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<b>let </b><font color="Maroon" title="c1">r3</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c2">T</font>;<br/>





<b>assume </b><a NAME="E1:88"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pscomp_1.html#D25" target="_self" title="PSCOMP_1:def.25">PSCOMP_1:def 25</a><br/>

<b>assume </b><a NAME="E2:88"/>
<font color="Maroon" title="c4">X</font> is <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>
 ;<br/>

<a NAME="E3:88"/><b>then </b><i><font color="Green" title="E57">A2</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c4">X</font> is <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T27" target="_self" title="PSCOMP_1:th.27">Th27</a></i>;<br/>
<a NAME="E4:88"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">r3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c4">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T45" target="_self" title="PSCOMP_1:th.45">Th45</a></i>;<br/>
<b>hence </b><a NAME="E5:88"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">r3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c4">X</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:88"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E3:88"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="pscomp_1.html#D25" target="_self" title="PSCOMP_1:def.25">Def25</a></i>;<br/>


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