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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> holds  <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="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">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="Olive" title="b1">p</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">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>)</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">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/>
<span class="kw">set </span><font color="Maroon" title="c4">R</font> =  <a href="t_0topsp.html#K1" title="T_0TOPSP:func.1">Indiscernibility</a> <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E1:11"/>
<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> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a> <font color="Maroon" title="c1">T</font></span>)</span>
 
;<br/>
<a NAME="E2:11"/><span class="kw">then </span>
<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> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="t_0topsp.html#K2" title="T_0TOPSP:func.2">Indiscernible</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D7" onmouseover="rs('borsuk_1/D7')" onmouseout="rh()">BORSUK_1:def 7</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E4:11"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">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="c5">y</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T36" onmouseover="rs('eqrel_1/T36')" onmouseout="rh()">EQREL_1:36</a></span>;<br/>
<a NAME="E5:11"/>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">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="c5">y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="borsuk_1.html#T28" onmouseover="rs('borsuk_1/T28')" onmouseout="rh()">BORSUK_1:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:11"/>
<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="eqrel_1.html#T23" onmouseover="rs('eqrel_1/T23')" onmouseout="rh()">EQREL_1:23</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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