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<b>set </b><font color="Maroon">c</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="finsop_1.html#K3">--&gt;</a> 0 as   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">T</font> ;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<a NAME="E2:86_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:86_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<b>let </b><font color="Maroon">Y</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="E4:86_1_1"/>
<font color="Maroon">Y</font> is <a href="rcomp_1.html#V2">closed</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_1_1_1"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> or  not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_1_1"><b>suppose </b></a><a NAME="E1:86_1_1_1_1"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">Y</font> = 
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T168">RELAT_1:168</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T169">RELAT_1:169</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>
;<br/><b>hence </b><a NAME="E4:86_1_1_1_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">Y</font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_1_2"><b>suppose </b></a><a NAME="E1:86_1_1_1_2"/>
not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">Y</font> = 
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T168">RELAT_1:168</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>
<br/>.= 
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="relat_1.html#T171">RELAT_1:171</a></i>
;<br/><b>hence </b><a NAME="E4:86_1_1_1_2"/>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">Y</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T22">TOPS_1:22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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