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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</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>2</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:71"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topalg_2.html#K3">R^1</a>  <b>by </b><i><a class="txt" href="rcomp_3.html#E1:71"><i><font color="Green">E50</font></i></a>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:71_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="connsp_1.html#V2">connected</a>
 ;<br/><a NAME="E2:71_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#T24">CONNSP_1:24</a></i>;<br/><b>hence </b><a NAME="E3:71_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="jct_misc.html#V1">connected</a>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:71"><i><font color="Green">E50</font></i></a>, <a class="ref" href="rcomp_3.html#T52" target="_self">Th52</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:71"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="jct_misc.html#V1">connected</a>
 ;<br/>

<a NAME="E5:71"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:71"><i><font color="Green">E50</font></i></a>, <a class="ref" href="rcomp_3.html#T52" target="_self">Th52</a></i>;<br/>
<b>hence </b><a NAME="E6:71"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#T24">CONNSP_1:24</a></i>;<br/>


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