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<b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">s</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font></span>)</span>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="rcomp_3.html#M1" target="_self">IntervalCover</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="rcomp_3.html#M2" target="_self">IntervalCoverPts</a> of <font color="Maroon">C</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:97"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="pre_topc.html#R1">is_a_cover_of</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E2:97"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">F</font> is <a href="tops_2.html#V1">open</a>
 <b>and </b><br/><a NAME="E3:97"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">F</font> is <a href="rcomp_3.html#V1" target="_self">connected</a>
 <b>and </b><br/><a NAME="E4:97"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E5:97"/><i><font color="Green">E46</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E6:97"/><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T22" target="_self">Th22</a>, <a class="ref" href="rcomp_3.html#T23" target="_self">Th23</a>, <a class="ref" href="rcomp_3.html#T25" target="_self">Th25</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E7:97"/>
( <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T22" target="_self">Th22</a>, <a class="ref" href="rcomp_3.html#T23" target="_self">Th23</a>, <a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T25" target="_self">Th25</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E8:97"/>
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>


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