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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">H</font> is <a href="tops_2.html#V1" target="_self">open</a>
 ;<br/>

<b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E3:49"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">H</font>
 ;<br/>

<b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1" target="_self">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E4:49"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:49"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E7:49"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font>
 <b>and </b><br/><a NAME="E8:49"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3">"</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<a NAME="E10:49"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , <a class="ref" href="funct_3.html#T24">FUNCT_3:24</a></i>;<br/>
<a NAME="E11:49"/>
<font color="Maroon">Y</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E12:49"/>
<font color="Maroon">X</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, , </i>;<br/>


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