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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="relat_2.html#V8">(F2)</a> <a href="armstrng.html#V3" target="_self">(F1)</a> <a href="armstrng.html#V4" target="_self">(F3)</a> <a href="armstrng.html#V5" target="_self">(F4)</a> <a href="armstrng.html#NM2">Dependency-set</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="armstrng.html#NM5">Full-family</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="armstrng.html#D15" target="_self">Def15</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<a NAME="E3:57_1_1"/>
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T24">FINSET_1:24</a></i>;<br/>
<a NAME="E4:57_1_1"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T19">FINSET_1:19</a></i>;<br/>
<b>hence </b><a NAME="E5:57_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


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