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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>set </b><font color="Maroon" title="c4">F</font> =  <a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font>;<br/>
<b>set </b><font color="Maroon" title="c5">R</font> =  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:13_1"/>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 ;<br/><a NAME="E2:13_1"/><b>then </b>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="t_0topsp.html#E9"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><a NAME="E3:13_1"/><b>then </b>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="t_0topsp.html#T8" target="_self" title="T_0TOPSP:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E4:13_1"/>
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T27" title="EQREL_1:th.27">EQREL_1:27</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:13"/>
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>
 ;<br/>

<a NAME="E3:13"/><b>then </b>
 <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T44" title="EQREL_1:th.44">EQREL_1:44</a></i>;<br/>
<a NAME="E4:13"/><b>then </b>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font></span>)</span>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="t_0topsp.html#T8" target="_self" title="T_0TOPSP:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
<span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="t_0topsp.html#K4" title="T_0TOPSP:func.4">T_0-canonical_map</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="t_0topsp.html#T8" target="_self" title="T_0TOPSP:th.8">Th8</a></i>;<br/>


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