<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:65_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p2">(<span class="default"><a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D9" target="_self" title="PBOOLE:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="pboole.html#T5" target="_self" title="PBOOLE:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>

;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:65"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <span class="p1">(<span class="default"><a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" target="_self" title="PBOOLE:th.3">Th3</a></i>;<br/>


</div>
