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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM8">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">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</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">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<a NAME="E1:39"/><i><font color="Green">E33</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="topreal3.html#T26">TOPREAL3:26</a></i>;<br/>
<b>assume </b><a NAME="E2:39"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:39"/><i><font color="Green">E35</font></i>: 
 <a href="jordan3.html#K2" target="_self">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_sim1.html#K10">min</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E5:39"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="jordan3.html#E1:39"><i><font color="Green">E33</font></i></a>, <a class="ref" href="jordan3.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E6:39"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan3.html#E2:39"><i><font color="Green">E34</font></i></a>, <a class="txt" href="jordan3.html#E5:39"><i><font color="Green">E36</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
 <a href="jordan3.html#K2" target="_self">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="jordan3.html#E4:39"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cqc_sim1.html#D8">CQC_SIM1:def 8</a></i>;<br/>


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