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<b>let </b><font color="Maroon">C</font> be  <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">C</font> <a href="subset_1.html#K3">`</a>  as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">Om1</font> = <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">C1</font>;<br/>
<a NAME="E2:144"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">C1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">UB</font> =  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">C</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">C1</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E4:144"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">UB</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T24">CONNSP_1:24</a></i>;<br/>
<a NAME="E5:144"/>
<font color="Maroon">UB</font> is  non <a href="xboole_0.html#V1">empty</a>  <a href="connsp_3.html#M1">a_union_of_components</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">C1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:144"/><b>then </b>
<font color="Maroon">UB</font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T35" target="_self">Th35</a>, <a class="ref" href="connsp_3.html#T36">CONNSP_3:36</a></i>;<br/>
<b>hence </b><a NAME="E7:144"/>
 <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">C</font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="connsp_1.html#D6">CONNSP_1:def 6</a></i>;<br/>


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