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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="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D12">PRE_TOPC:def 12</a><br/>

<a NAME="E3:47"/><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T181">RELAT_1:181</a></i>;<br/>
<b>assume </b><a NAME="E4:47"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<a NAME="E5:47"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="tops_2.html#E2:47"><i><font color="Green">E24</font></i></a>, <a class="ref" href="pre_topc.html#D12">PRE_TOPC:def 12</a></i>;<br/>
<b>hence </b><a NAME="E6:47"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tops_2.html#E1:47"><i><font color="Green">E23</font></i></a>, <a class="txt" href="tops_2.html#E3:47"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pre_topc.html#D12">PRE_TOPC:def 12</a></i>;<br/>


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