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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="rcomp_3.html#M1" target="_self">IntervalCover</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:85"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pre_topc.html#R1">is_a_cover_of</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:85"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="tops_2.html#V1">open</a>
 <b>and </b><br/><a NAME="E3:85"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="rcomp_3.html#V1" target="_self">connected</a>
 ;<br/>

<a NAME="E4:85"/><i><font color="Green">E63</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T14">RCOMP_1:14</a></i>;<br/>
<a NAME="E5:85"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E6:85"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E4:85"><i><font color="Green">E63</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:85"/><b>then </b>
<span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:85"><i><font color="Green">E60</font></i></a>, <a class="ref" href="rcomp_3.html#T60" target="_self">Th60</a></i>;<br/>
<b>hence </b><a NAME="E8:85"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:85"><i><font color="Green">E60</font></i></a>, <a class="txt" href="rcomp_3.html#E2:85"><i><font color="Green">E61</font></i></a>, <a class="txt" href="rcomp_3.html#E3:85"><i><font color="Green">E62</font></i></a>, <a class="txt" href="rcomp_3.html#E4:85"><i><font color="Green">E63</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self">Def2</a></i>;<br/>


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