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<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E2:32_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rltopsp1.html#D3" target="_self">RLTOPSP1:def 3</a><br/>

<b>assume </b><a NAME="E3:32_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:32_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:32_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="convex1.html#V1">convex</a>
 <b>by </b><i><a class="ref" href="convex1.html#T10">CONVEX1:10</a></i>;<br/>


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