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<a NAME="E1:154_1_1"/>
<font color="Maroon">C</font> is <a href="jordan1.html#V2">Jordan</a>
 
<b>by </b><i/>;<br/>
<a NAME="E2:154_1_1"/><b>then </b>
 <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font> <a href="jordan2c.html#R1">is_inside_component_of</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T116">JORDAN2C:116</a></i>;<br/>
<a NAME="E3:154_1_1"/><b>then </b>
 <a href="jordan2c.html#K1">BDD</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="jordan2c.html#D3">JORDAN2C:def 3</a></i>;<br/>
<a NAME="E4:154_1_1"/><b>then </b>
 ex <font color="Olive">B1</font> being  <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> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> st <br/>( <font color="Olive">B1</font> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font> &amp; <font color="Olive">B1</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> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="connsp_1.html#D6">CONNSP_1:def 6</a></i>;<br/>
<a NAME="E5:154_1_1"/><b>then </b>
 <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_topc.html#K1">{}</a> <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> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T34">CONNSP_1:34</a></i>;<br/>
<b>hence </b><a NAME="E6:154_1_1"/>
not  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


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