="E5:18"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">g</font>,<font color="Maroon">k</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, <a class="ref" href="finset_1.html#T15">FINSET_1:15</a></i>;<br/>


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