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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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="equation.html#K1" target="_self">""</a> <span class="p2">(<span class="default"><a href="extens_1.html#K2">rngs</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extens_1.html#K2">rngs</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="mssubfam.html#T13">MSSUBFAM:13</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T169">RELAT_1:169</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="extens_1.html#K1">doms</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="mssubfam.html#T14">MSSUBFAM:14</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15"/>
<font color="Maroon">f</font> <a href="equation.html#K1" target="_self">""</a> <span class="p1">(<span class="default"><a href="extens_1.html#K2">rngs</a> <font color="Maroon">f</font></span>)</span> <a href="pboole.html#R6">=</a>  <a href="extens_1.html#K1">doms</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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