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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:51"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E2:51"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:51"/><i><font color="Green">E42</font></i>: 
 <a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:51"/>
(  <a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>4</sub></font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="connsp_1.html#E1:51"><i><font color="Green">E40</font></i></a>, <a class="ref" href="connsp_1.html#T43" target="_self">Th43</a></i>;<br/>
<a NAME="E5:51"/><b>then </b>
 <a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E3:51"><i><font color="Green">E42</font></i></a>, <a class="ref" href="connsp_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E6:51"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E7:51"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="connsp_1.html#K1" target="_self">skl</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T40" target="_self">Th40</a></i>;<br/>
<b>hence </b><a NAME="E8:51"/>
contradiction
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:51"><i><font color="Green">E41</font></i></a>, <a class="txt" href="connsp_1.html#E6:51"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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