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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:7_1_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="subset_1.html#T55">SUBSET_1:55</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<a NAME="E4:7_1_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="setfam_1.html#V2">with_non-empty_element</a>
 <b>by </b><i><a class="ref" href="setfam_1.html#D11">SETFAM_1:def 11</a></i>;<br/>


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