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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">R</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">T</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">R</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:73"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E2:73"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">h</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ;<br/>

<a NAME="E3:73"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">h</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">R</font> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> )
 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a>, </i>
<br/>.= 
<font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
<br/>.= 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">R</font>
<b>by </b><i>, <a class="ref" href="tops_2.html#T65">TOPS_2:65</a></i>
;<br/>


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