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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:2_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/><a NAME="E2:2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finsub_1.html#K2">\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D6">PRE_TOPC:def 6</a></i>;<br/><b>hence </b><a NAME="E3:2_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>hence </b><a NAME="E3:2_1_1"/>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finsub_1.html#K2">\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D6">PRE_TOPC:def 6</a><br/>


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