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<div class="add">

<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">I</font> <a href="pboole.html#K9">--&gt;</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="seq_4.html#K1">}</a></span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E2:13_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E4:13_1_1"/>
<font color="Maroon">f</font> is <a href="relat_1.html#V2">non-empty</a>
 ;<br/>

<b>thus </b><a NAME="E5:13_1_1"/>
<font color="Maroon">f</font> is <a href="finset_1.html#V2">locally-finite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_circ.html#D3" target="_self">PRE_CIRC:def 3</a><br/>

<b>assume </b><a NAME="E1:13_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>hence </b><a NAME="E2:13_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>


</div><b>end;</b></div>


</div>
