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

<b>thus </b><a NAME="E1:24_1_1"/>
( <font color="Maroon" title="c3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <span class="p1"><a href="closure2.html#K3" title="CLOSURE2:func.3">|.</a><span class="default"><font color="Maroon" title="c3">S</font></span><a href="closure2.html#K3" title="CLOSURE2:func.3">.|</a></span> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1_1_1"/>
<font color="Maroon" title="c3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E2:24_1_1_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1"><a href="closure2.html#K3" title="CLOSURE2:func.3">|.</a><span class="default"><font color="Maroon" title="c3">S</font></span><a href="closure2.html#K3" title="CLOSURE2:func.3">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="closure2.html#T14" target="_self" title="CLOSURE2:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E3:24_1_1_1"/>
<span class="p1"><a href="closure2.html#K3" title="CLOSURE2:func.3">|.</a><span class="default"><font color="Maroon" title="c3">S</font></span><a href="closure2.html#K3" title="CLOSURE2:func.3">.|</a></span> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E2:24_1_1"/>
( not <font color="Maroon" title="c3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> )
 ;<br/>


</div>
