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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:90"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 ;<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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pscomp_1.html#D25" target="_self">PSCOMP_1:def 25</a><br/>

<b>assume </b><a NAME="E2:90"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="rcomp_1.html#V2">closed</a>
 ;<br/>

<a NAME="E3:90"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>4</sub></font> is <a href="rcomp_1.html#V2">closed</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E4:90"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pscomp_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T45" target="_self">Th45</a></i>;<br/>
<b>hence </b><a NAME="E5:90"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="pscomp_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:90"><i><font color="Green">E59</font></i></a>, <a class="txt" href="pscomp_1.html#E3:90"><i><font color="Green">E60</font></i></a>, <a class="ref" href="pscomp_1.html#D25" target="_self">Def25</a></i>;<br/>


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