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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1_1_1"/>
(  not <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1"><b>suppose </b></a><a NAME="E1:42_1_1_1_1"/>
not <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_1_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T70" title="TOPS_2:th.70">TOPS_2:70</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_2"><b>suppose </b></a><a NAME="E1:42_1_1_1_2"/>
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ;<br/><div class="add"><a NAME="E2:42_1_1_1_2"/><b>then </b><i><font color="Green" title="E25">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/><a NAME="E3:42_1_1_1_2"/><b>then </b><i><font color="Green" title="E26">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:42_1_1_1_2"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="relset_1.html#K6" title="RELSET_1:func.6">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a>, <a class="ref" href="relat_1.html#T66" title="RELAT_1:th.66">RELAT_1:66</a></i>;<br/><a NAME="E5:42_1_1_1_2"/><b>then </b><i><font color="Green" title="E27">A3</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#D9" title="FUNCT_1:def.9">FUNCT_1:def 9</a></i>;<br/><a NAME="E6:42_1_1_1_2"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="topgrp_1.html#E2:42_1_1_1_2"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="topgrp_1.html#E3:42_1_1_1_2"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a>, <a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></i>;<br/><b>then </b><font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  = 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> 
<b>by </b><i><a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>
<br/>.= 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">T</font>
<b>by </b><i><a class="txt" href="topgrp_1.html#E2:42_1_1_1_2"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="topgrp_1.html#E5:42_1_1_1_2"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a>, <a class="ref" href="relat_1.html#T81" title="RELAT_1:th.81">RELAT_1:81</a></i>
;<br/><b>hence </b><a NAME="E8:42_1_1_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 <b>by </b><i><a class="ref" href="topgrp_1.html#T20" target="_self" title="TOPGRP_1:th.20">Th20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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