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<b>let </b><font color="Maroon">c<sub>6</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>7</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>7</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>8</sub></font> is <a href="connsp_2.html#V2">locally_connected</a>
 ;<br/>

<a NAME="E3:14"/>
<font color="Maroon">c<sub>6</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="topalg_5.html#E1:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="topalg_5.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E4:14"/>
<font color="Maroon">c<sub>7</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>9</sub></font> is <a href="connsp_2.html#V1">locally_connected</a>
 <b>by </b><i><a class="txt" href="topalg_5.html#E2:14"><i><font color="Green">E20</font></i></a>, <a class="ref" href="connsp_2.html#D6">CONNSP_2:def 6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_2.html#D6">CONNSP_2:def 6</a><br/>


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