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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="pboole.html#NM2">ManySortedFunction</a> of <font color="Maroon">I</font>;<br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green">E36</font></i>: 
 <a href="mssubfam.html#K1" target="_self">doms</a> <font color="Maroon">F</font> is <a href="finset_1.html#V2">locally-finite</a>
 ;<br/>

<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">PRE_CIRC:def 3</a><br/>

<b>assume </b><a NAME="E2:37"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E4:37"/>
<span class="p1">(<span class="default"><a href="mssubfam.html#K1" target="_self">doms</a> <font color="Maroon">F</font></span>)</span> <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="pre_circ.html#D3">PRE_CIRC:def 3</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:37"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T26">FINSET_1:26</a></i>;<br/>
<b>hence </b><a NAME="E7:37"/>
<span class="p1">(<span class="default"><a href="mssubfam.html#K2" target="_self">rngs</a> <font color="Maroon">F</font></span>)</span> <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>, </i>;<br/>


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