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<b>let </b><font color="Maroon">A</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">C</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">B</font>
 ;<br/>

<b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">C</font>;<br/>

<b>assume </b><a NAME="E3:72"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E4:72"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">B</font> <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<a NAME="E6:72"/>
<font color="Maroon">g</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T10">TOPMETR:10</a></i>;<br/>
<b>hence </b><a NAME="E7:72"/>
<font color="Maroon">h</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i>, , <a class="ref" href="topmetr.html#T8">TOPMETR:8</a></i>;<br/>


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